Question

If I'm working with sets, is there such a thing as subtracting cardinality? Like, |A-B|?

Answer 1

Sure, for finite sets this is no problem. Let ||A|| denote the cardinality of a set A. Then ||A-B|| = ||A|| - ||A n B|| where n is intersection.

The same can be extended to the Cantor infinities:
\[\aleph_0, \aleph_1, ...\]
provided you have the right set of rules.

But honestly, you have to be very careful and it is usually best to consider the set A - B and its cardinality directly.

Answer 2

Ok James, in this case, please help me out on my other question :)