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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.
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On July 15 2013 21:05 xM(Z wrote:just look at it, marvel at its beauty.  someone will always try and go beyond something that is already known. it's what fuels the motion of 0 and 1. if it helps, see determinism and nondeterminism only as believes subjective to the human mind one preceding the other ad infinitum. they have no effect on the universe be it known or unknown. then, the question becomes not whether or not 0 is truer then 1 but rather what can come of this sucession of ones and zeroes. you will then start to decipher/decode the software.
Determinism and non determinism are not subjective believes. They are concept with concrete possible real world application, especially when it comes to the brain. The more you post the more it is clear that you have absolutely no common sense when it comes down to this subject, or that you are just trolling.
Either way, don't bother responding to that.
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On July 15 2013 21:31 Umpteen wrote:Show nested quote +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 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?
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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. Show nested quote +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)
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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. 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 again.
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On July 15 2013 21:47 Reason wrote:Show nested quote +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
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On July 15 2013 21:50 beg wrote:Show nested quote +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
That doesn't change the probability.
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On July 15 2013 21:53 Reason wrote:Show nested quote +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 That doesn't change the probability.
if my sequence doesnt contain the number 1 by assumption, the probability would be 0, imho.
anyway... guess my link answers the pi-question sufficiently.
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On July 15 2013 21:50 beg wrote:Show nested quote +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.
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On July 15 2013 21:54 beg wrote:Show nested quote +On July 15 2013 21:53 Reason 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 That doesn't change the probability. if my sequence doesnt contain the number 1 by assumption, the probability would be 0, imho.
anyway... guess my link answers the pi-question sufficiently.
That's because you don't understand probability.
What you've done is proven that the probability of a random infinite non repeating sequence of integers containing every integer or every set of integers isn't 1 (sure).
That's already been established and why I'm specifically stating the probability is 1 (almost sure).
http://en.wikipedia.org/wiki/Almost_surely
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This reminds me of my courses on ergodic theorems... Fun results, horrible to prove. Oh yeah, and Poincaré reccurence theorem. You can look up this one, it's pretty fun considering the second principle of thermodynamic.$
Edit : Reason knows what he's talking about btw.
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On July 15 2013 21:55 Tobberoth wrote:Show nested quote +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.
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On July 15 2013 22:01 beg wrote:Show nested quote +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 while simultaneously misrepresenting what I said 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.
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On July 15 2013 21:19 MiraMax wrote:
Oh my ... if the structure of pi does not contain information I wonder how it's used to compute the circumference of circles for instance ...
It conveys information (as in reducing uncertainty) in the context of the question "If my radius is X, what is my circumference?".
That does not mean it conveys information when used solely as a source of all possible integers.
I confess I was quite wrong before, however. The information is not solely in the key (since you could give me the key and not the digits and that wouldn't help either) Duh.
Finally, the fact that the index without pi (or a process to compute pi) would be equally useless should show you that some relavant information is in fact stored in pi. I realize that this is taking it way too far though, so maybe we should move it to pm. Cheers!
Yes to the 'equally useless', no to the 'some relevant information stored'.
His whole claim was that pi (as a data storage) is "complex" enough to store all the information of the universe using some deterministic coding scheme.
The number '1' is also complex enough to perform the same job.
Whoops, sorry, just read the PM part- I agree.
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On July 15 2013 22:01 beg wrote:Show nested quote +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 he said. There's a difference between sure and almost sure. Basically what he is saying is that there is a probability that a certain number sequence does not show up in Pi (or any non-recurring infinitely long random number-sequence) but the odds of that happening is infinitely small.
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On July 15 2013 22:03 Reason wrote:Show nested quote +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.
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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 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.
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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.
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 
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On July 15 2013 21:31 DertoQq wrote:Show nested quote +On July 15 2013 21:05 xM(Z wrote:just look at it, marvel at its beauty. someone will always try and go beyond something that is already known. it's what fuels the motion of 0 and 1. if it helps, see determinism and nondeterminism only as believes subjective to the human mind one preceding the other ad infinitum. they have no effect on the universe be it known or unknown. then, the question becomes not whether or not 0 is truer then 1 but rather what can come of this sucession of ones and zeroes. you will then start to decipher/decode the software. Determinism and non determinism are not subjective believes. They are concept with concrete possible real world application, especially when it comes to the brain. The more you post the more it is clear that you have absolutely no common sense when it comes down to this subject, or that you are just trolling. Either way, don't bother responding to that.
that was just an analogy ... ?
either way, just look at it unfold. it stares back at you, open your mind.
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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.
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"
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EPT
