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.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
OK so i agree with the poster here on the fact that theorem is completely plausible... for the people remarking on the multiplying of pi by 10^(1000001) this is a counter proof for the corollaries and not the original theorem.
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
Possible? Indeed. Practical to find it anytime soon? Near impossible.
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
Last edited by Alex23 (2012-02-06 22:06:23)
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