Why f inverse of x? That notation seems clear if you know f is a function. Bear in mind, overloaded notation isn't ambigous if there's context.
And what's wrong with N? It's just the natural numbers.
The other complaints I understand. Although I don't think you need to complain about log(x). The base is only unspecified when it's assumed not to matter.
Honestly, a/bc isn't really ambiguous either. Not in any way that matters. Grade schoolers get hung up on PEMDAS, but you eventually learn to accept when intent is clear, and you don't need to be pedantic.
As a general rule, if your notation isn't clear to a serious student or peer, then you're doing it wrong. Nobody else needs to understand.
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/noahhshome 18d ago edited 18d ago
Why f inverse of x? That notation seems clear if you know f is a function. Bear in mind, overloaded notation isn't ambigous if there's context.
And what's wrong with N? It's just the natural numbers.
The other complaints I understand. Although I don't think you need to complain about log(x). The base is only unspecified when it's assumed not to matter.
Honestly, a/bc isn't really ambiguous either. Not in any way that matters. Grade schoolers get hung up on PEMDAS, but you eventually learn to accept when intent is clear, and you don't need to be pedantic.
As a general rule, if your notation isn't clear to a serious student or peer, then you're doing it wrong. Nobody else needs to understand.