EPTOn July 15 2013 22:49 beg wrote:
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.
Show nested quote +
On July 15 2013 22:40 Tobberoth wrote:
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 22:38 beg wrote:
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 22:37 Reason wrote:
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.
On July 15 2013 22:35 beg wrote:
again, this isn't true for all random non repeating infinite series. see my counter example (:
On July 15 2013 22:32 Reason wrote:
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 22:26 beg wrote:
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 Reason wrote:
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 22:06 beg wrote:
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.
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.
[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:
that's anecdotal and not proof.
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 22:08 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. 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.
On July 15 2013 22:06 beg wrote:
observed evidence =! proof
i dont care if you say it's sure or almost sure. you have to prove both. you cant.
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.
[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:
Note "systematic observation"
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.
No, the probability of 1 being in that sequence is obviously 0 (sure). However, the probability that an infinitely long, non-recurring, random number-sequence turns out to be a random, infinite, non-recurring sequence without 1 is 0 (almost sure). However, if it did, obviously 1 isn't part of it. That's why the probability is only 1 (almost sure) that the number 1 will show up in a random, inifinite, non-recurring number sequence.
