I read this recently on Pharyngula. It's an example of an argument I think is fallacious, but I've never seen anyone called on it.
If life is constant change and you are never the same person you were at any previous time, then if you lived forever, you would eventually become every possible person there is.
I've seen the same argument used as proof that there must be intelligent aliens somewhere if time/space is infinite. Consider a similar argument phrased in terms of integers.
There are an infinite number of integers. If I randomly pick an integer an infinite number of times, I must eventually pick '2'.
This sounds plausible, but it would be possible to randomly only pick odd numbers forever, which would clearly not produce a '2'. There are an infinite number of odd numbers, and even the same infinity as there are integers, but let's not go there.
So, is this a fallacy? What is it called?