On Sun, 21 Aug 2016 09:47:45 -0700
Marc Perkel <supp...@junkemailfilter.com> wrote:

> So we define set B as everything in the universe that is not in set A.

That's a very specific kind of infinite set.  It's the complement of a finite 
set.

Try this one on for size:

Consider the set A of all positive integral powers of pi (pi, pi^2, pi^3, etc.)
That's clearly infinite.

Set B is every element x of A such that the googolth digit (that is,
the 10^100th digit) after the decimal point of the decimal expansion
of x is 7.

Good luck matching B.  It's not even clear to me whether B is infinite
or finite, though I suspect it's infinite.

There are also sets with an uncountable infinity of elements, such as
the real numbers, for which "matching" has little meaning.

Regards,

Dianne.

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