Is restricting range spaces necessary if the restriction is inferrable?

[left ermine]

I want to denote that a given atomic action can only be performed $1$, $[0, 1]$, $[1, \infty)$ or $[0, \infty)$ times depending on some environmental circumstances.
Would it be worthwhile to explicitly restrict each range to be $\in \mathbb{N}_0$? Or, given that the action is atomic, does this suffice as context that it won't ever be performed "fractional" times?

(I've been using the latter notion in the past, but my maths teacher recently came up to me and said that if left unspecified, ranges can be anything, so I should either use the set syntax (e.g. ${ 0, ..., \infty }$) or explicitly restrict the range (e.g. $[0, \infty) \in \mathbb{N}_0$). However, in this case the context is clear, so I was wondering if even given the atomicity it's still necessary to do so
This is not in the context of my maths course, so the teacher couldn't say that much about it)
(Yes, this is kinda silly, but I'd like to have it resolved in my mind for once and ever)

[sage dragon]

multisn8

[serene sorrel]

Even if the context is clear, you want your mathematical model to actually correspond to what you wish to say. A tiny bit of repetition won't kill anybody.

If you're telling me your action number lives in [0, 1], I'm gonna think it could be pi/4 if I want to.

[left ermine]

Alright, sounds sensible, thanks! Great to have that clarified

.close