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 Originally Posted by evman150
 Originally Posted by Cocco_Bill
 Originally Posted by evman150
 Originally Posted by Cocco_Bill
On an infinite timeline there will come along not one but an infinite amount of poker player who get nothing but pocket aces throughout their whole career! No results are impossible to attribute to luck unless we have some kind of hand histories to prove that luck is not the only thing to blame!
I really don't think this statement is truthful. Obviously in reality it's hogwash, but I' m thinking mathematically. I might be totally wrong, but....
lim(n->oo) 1/221^n = 0
Does that not say that given infinite time (hands), no one will get pocket aces forever?
Yes, you are wrong! We don't live forever, so it would only need to apply for the number of hands someone would play throughout their career!
Anything that is not entirely impossible repeats itself infinitely many times in infinity. This has some very weird consequences which defy logic. For example if we assume that space and matter are infinite, then exact copies of yourself, planet earth and even this galaxy should repeat itself infinitely many times!
The thing is, nothing is infinite. Infinity is just a mathematical concept and has no application in the real world.
It's like quantum mechanics, which says if you tap your finger on your desk an infinite number of times eventually your finger will go through the desk. Yes that is true, but it is not an application of the truth, it is the application of a concept which is simply the means to finding the truth. But infinity itself is not the truth, merely a means to an end. Just a mathematical concept which creates beauty from chaos.
I really need some sleep. I have exams in three days.

Could you give me an upper limit for the mass of the universe (including the non observable) and the reasoning behind setting that upper bound! As far as I know this is not a settled issue even though there are certain models which do estimate it.
Anyhow about infinities...
There are infinite (cardinal) numbers of various "sizes."
For example the infinite number of primes is indeed the same as the infinite number of integers. Both the set of primes and the set of integers are countable, which is the smallest infinity of them all.
There is an arithmetic also for transfinite numbers. For example, if A is the number of primes, then
A+A = A
k*A = A for every positive number k
A*A = A
A^p = A for every positive power p
These first four "rules" are not as strange as they look. Find another usual (everyday) number that satisfies those rules! (There is only one.) Then you also have
2^A = 10^A = A^A > A,
but that's another story...
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