Eternal the originator of time - proof.

[Alex K]

Things tend to get wonky when we start throwing infinity around.

I always found it weird 1 - .999 repeating = 0.  

Or that there are the same number of even numbers as there are integers.  Seems like there would be twice as many integers.  Not so, apparently.  Something to do with 1 to 1 correlation, or matrices or whatever.  Who knows really (aside from math people).  

The math people are among us, you know?
Two sets of infinite cardinality are defined to have the same "size" if a one-to-one map of their elements can be shown to exist. That makes intuitive sense, doesn't it? For the natural integer numbers versus even numbers, this so-called bijection simply is

f: N->2N, x |-> 2 x

and its inverse

f^-1: 2N->N, x |-> x/2

This is proof that they are of the same cardinality. What's strange is that if you add a finite number of elements to these sets, their "size" (cardinality) doesn't change.

The point being, if I say there are less even numbers from 1 to 100 than integers , I'm correct.  (50 < 100).  And that works for any number.  But it doesn't work for infinity, because as I said, things get wonky at infinity.

Right, it doesn't work for any finite subset.