|
On July 15 2013 22:08 Tobberoth wrote:Show nested quote +On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient. On July 15 2013 21:31 Umpteen wrote:
[quote]
Ok, I'll try to explain:
Suppose you take a box which has every number from 1 to 1,000,000,000 in it and remove a number before giving it to me. I then pick a number at random and look for it in the box. The odds are overwhelmingly high that I will find what I'm looking for. But the answer to the question "Does the box contain all numbers from 1 to 1,000,000,000?" is no.
Now, if I looked in the box 1,000,000,000 times it's certain I would find the answer. But with Pi we're talking about an infinite box, with an infinite quantity of different numbers in it. There is no finite number of times I could look in the box that would give me any information about whether all the numbers are in there. However many I check and find are there, infinitely more remain unchecked and possibly missing. Okay I get that 100%. However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers? Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated? If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers  http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes.
that's anecdotal and not proof.
On July 15 2013 22:21 Penev wrote:Show nested quote +The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation"
we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof.
|
On July 15 2013 22:06 beg wrote:Show nested quote +On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient. On July 15 2013 21:31 Umpteen wrote:On July 15 2013 21:15 Reason wrote:
So I guess I'm really just asking you, why do you feel comfortable with a statistics based "yes" to the single integer question but not the integer sequence question? Ok, I'll try to explain: Suppose you take a box which has every number from 1 to 1,000,000,000 in it and remove a number before giving it to me. I then pick a number at random and look for it in the box. The odds are overwhelmingly high that I will find what I'm looking for. But the answer to the question "Does the box contain all numbers from 1 to 1,000,000,000?" is no. Now, if I looked in the box 1,000,000,000 times it's certain I would find the answer. But with Pi we're talking about an infinite box, with an infinite quantity of different numbers in it. There is no finite number of times I could look in the box that would give me any information about whether all the numbers are in there. However many I check and find are there, infinitely more remain unchecked and possibly missing. Okay I get that 100%. However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers? Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated? If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof.
I did not equate observed evidence with proof. I was responding to two different parts of your post.
I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you.
You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).
Well done, nobody is disagreeing with that.
You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations.
If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't.
I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not.
Make of that what you will...
Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ?
|
On July 15 2013 22:15 beg wrote:Show nested quote +On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
[quote]
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. i dont see how it's proven by definition. it seems likely that it's almost sure for pi, but that's not a proof 
It is a mathematical proof. The longer a number sequence, the higher the probability at a certain sequence shows up in it. As the sequence gets infinitely long, the probability thus becomes infinitely high. However, has you have demonstrated, there could theoretically be an infinitely long random number without the digit "1". This is infinitely improbable, but still theoretically possible. That's why you say it's almost sure, that's the definition: It's when the probability is 100%, but there's still a theoretical possibility it's different.
|
On July 15 2013 22:22 beg wrote:Show nested quote +On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
[quote]
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof.
No, it's proof. If you understand what almost sure means (wikipedia article has been linked), you would see that.
|
On July 15 2013 22:22 Reason wrote:Show nested quote +On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient. On July 15 2013 21:31 Umpteen wrote:
[quote]
Ok, I'll try to explain:
Suppose you take a box which has every number from 1 to 1,000,000,000 in it and remove a number before giving it to me. I then pick a number at random and look for it in the box. The odds are overwhelmingly high that I will find what I'm looking for. But the answer to the question "Does the box contain all numbers from 1 to 1,000,000,000?" is no.
Now, if I looked in the box 1,000,000,000 times it's certain I would find the answer. But with Pi we're talking about an infinite box, with an infinite quantity of different numbers in it. There is no finite number of times I could look in the box that would give me any information about whether all the numbers are in there. However many I check and find are there, infinitely more remain unchecked and possibly missing. Okay I get that 100%. However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers? Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated? If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ?
glad you admit there's no proof. why the fuck did we discuss this for ages then?
yes i understand the latter.
|
On July 15 2013 21:35 Reason wrote:
However, what reason do you have to believe that all the numbers aren't in there compared to any other random infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard?
