If you re-read my post, you'll see that I said you can't stop at the 'end' of infinity, as it does not exist. But I do agree with what you are saying, and understand it. My main problem is that it is possible for the monkeys to continuously hit one letter, forever. This of course would not result in shakespere.benylor said:Objection.
You do not understand what infinity is. This is no criticism, as neither do I. It's actually a relatively non-intuitive term. The misconception that you have made is that infinity is finite. You said "the end of infinity". There is no such thing.
In fact, you only need one or the other - infinite time OR infinite monkeys. Either one would be enough to guarantee Shakespeare - because there would be a set S defined as {M : M writes Shakespeare immediately upon coming across the timewriter}. Don't concern yourself that it's very unlikely - just the fact that it's physically possible is enough to guarantee that it will happen, an infinite amount of times! (Of course, it will be a miniscule fraction of the infinite amount of monkeys you have. That's another funny thing about infinity, you can have two infinite numbers that are different. Try looking at the limit of n/(n^2) compared to (n^2)/n if you don't believe me.)
But then you went and demonstrated that you do seem to understand infinity. It is impossible to write everything that you could write, because the limit of the length of each work is unbounded. You can indeed always +1 to the number of letters. That's correct. On the other hand... The monkeys will definitely reproduce everything that has ever been written up til this point (using the same alphabet as the typewriter, of course). And they'll reproduce an infinite amount of copies of it too.
This leads to another problem, though. The moment you set your infinite monkeys off, you'll have an infinite amount of works coming back at you. The fraction of them which are even legible, let alone Shakespeare, would be beyond tiny. Actually finding the Shakespeare is like finding a needle in a haystack the size of star, in a field the size of Wales full of haystacks the size of stars, on a farm with... um... a lot of fields. Possibly even less easy than that. I'm not sure, I haven't done the calculations
A stalemate indeed. I suppose the only way we can really sum this up is by saying that the concept of infinity is so forking wierd that we can't really use common sense logic to figure it out.Pararaptor said:
I'll leave it to somone with better math ability than I do to prove this argument, one way or the other.
