In article <email@example.com>, Craig Feinstein <firstname.lastname@example.org> wrote:
> Let's say I have a drawer of an infinite number of identical socks at time > zero. I take out one of the socks at time one. Then the contents of the > drawer at time zero is identical to the contents of the drawer at time one, > since all of the socks are identical and there are still an infinite number > of them in the drawer at both times. But the contents of the drawer at time > zero is also identical to the contents of the drawer at time one plus the > sock that was taken out, since they are exactly the same material. So we have > the equations: > > Contents of drawer at time 0 = Contents of drawer at time 1 > Contents of drawer at time 0 = (Contents of drawer at time 1) plus (sock > taken out of drawer). > > Subtracting the equations, we get > > Nothing = sock taken out of drawer. > > This is false, so infinity cannot exist. > > How does modern mathematics resolve this paradox?
* Let k = the number of numbers. Let q = the number of even numbers.