Re: Cantor's definition of set

On Thu, 25 Oct 2007 12:51:35 -0700, John Jones <jonescardiff@xxxxxxx>
wrote:


OK. But if the members of a set have nothing in common, then how can
we have a set of numbers, for numbers are derived from each other -
they have something in common.

Well at least in ZFC (our "standard" set theory) ALL objects considered
(in this theory) have something in common: they are sets.

Usually, we define

0 =df {}

1 =df {0}

2 =df {0,1}

:

Hence there's no problem with numbers in this theory.

Even if we would consider the natural numbers

0, 1, 2, 3, ...

as "urelements" we would meet your "condition". In this case, all
numbers would be "urelements" - hence they would have "something in
common" (i.e. the property to be an urelement).


F.

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