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> This is similar to saying that, since the set of integers is infinite, it must contain Pi. Not exactly. Pi has no chance of occurring in an infinite set of
by Sam_Odio 16y ago
> This is similar to saying that, since the set of integers is infinite, it must contain Pi.
Not exactly. Pi has no chance of occurring in an infinite set of integers.
- someone_here 16y agoOkay, so how about "Given a number generator that produces numbers for an infinite amount of time, it will produce Pi" This, of course, is impossible.
- twymer 16y agoI think you're missing the point. While it's _extremely_ unlikely that the next random number produced would be Pi, in an infinite scale it can (and theoretically would) happen because it is, in fact, possible to occur.
- yummyfajitas 16y agoNo, it theoretically would not happen. Proof: let X[n] be the set of numbers with non-zero probability of being produced at the n'th trial. X[n] must be countable, since sum(X[n]) = 1 and the sum of any uncountably infinite set of non-zero numbers must be infinite. Let X = union(X[n], n=0...infinity). X is countable, being the countable union of countable sets. The reals are uncountable. Thus, most real numbers will NOT eventually be produced. (It's true, pi in particular could be in X, but the vast majority of numbers could not be in X.)
- eru 16y agoBy a similar argument, at least half of all natural numbers are completely random.
- twymer 16y agoI'm not entirely sure I understand the logic here, and being not a math student myself I'm sure my original statement is likely to be wrong. However, I don't see how the set of numbers found in an infinite number of trials would be countable. Edit: I googled some about this and can say I definitely learned some math today..
- yummyfajitas 16y agoCountably infinite - like the integers. I.e., if you start counting the integers (1, 2, 3, etc), you will eventually reach any given integer. Count the first element from set 1, first element from set 2, second element set 1, second element set 2, first element set 3, third element set 1, etc. Eventually you will count every element from every set. You can't do that for the real numbers.
- d0mine 16y ago4 - 4/3 + 4/5 - 4/7 + ...
- viggity 16y agoI'm pretty sure that is the message he was trying to convey. He is saying the scientist's point doesn't make any sense.