(Having huge fun here, btw; hope it's mutual  )
If a sequence is known to be truly random (each digit independent), we can be 'almost sure' it'll eventually yield any given sequence.
We don't know that of Pi. It generates a sequence that 'measures well' in terms of randomness, but there are infinitely many sequences that would 'measure well' which exclude one or more possible subsequences. How do you estimate probability here?
|
On July 15 2013 22:23 Tobberoth wrote:Show nested quote +On July 15 2013 22:15 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:
[quote]
like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. i dont see how it's proven by definition. it seems likely that it's almost sure for pi, but that's not a proof It is a mathematical proof. The longer a number sequence, the higher the probability at a certain sequence shows up in it. As the sequence gets infinitely long, the probability thus becomes infinitely high. However, has you have demonstrated, there could theoretically be an infinitely long random number without the digit "1". This is infinitely improbable, but still theoretically possible. That's why you say it's almost sure, that's the definition: It's when the probability is 100%, but there's still a theoretical possibility it's different.
it's anecdotal and not a proof. there's a difference.
we all think it's likely that this is true for pi... so what? there's no proof.
|
On July 15 2013 22:28 beg wrote:Show nested quote +On July 15 2013 22:23 Tobberoth wrote:On July 15 2013 22:15 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:
[quote]
Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never)
Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure).
That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. i dont see how it's proven by definition. it seems likely that it's almost sure for pi, but that's not a proof It is a mathematical proof. The longer a number sequence, the higher the probability at a certain sequence shows up in it. As the sequence gets infinitely long, the probability thus becomes infinitely high. However, has you have demonstrated, there could theoretically be an infinitely long random number without the digit "1". This is infinitely improbable, but still theoretically possible. That's why you say it's almost sure, that's the definition: It's when the probability is 100%, but there's still a theoretical possibility it's different. it's anecdotal and not a proof. there's a difference. we all think it's likely that this is true for pi... so what? there's no proof.
It is proof for a true random non-recurring infinite number sequence, it's not anecdotal. It's proof, 100%.
Now, whether or not Pi is a true random non-recurring infinite number? THAT might very well be up for debate.
|
On July 15 2013 22:29 Tobberoth wrote:Show nested quote +On July 15 2013 22:28 beg wrote:On July 15 2013 22:23 Tobberoth wrote:On July 15 2013 22:15 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. i dont see how it's proven by definition. it seems likely that it's almost sure for pi, but that's not a proof It is a mathematical proof. The longer a number sequence, the higher the probability at a certain sequence shows up in it. As the sequence gets infinitely long, the probability thus becomes infinitely high. However, has you have demonstrated, there could theoretically be an infinitely long random number without the digit "1". This is infinitely improbable, but still theoretically possible. That's why you say it's almost sure, that's the definition: It's when the probability is 100%, but there's still a theoretical possibility it's different. it's anecdotal and not a proof. there's a difference. we all think it's likely that this is true for pi... so what? there's no proof. It is proof for a true random non-recurring infinite number sequence, it's not anecdotal. It's proof, 100%. Now, whether or not Pi is a true random non-recurring infinite number? THAT might very well be up for debate.
that's why i say he needs proof, duh.
let me quote you again to be a complete dick:
On July 15 2013 22:08 Tobberoth wrote:
He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic.
|
On July 15 2013 22:26 beg wrote:Show nested quote +On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
[quote]
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter.
On July 15 2013 22:22 beg wrote:Show nested quote +On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
[quote]
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. Show nested quote +On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof.
That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).
If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?"
|
On July 15 2013 22:30 beg wrote:Show nested quote +On July 15 2013 22:29 Tobberoth wrote:On July 15 2013 22:28 beg wrote:On July 15 2013 22:23 Tobberoth wrote:On July 15 2013 22:15 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:
[quote]
Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. i dont see how it's proven by definition. it seems likely that it's almost sure for pi, but that's not a proof It is a mathematical proof. The longer a number sequence, the higher the probability at a certain sequence shows up in it. As the sequence gets infinitely long, the probability thus becomes infinitely high. However, has you have demonstrated, there could theoretically be an infinitely long random number without the digit "1". This is infinitely improbable, but still theoretically possible. That's why you say it's almost sure, that's the definition: It's when the probability is 100%, but there's still a theoretical possibility it's different. it's anecdotal and not a proof. there's a difference. we all think it's likely that this is true for pi... so what? there's no proof. It is proof for a true random non-recurring infinite number sequence, it's not anecdotal. It's proof, 100%. Now, whether or not Pi is a true random non-recurring infinite number? THAT might very well be up for debate. that's why i say he needs proof, duh.
