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ok, heres my dilema. it is generaly accepted that the number pi is an irrational, infinatly progressive decimal that never repeates. I propesed in class today (we are working on discrete mathematics and, well, one thing led to another) that if pi where truly infinate that it MUST repeate, my idea being that as the sequence progresses the number of possible permutations that yeild a non-repeating decimal decreases. For example:
lets say that you have a ten sided die containing the numbers 0-9 and you roll the die an infinate number of times, what is the probability that the sequence of numbers that you roll will repeate?
The answer (IMO):
100% since the number of sides on the die is finite and the number of chances for repition is infinate then the probability for sucess is 100%
lets say the universe is infinatly large. assuming that this is true then it must therefore hold an infinate number of planets. lets say that each planet has a small chance of supporting life. what is the probability that a number of planets will support life and how many are there?
100% and an infinate number of planets. Why? lets say that you can (somehow) express all the numbers in the sequence
what if you removed all even numbers from the sequence, how many total numbers will you have?
therefore infinity divided by 2 = 2 times infinity o.O
back to pi...
the point is that 14159 ect... must repeate given given that it is observed for an infinate perspective. I.e. after a certain point the sequence will repeate simply because there is no other alternative.
if you can please, PLEASE, PROVE ME WRONG. i need to know for sure, its keeping me up at night and i need to get some sleep.
therefore infinity divided by 2 = 2 times infinity
Originally posted by Kano
Certain groups of numbers in the Pi series do repeat. Random chance dictates that. There is even a Pi calculator which gave the largest repeating section and allowed you to call up any of the series. (I don't remember the link though)
To really be a repeating number it would have to repeat a series over and over, in its entirety. This is something Pi will not do before reaching infinity.
Originally posted by quiksilver
...but the chance of having an infinite number that repeats itself out of an inifnity of numbers is quite impossible, so therefore pi must start repeating itself.