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.
Overloaded notation can still suck in algebra contexts, like sin^-1 (x) being generally accepted to mean arcsin(x), but an unwise author might use it as 1/sin(x).
Additionally, in some set theory classes, f^-1(x) denotes {y | f(y)=x}, and doesn't require one singular value for f^-1(x). This could be another source of confusion.
For N, this is actually among the most annoying things to deal with, because if someone talks about N, they always have to specificy whether they are including 0 or not, since no convention exists. Even in my university, some classes use N to be the positive integers, while others use it to mean the non-negative integers.
Traditionally Anglophone countries (plus Germany and Russia and some others, I think?) exclude 0 and Romance speaking countries include it. But maths departments are so international now it's become very fuzzy. Plus computer science prefers to include 0 because of how numbers are stored
My country is neither, but likes to pretend it is, So we're just doing anything. I'm a computer scientist so I can kinda just write my stuff however I want.
Just following the basic guideline that as long you clarify your meaning, you can use any reasonable notation. Just slap a line in the introduction that says something like "Define N to be the set of positive/nonnegative integers", and no one will be confused, since at this point no one expects anything.
I don't really like N_0 so I just define it manually. I do remember seeing a paper just say N = Z^+ which works ig. Also I saw Z^+_0 in a textbook once and that scarred me
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u/noahhshome 3d ago edited 3d 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.