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.