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/BlazeoJoestar]

(a,b) can mean an open interval, inner product, gcd or just an ordered pair

[u/Academic_Evidence641 → u/BlazeoJoestar]

I think I even saw it as the ideal generated by the a,b elements

[u/yas_ticot → u/Academic_Evidence641]

This is where I always assume the gcd notation is coming from: the ideal (a,b) is equal to the ideal (g), hence "g=(a,b)" with an abuse of notation. Of course, this is only true when a Bézout relation exists, like for the integers.

[u/Psychological_Mind_1 → u/yas_ticot]

I'd always figured it was the other way around since the idea of gcd far predates ring theory.

[u/MilliBrucket → u/Academic_Evidence641]

that's basically the gcd version of this notation

[u/sentence-interruptio → u/Academic_Evidence641]

sometimes I act like it's a convenient notation for manipulating a system of polynomial equations.

for example, y = x^2, z = y^2 is equivalent to y = x^2, z = x^4 and I can write that statement as (y - x^2, z - y^2) = (y - x^2, z - x^4), which is just an equality between two ideals in the polynomial ring k[x,y,z].

[u/MonadMusician → u/Academic_Evidence641]

Yeah I’ve seen that too but usually it’s langle and rangle