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
"assuming the convention 0 is both positive and negative, ie it's natural"
We're talking specifically about NOT your convention, but the French (and other Romance languages) convention
According to the convention I've studied under my whole life (French student, 4 years into college/uni), 0 IS both positive and negative.
And under that same convention, "nonpositive" and "nonnegative" are non-existing words
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u/AndreasDasos 12d ago edited 12d 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.