What are numbers?

[struggle4progress]

17. Dunno. The finite whole numbers admit two interpretations:

as counting numbers ("cardinals" - 1, 2, 3, ...) and as ordering numbers ("ordinals" - 1st, 2nd, 3rd, ...): these ideas both generalize to infinite numbers, and (assuming the axiom of choice) all of the infinite cardinals can be regarded as ordinals, but only some of the infinite ordinals are cardinals

The complex numbers can be regarded as telling us something about the geometry of the real plane and can be generalized (somewhat) to Hamilton's quaternions, which can be used (for example) to code 3-dimensional rotations

So-called "nimbers" provide insight into short impartial two-person games; and John Conway has devised a notion of "two-person game" that includes many things normally called "numbers" as particular examples