No, that's not why you said it at all. He specifically asked if you doubted the probability of a number sequence showing up in a random non-recurring infinite number sequence, or whether Pi was such a number. You specifically bolded the part "Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1" and asked for proof. I have posted proof for that.
|
^ Yes Tobberoth that's exactly what he did, here it is:
On July 15 2013 21:44 beg wrote:Show nested quote +On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1)
|
On July 15 2013 22:32 Reason wrote:Show nested quote +On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:
[quote]
like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. Show nested quote +On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:
[quote]
like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?"
again, this isn't true for all random non repeating infinite series. see my counter example (:
On July 15 2013 22:33 Tobberoth wrote:
No, that's not why you said it at all. He specifically asked if you doubted the probability of a number sequence showing up in a random non-recurring infinite number sequence, or whether Pi was such a number. You specifically bolded the part "Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1" and asked for proof. I have posted proof for that.
yea, and i showed the statement was wrong. i'm being very strict here, but the statement is wrong. sorry!
|
On July 15 2013 22:35 beg wrote:Show nested quote +On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:
[quote]
Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never)
Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure).
That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:
[quote]
Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never)
Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure).
That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (:
How many times do you need to have this explained to you?
Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does.
The statement is that the probability of a random non repeating infinite set of integers containing every integer and every finite set of integers is 1 (almost sure).
|
On July 15 2013 22:37 Reason wrote:Show nested quote +On July 15 2013 22:35 beg wrote:On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (: How many times do you need to have this explained to you? Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does.
since it doesnt contain the number 1 by definition, i dont see how it could be almost sure. so you gonna have to explain this many more times.
|
On July 15 2013 22:38 beg wrote:Show nested quote +On July 15 2013 22:37 Reason wrote:On July 15 2013 22:35 beg wrote:On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:
[quote]
Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:
[quote]
Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (: How many times do you need to have this explained to you? Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does. since it doesnt contain the number 1 by definition, i dont see how it could be almost sure. so you gonna have to explain this many more times.
Your example is the very reason that the probability is 1 (almost sure) and not 1 (sure).
You have proven this. Everybody understands that already.
You've separately disagreed with the statement:
The probability of a random non repeating infinite set of integers containing every integer and every finite set of integers is 1 (almost sure).
You are wrong to disagree with this. It's a mathematical concept that I'm beginning to wonder whether you're pretending not to understand or are just incapable of understanding.
|
On July 15 2013 22:38 beg wrote:Show nested quote +On July 15 2013 22:37 Reason wrote:On July 15 2013 22:35 beg wrote:On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:
[quote]
Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:
[quote]
Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (: How many times do you need to have this explained to you? Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does. since it doesnt contain the number 1 by definition, i dont see how it could be almost sure. so you gonna have to explain this many more times.
I don't know if you're being dense on purpose right now. We have proven that the probability of a certain sequence of numbers showing up in a random non-recurring infinite number sequence is infinitely high. You have showed an example of a random non-recurring infinite number which does NOT contain a certain sequence. This is perfectly fine because that's EXACTLY what almost sure means in probability: the probability is infinitely high, but there are theoretical exceptions.
EDIT: When I'm saying infinitely high, I technically mean "infinitely close to 100%".
|
On July 15 2013 22:22 beg wrote:Show nested quote +On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:On July 15 2013 21:55 Tobberoth wrote:On July 15 2013 21:50 beg wrote:On July 15 2013 21:47 Reason wrote:On July 15 2013 21:44 beg wrote:On July 15 2013 21:35 Reason wrote:
I've been using the word random redundantly which can only confuse matters, I apologise. Non repeating is sufficient.
[quote]
Okay I get that 100%.
