Re: infinity

In article <MPG.1d88f2fbee757c998a212@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> > [1] this specific argument was presented by Daryl McCullough
> >
> >
> Yes, I saw it. It's basically the "largest finite" argument. If I claim n is
> the largest finite I get a contradiction too. This comes from any claim to
> have
> identified and enumerated all the finite naturals, since for any one you
> identify, you can always identify a larger one. The set is unbounded, but not
> infinite unless it has infinite elements.

The assumption that the set of finite naturals is finite leads directly
to a self-contradiction. No finite set of more than two finite naturals
can ever contain the sum of all its members, but that sum must always be
a finite natural number.

If the set of all finite naturals were to be finite, it would have to
contain a finite natural that it cannot contain, namely the sum of all
its members. This contradiction arises from the assumprion that the set
of all finite naturals is finite, so that the set of all finite naturals
cannot be finite.

And, to the surprise of no one except TO, TO is again proved wrong!
.

Relevant Pages

  • Re: infinity
    ... >>> how you can believe a and b and not believe that the sum of all finite ... >> Taking the sum of all finite naturals depends on identifying the last of them ... >> the set of finite numbers is infinite derives from the contradiction inherent ...
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  • Re: infinity
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  • Re: Cantorian pseudomathematics
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  • Re: infinity
    ... >>> necessarily indicates a finite set, therefore I see no contradiction between ... >>> the set of finite naturals being finite and not having a last element. ... >> world infinite things end, ... if there exists a bijection from S to a proper subset of itself. ...
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