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.