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Topic: Re: WMytheology § 293
Replies: 10   Last Post: Jun 30, 2013 4:30 PM

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Posts: 1,845
Registered: 11/29/07
Re: WMytheology § 293
Posted: Jun 20, 2013 3:27 PM
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On Jun 20, 12:09 pm, WM <> wrote:
> Two sets can be unioned.
> n sets can be unioned.
> aleph_0 sets can be unioned.

More of your ambiguity.

There is the kindergarten union of two sets A u B.

By induction/recursion we can extend that concept unambiguously
to the union of a finite collection of sets A1 u A2 u A3 u ... An
we can remove the parentheses from
A1 u (A2 u (A3 u (...))) and get the same result as
(A1 u A2) u (A3 u (...))

But when we take the union of an infinite collection of sets we do not
infinitely many pairwise unions any more than when we find the sum of
convergent infinite series we add infinitely many pairs of numbers.

> Whether or not they belong to a sequence does not matter.

They DO NOT belong to a sequence. They belong to the range of the

> Otherwise
> the axioms should indicate that unioning sets that belong to a
> sequence is prohibited.
"for any set x there is a set y whose elements are precisely the
elements of the elements of x"

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