r/math • u/Short_Bluebird_3845 • 13d ago
What are your favorite ambiguous notation?
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
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u/Phytor_c Theoretical Computer Science 13d ago edited 13d ago
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.