It's not about

__whether__ the number can change. (That would be "variable".)

Rather, it's about

**whether values are numbers** (they are, so it's numerical rather than categorical); and then

__how__ they differ: whether the numbers differ by jumps. like integers (which differ by at least 1 from one another), or can vary smoothly, like real numbers (which can differ by very small amounts).

So, is it

discrete or continuous, based on this thinking?