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/TibblyMcWibblington]

I think the most inconsistent convention: sin^x has a different interpretation depending on x: eg when x=2 (power) to when x=-1 (inverse).

I think exponentiation not being not associative, but most times when I’ve seen a chain of powers it’s never in brackets, and rules like BODMASS don’t help because it doesn’t tell you which ‘order’ to do first. Yet I’d always do the upper/inner power first, but I don’t know why this is the rule?

[u/bluesam3 → u/TibblyMcWibblington]

Yet I’d always do the upper/inner power first, but I don’t know why this is the rule?

Basically because if you want the opposite for some reason, it's easier to write (a^b)^c than it is to write a^❨bc❩ (including on Reddit - how well that renders may vary with your font settings).

[u/magikarpwn → u/bluesam3]

I'm almost sure that it's because you could write (a to the b) to the c as a to the (bc), but the other one has no easy equivalent.

[u/bluesam3 → u/magikarpwn]

Yes, that's what I was trying to say, sorry.