However, what reason do you have to believe that all the numbers aren't in there compared to any other infinite non repeating sequence of integers?
Are you saying you don't believe the probability of all integer sequences appearing with an infinite non repeating sequence is 1 (almost sure) or are you differentiating between Pi and these other infinite sequences purely because Pi can be calculated?
If so, why is the fact that Pi can be calculated so troubling in this regard? like it has been said several times already... you need to prove this. it is easy to prove that it's not necessarilly true (assume non-repeating infinite sequence without the number 1) Pick a real number between 0 and 1. The probability of choosing a specific number is 0 (almost never) Take a random infinite non repeating sequence. The probability of it containing every set of integers is 1 (almost sure). That's been established already, I don't need to prove it. i already gave an example for a random infinite non repeating sequence that does not contain every set of integers http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations Your example is not applicable since you're basically saying "A random non repeating infinite sequence of numbers excluding 1". There's no such limitation to Pi, it can (and does) contain every digit, and since the probability of a certain number showing up gets closer to 1 the longer the number sequence, one would say it's 1 if the number is infinitely long. he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof. pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. Show nested quote +On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof.
The proof you want is, probably, impossible to obtain because of the "infinite nature" of pi. The only way we can get this proof (as far as we know) is by running a simulation. If you take the four color map theorem for instance the "proof" you get is, well, large, if you know what I mean. And it's essentially a simulation; It doesn't really have a practical use (because of it's size). It's unreasonable to ask Reason for proof. But it's reasonable to assume that any number sequence will show up in pi based on the simulations run until now.
|
On July 15 2013 22:40 Tobberoth wrote:Show nested quote +On July 15 2013 22:38 beg wrote:On July 15 2013 22:37 Reason wrote:On July 15 2013 22:35 beg wrote:On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:
[quote]
he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof.
pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:On July 15 2013 22:01 beg wrote:
[quote]
he said a random infinite non repeating sequence does contain every set of integers. i proved that this statement is wrong. sorry if you dont like the proof.
pi might not have the limitation i assumed, but it might have other limitations. you have to prove that it doesnt. That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct. Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (: How many times do you need to have this explained to you? Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does. since it doesnt contain the number 1 by definition, i dont see how it could be almost sure. so you gonna have to explain this many more times. I don't know if you're being dense on purpose right now. We have proven that the probability of a certain sequence of numbers showing up in a random non-recurring infinite number sequence is infinitely high. You have showed an example of a random non-recurring infinite number which does NOT contain a certain sequence. This is perfectly fine because that's EXACTLY what almost sure means in probability: the probability is infinitely high, but there are theoretical exceptions. EDIT: When I'm saying infinitely high, I technically mean "infinitely close to 100%".
assumption: random infinite non repeating series not containing the number 1
question: what's the probability of 1 being in the series?
answer: almost sure????
while my example seems a little lame, i only wanted to point you towards the fact that we don't know whether pi is actually a truly random series.
|
On July 15 2013 22:49 beg wrote:Show nested quote +On July 15 2013 22:40 Tobberoth wrote:On July 15 2013 22:38 beg wrote:On July 15 2013 22:37 Reason wrote:On July 15 2013 22:35 beg wrote:On July 15 2013 22:32 Reason wrote:On July 15 2013 22:26 beg wrote:On July 15 2013 22:22 Reason wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:
[quote]
That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct.
Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you still have to prove. you cant. nothing is up to me to prove, cause i'm not making any statements, except that you're lacking proof. I did not equate observed evidence with proof. I was responding to two different parts of your post. I've already (and so has Tobberoth) explained this to you, but I'll try again because I don't want you to think I'm just ignoring you. You have proven that the probability of a random non repeating infinite sequence of integers containing every integer and finite sequence of integers is not 1 (sure).Well done, nobody is disagreeing with that. You said Pi might have other limitations and I have to prove that. The fact is a lot of smart people have spent a lot of time looking at Pi and no limitations have been found. I'm going to assume it doesn't have any limitations. If you're not comfortable with regarding Pi as a random non repeating infinite sequence of numbers then you'd better have a good reason for doing so, and you don't. I'm not here to debate with you whether Pi is or is not a random non repeating infinite sequence of numbers as neither of us can prove or disprove this, nobody can (yet?), however all observed evidence suggests that it is and there is no evidence to suggest that it is not. Make of that what you will... Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter. On July 15 2013 22:22 beg wrote:On July 15 2013 22:08 Tobberoth wrote:On July 15 2013 22:06 beg wrote:On July 15 2013 22:03 Reason wrote:
[quote]
That's not what I said. Pay attention. I've already explained what you've proven, you can choose to ignore that if you so desire but it won't make you correct.
