[auggierose]

By convenience I mean "convenient from a technical perspective", and yes, you often need 0 in there.

Your other argument doesn't make much sense. I learnt both in school and at university ℕ, ℕ₀, and ℤ as THE symbols for the natural numbers, the natural numbers including 0, and the whole numbers.

Fuck convenience. ℕ, ℕ₀, and ℤ it is :-) It is just so much prettier (ℤ⁺ is a really ugly symbol for such a nice set). It is actually also not inconvenient if you don't use static types.

[auggierose]

On the other hand, even for writing a perfectly fine natural number like "10", you need the zero... Maybe it is just ℕ and ℤ after all.

And round we go.

[thaumasiotes]

What do you use for the negative integers?

[auggierose]

I very rarely use just the negative integers, so I don't need a symbol for it.