Which is the greatest whole?

Answer 1

It does not exist.

Proof: Indeed, suppose that this number exists, and denote it by X.

Then X+1 is also a whole number (by definition of the whole numbers). So X cannot be the greatest number since X+1 is even greater, which contradicts the assumption of the first line. The same argument follows for X+1 (compared to X+2), and so on.

Consequently, there is not a greatest whole number.

Remark: One may consider that infinite is the greatest whole number (without such an above contradiction, since infinite+1=infinite), however infinite is not defined to be a whole number.