Nobody has to prove Pi doesn't have limitations, all observed evidence shows it has no limitations so if you want to state it has limitations you are the one that has to prove it. observed evidence =! proof i dont care if you say it's sure or almost sure. you have to prove both. you cant. He doesn't have to prove anything, it is proven by definition that it's almost sure that any number sequence will show up in Pi and that proof has been posted several times in the topic. If you want to prove that it's not sure, go ahead, no one is contesting that. EDIT: Here's the proof again, in case you missed it: "1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits?" That right there proves that it's almost sure. It doesn't prove that it's sure, and Reason hasn't tried to prove that. But you can stop asking him for proof that it's almost sure, because the proof is right before your eyes. that's anecdotal and not proof. On July 15 2013 22:21 Penev wrote:The Oxford English Dictionary defines the scientific method as: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses Note "systematic observation" we're talking about math, not physics. in math you actually need proof. sometimes you might think certain statements are likely, but you'll still want proof. That's not anecdotal, it alludes to the fact that as a random non repeating sequence of integers tends towards infinity in length the probability of it containing all integers and every finite set of integers tends towards 1 (sure) but never actually reaches it. This is why you refer to the probability of a random non repeating infinite sequence of integers containing every integer and every finite set of integers as 1 (almost sure).If you'd just said "Pi hasn't been proven to be a random non repeating infinite series of integers though every piece of observed evidence suggests that it is" then there would have been no problem and the only response you'd have gotten was "duh, so fucking what?" again, this isn't true for all random non repeating infinite series. see my counter example (: How many times do you need to have this explained to you? Your counter example proves why it's 1 (almost sure) and not 1 (sure). That's all it does. since it doesnt contain the number 1 by definition, i dont see how it could be almost sure. so you gonna have to explain this many more times. I don't know if you're being dense on purpose right now. We have proven that the probability of a certain sequence of numbers showing up in a random non-recurring infinite number sequence is infinitely high. You have showed an example of a random non-recurring infinite number which does NOT contain a certain sequence. This is perfectly fine because that's EXACTLY what almost sure means in probability: the probability is infinitely high, but there are theoretical exceptions. EDIT: When I'm saying infinitely high, I technically mean "infinitely close to 100%". assumption: random infinite non repeating series not containing the number 1 question: what's the probability of 1 being in the series? answer: almost sure???? while my example seems a little lame, i only wanted to point you towards the fact that we don't know whether pi is actually a truly random series.
Nobody is saying that. Your example isn't lame, you're just drawing the wrong conclusions from it. We don't know whether Pi is actually a truly random series, but everything we've observed suggests that it is. That aside, you then went on to a separate topic and actually tried to disagree with something that is mathematically proven.
On July 15 2013 22:26 beg wrote:Show nested quote +On July 15 2013 22:22 Reason wrote:
Do you understand why the probability of picking a specific real number between 0 and 1 is 0 (almost never) ? glad you admit there's no proof. why the fuck did we discuss this for ages then? yes i understand the latter.
The statement that the probability of a random non repeating infinite set of integers containing every integer and every finite set of integers is 1 (almost sure) uses the exact same principle. To understand one and not the other is something I find very difficult to understand.
This is what we're saying, using the format you've given there....
assumption: a random non repeating infinite sequence with no special criteria
question: what's the probability of this sequence containing every integer and every set of finite integers?
answer: 1 (almost sure)
Proof that it's not 1 (sure) : An example for a random infinite non repeating sequence that does not contain every set of integers. Some are found here: http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations
|
|
|
|
|
|
EPT
