Date: Feb 12, 2013 1:24 PM
Author: Bart Goddard
Subject: Re: infinity can't exist
Craig Feinstein <firstname.lastname@example.org> wrote in
> 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?
By means of limits. Infinity minus infinity is an indeterminate
form, and no said that the rules of finite arithmetic apply to
non-finite things. We invented limits to deal with non-finite things.