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

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FredJeffries@gmail.com

Posts: 1,056
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 <mueck...@rz.fh-augsburg.de> 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
because
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
take
infinitely many pairwise unions any more than when we find the sum of
a
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
sequence.

> Otherwise
> the axioms should indicate that unioning sets that belong to a
> sequence is prohibited.


http://en.wikipedia.org/wiki/Axiom_of_union
"for any set x there is a set y whose elements are precisely the
elements of the elements of x"



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