Question

how do i know if a number a integer whole number or natural number

Answer 1

"You should be aware that some definitions of ℕ include zero. In and of itself, this isn't serious since the properties of the set are preserved: there is a bijection between ℕ with zero and ℕ without zero, both are well-ordered, etc (effectively we've done nothing but "relabel" the elements).

Only when we start adding structure to these elements does the distinction become important - e.g. we might make 0 an additive identity. Therefore, when one writes ℕ in such a scenario (most scenarios), then it should be made clear which definition the author intends.

Now, if we take both to mean the set {1,2,3,⋯}, then whether one writes ℕ or ℤ+ ultimately doesn't matter at all. However, using ℤ+ can remove confusion since ℤ+ definitively does not include zero, and we would not have to go out of our way defining ℕ."
-- Kaj Hansen, Math.Stackexchange.com