Re: Infinity is not that big!

From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 10/30/04 

Date: 30 Oct 2004 21:50:24 GMT

jesse@phiwumbda.org (Jesse F. Hughes) wrote:
> twizlewink@hotmail.com (Abraham Buckingham) writes:
>
> > herc777@hotmail.com (HERC777) wrote in message
> > news:<d8422d00.0410281515.4c290ad2@posting.google.com>...
> >> oo is not a number
> >
> > [snip]
> >
> >> if infinity was a number then oo = 0
> > [snip]
> >
> > Also note that if infinity was a number lions would fall from the sky,
> > and moon pies would be movie critics. Start with a contradiction, and
> > you can prove anything.
>
> The claim that infinity is a number is contradictory only given his
> other claim that infinity is not a number.
>
> Without some hint of what one means by infinity and number, neither
> claim is meaningful.

Exactly.

I'd been puzzled why AB claimed that considering infinity to be a number
would lead to a contradiction. But then I noticed he said the following in
an older thread:

"You seem to still be thinking of inifinity as a number like 4 or 7,
but we know it's different. For example what's 4*oo? If we assume our
intuition is right, it would just be oo again. Now we then go what is
2*oo? oo again. So by this we could say that 4*oo/2*oo = oo/oo = 2.
But, I could just as easily write 6*oo/2*oo = oo/oo = 3 = 2? This
obvious contradiction means we made a mistake by assuming that oo is a
number."

This argument is not valid, of course. For example, one can replace every
instance of oo above by 0 and thereby neatly "prove" that 0 cannot be a
number either.

David Cantrell, who's _still_ singing
"Aleph_nought bottles of beer on the wall..."

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