Lucas,

you mention that pi divided by 10000..... million is proof. However, then its not pi. The value of pi is changed. You are dealing with the unaltered value of Pi, that is in the order of 3.14159......

so I do not think your disproof is correct

The disproof is correct (as long as he divides by 10^(10^6) rather than 10^6). The product of a (non-zero) rational number with an irrational number is always irrational, and the statement in question was about irrational numbers, not π.

]]>you mention that pi divided by 10000..... million is proof. However, then its not pi. The value of pi is changed. You are dealing with the unaltered value of Pi, that is in the order of 3.14159......

so I do not think your disproof is correct

]]>The statistics suggest you have to search for googol^googol digits of pi to find such "ordered" digits; be it the millions of repeats of the same digit, or a progression.

But, if we ever harness the power of quantum mainframe supercomputers, I can easily see newspaper news about those special sequences of digits of pi. When, and if, this happens it will make Chudnovski brothers' efforts seem like play in the sand!

Nice food for thought: "We are in Digits of Pi and Live Forever": http://sprott.physics.wisc.edu/pickover/pimatrix.html

]]>As for the probability rebutle... pi is not considered to be random it is infinite not random just as to see no repetition is all that makes it an irrational the fact that the number is in existence proves it is not random. whether or not naturally pi has shown this chain of digits is up to interpretation... personally iwould say no....

and last but not least i see replies based on the basis that an irrational number cannot contain patterns this is false irrational numbers can contain a pattern just not repetition for example the following is indeed irrational however contains a very easy pattern

0.01020304050607080910111213141516171819202122232425262728293031323334353637383940....

]]>I think pi/1 million will satisfy ganish's proposal.

I believe you mean contradict? This was suggested by mathsyperson, and is pretty much correct, so long as it is 10^1.000.000.

]]>If this discussion is to take a larger form about Irrational numbers then i think you should check something which is called as the Liouville's number. It is irrational as far as i know and it does contain a million zeroes back to back. it is defined as the summation of 10^(-n!) for n = 1 to infinity.

Simply put 0.1100010000000000000000010000000000000.................

Giving 1's only for the digits which are factorial numbers 1 2 6 24 120 and so on.

so there is bound to be a value of some factorial greater than 1.

It is irrational because it neither terminates nor repeats.

Dont have any idea about the pi part though. And some guy called Mahler proved that pi is not a Liouville number. I could not understand this part though.

please rectify me if i am wrong. Thanks

]]>Probability only makes sense when there is a concept of chance. Pi's digits are determined whether you know them or not.

Determined? yes, I agree; known? Not at all. At least not after *n* number of decimal places. I'm not, however, saying that this is a valid counter-arguement, because I don't subscribe to the thinking of if we can't disprove it, it must exist. I will however still believe that in the higher decimal places if pi, its digits become a faith, in a sense. What I mean is that after *n* digits, we have to accept the fact that there is still an inifinite number of digits left. So, with that said, probability could very well be involved in pi, in that the division could take a turn for one million continuous zeros.

Im just a noob math major, hopefully I can become knowledgeable as all you guys.

]]>There are so many weird things in mathematics, I don't know how you could say that.

True, but there are even more elegant things. Maths works out nicely so often, and π is crucial to so many of its branches, so for π's digits to be so very uniform for the first 30 million and then stop later on is inconceivable to me.

Still, I fully realise that that's not a rigorous argument (or anywhere close), and we both agree that if we had to guess then we'd go with pi being normal, so I don't think there's much more to discuss.

]]>That BBP formula finds the nth digit of π in base 16, which makes it largely irrelevant to this discussion since there's no easy way of converting infinite (or very large) strings of digits between bases. Not that I know or can think of, anyway.

However, they do determine the digits of base 10. And if the base 16 digits are not random and determine the base 10 digits, then...

So I suppose I'm conjecturing again. I'd say it's almost certainly true though, and the only reason it's not definite is that it's (virtually) impossible to prove.

(Incidentally, I like how those two people get credited for saying they don't know something.)

There are so many weird things in mathematics, I don't know how you could say that. I do agree that if I was a betting man, all my money would go in on pi's normality. However, mathematics isn't about betting.

Typically, people get credit for saying they don't know something only once they have shown that there really is no easy way of approaching it.

]]>Ricky wrote:

It is still an open question whether or not pi is normal.

Fine, I'll settle for pi's first 30 million digits exhibiting normality.

Ricky's link wrote:

It is not known if π is normal (Wagon 1985, Bailey and Crandall 2001), although the first 30 million digits are very uniformly distributed (Bailey 1988).

So I suppose I'm conjecturing again. I'd say it's almost certainly true though, and the only reason it's not definite is that it's (virtually) impossible to prove.

(Incidentally, I like how those two people get credited for saying they don't know something.)

]]>Specifically, look for BBP formula.

Besides, the point is that pi's digits have the properties of randomness: unpredictability and uniform distribution. Therefore even if they actually aren't random, it's not unreasonable to analyse them as if they are.

This is also not known to be true. It is still an open question whether or not pi is normal.

]]>Just because you don't know what digit is next does not imply it is random. Pi is by all means not random.

And just because you know what digit is next does not imply it is not random.

Here's a list of (pseudo-)random numbers that I'm getting off my calculator:

87, 21, 5, 37, 96, 26, 9, 41, 84, 50.

What comes after the 37? Why, 96 of course. I knew that, and yet these numbers are still random.

Besides, the point is that pi's digits have the properties of randomness: unpredictability and uniform distribution. Therefore even if they actually aren't random, it's not unreasonable to analyse them as if they are.

You mean logarithmic. Any argument which involves the phrase "looks like" is simply a conjecture.

I was comparing n to s, so linear is right. And of course it's conjecture, the only way to completely prove it one way or another would be to actually find a string of a million digits somewhere (which is next to impossible). You say conjecture dismissively, but using evidence to suggest an answer is better than just using intuition to guess one.

Maybe off-topic, but:

Any argument which involves the phrase "looks like" is simply a conjecture.

Is that a conjecture?

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