Virgil
Posts:
4,666
Registered:
1/6/11
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Re: infinity can't exist
Posted:
Feb 12, 2013 6:18 PM
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In article <511AB48E.1B86E33A@btinternet.com>,
Frederick Williams <freddywilliams@btinternet.com> wrote:
> Craig Feinstein 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?
>
> If alpha - 1 is defined to be that beta such that alpha = beta + 1, then
> aleph_0 - 1 = aleph_0.
Works for me!
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