yes I agree that the name is bad. An alternative is "listable". A set is listable if you can enumerate all it's elements in a list (which can be infinite). You can do it for the real numbers, as shown with Cantor's diagonal argument
Discussion
yeah, so not real numbers, but integers, and all the various kinds of arithmetic groups
i remember, but not what, some insight a while back i had about how numbers have ways of "unfolding" something inside them quite a bit... i believe that this is what happens with discrete cosine transforms and cryptography too, there is almost always many other things that unpack out of a single integer, which does lead to an interesting other form of infinity, i believe that is what Cantor's theorem relates to - probably also hamming codes have this property being used in the opposite direction, also