[sdenton4]

For some added fun: algebraic numbers are the set of all numbers which are roots of rational polynomials. You know, things like sqrt 2, along with all the rationals themselves. Algebraic numbers comprise the vast majority of real numbers we ever have a reason to actually use.

These are also merely countable...

[petters]

t0mek noted that all possible definitions of a number are countable. That would include all algebraic numbers.