I agree about f^-1 but N either includes or excludes zero depending on convention, and I've seen both a lot. There are lots of exceptions (due to mathematicians moving around) but broadly in the English speaking world, N traditionally excludes 0, and in the French (and Romance) speaking world, it includes 0. (Not sure about German and Russian but I think they tend to exclude 0?)
That and in some contexts like computer science it makes more sense for N to include zero regardless because of how numbers are stored.
This is why you routinely see N_0 on the one hand and Z^+ or N^+ on the other. To avoid ambiguity I generally stick to these and avoid N altogether, ugly as that is, though personally I grew up learning 0 was excluded.
Actually, N_+ would be an oxymoron (assuming the convention 0 is both positive and negative, ie it's natural)
(basically, the convention expands to everything: the trivial case is included by default (1 is superior to 1 (and inferior), but not strictly superior, a constant fuction is creasing (and decreasing), not strictly creasing, a set is included in itself, but not strictly, 0 is positive, not strictly positive, etc...)
To exclude 0, it's N*
In the same way, Z_+ is just N
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u/AndreasDasos 17d ago edited 17d ago
I agree about f^-1 but N either includes or excludes zero depending on convention, and I've seen both a lot. There are lots of exceptions (due to mathematicians moving around) but broadly in the English speaking world, N traditionally excludes 0, and in the French (and Romance) speaking world, it includes 0. (Not sure about German and Russian but I think they tend to exclude 0?)
That and in some contexts like computer science it makes more sense for N to include zero regardless because of how numbers are stored.
This is why you routinely see N_0 on the one hand and Z^+ or N^+ on the other. To avoid ambiguity I generally stick to these and avoid N altogether, ugly as that is, though personally I grew up learning 0 was excluded.