
Re: infinity can't exist
Posted:
Feb 12, 2013 1:24 PM


Craig Feinstein <cafeinst@msn.com> wrote in news:13c1e093ab8645e694177526eb422a08@googlegroups.com:
> 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 nonfinite things. We invented limits to deal with nonfinite things.
B.

