Ridicolous to say, I am the last person apt to give a definitive answer. Mostly because I don't care about names, and simply try to understand from the context.
A rose without its name, wouldn't be a rose?
So I can ask the same question about numbers in "high" or "low" way:
example:
how many different decimal representation can a real number have?
Or
0,9999999999999999999....is or not equal to one?
To understand the second question implies to have understood the core of the first one.
(Anyway, Bean, you were perfect in your list of sets of numbers. Just a comment about irrational numbers . I have always seen them written as "R\Q" = real not rationa numbers)