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Re: WMytheology § 293
Posted:
Jun 20, 2013 3:27 PM


On Jun 20, 12:09 pm, WM <mueck...@rz.fhaugsburg.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"



