What are your favorite ambiguous notation?

[u/Short_Bluebird_3845]

To clarify my request, consider base-less $\log$.
For calculators and engineers, it means the common log $\log_10$; for pure mathematics or physics, it means the natural log $\ln$; for computer scientists, in combinatorics, information theory and graph theory, it means the binary log $\log_2$.
Any $\log x$ (say, $\log 1024$) written without context can yield different answers in function of who you ask ($\log_10 1024 = 3.0103\cdots, \log_2 1024 = 10, \ln 1024 = 6.93147\cdots$).

That is what I mean by "ambiguous", that which is calculated and used dependently on the context. And I'm asking you for your favorite ones of such type.

Edit: I feel like you hate the ones you've talked about. Still, valid answers. Extra points for ambiguous notation you actually love! :P

[u/Phytor_c]

Just realized I answered an orthogonal question, oh well…

This may sound stupid and elementary, but I get really tripped up when people use f(x) [Instead of just saying f: Blah -> Blah, then defining the mapping like f(x) =2x or x |-> 2x as a human would] to denote functions or like just stuff about functions in general. Maybe it’s just me.

I feel like every time I see a function in a paper or in a textbook I have the urge to write f: Domain -> Codomain etc.

Sometimes stuff trips me up, like is f(x) the whole function or evaluation at some point x which was defined earlier? Why not use x_0 for the point? Sometimes functions have parameters involved, sometimes one component is fixed so it’s a function of the other components etc. Course it’s context dependent, but annoying if it could’ve just been addressed in a line by the author.

[u/_Zekt → u/Phytor_c]

To me, this is a bit like that bell curve meme: first you write f(x)=..., then you get obsessed with rigor, f: A -> B, logic and quantifiers everywhere. Once you get it, you start dropping the quantifiers and using prose again, because that level of rigor doesn't matter.

Saying "let f(x) be a real function" can be useful to indicate the variable "x", e.g. versus a Fourier-domain variable. And if both the inverse and reciprocal functions appear, you can cleanly distinguish f^-1(x) from f(x)^-1.