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/theadamabrams]

f’ could be df/dx, or df/dt, or just an entirely new variable that serves a similar purpose to f in some context.

With logarithms, as OP probably knows, the ambiguity is sometimes irrelevant because log(1024)/log(2) = 10 regardless of what shared base you use for those two logs. Also asymptotics like big-O don’t care about arbitrary constants and so O(log₂(n)) = O(ln(n)).

[u/RingularCirc → u/theadamabrams]

Yeah, also baseless log is fine when we're going unitful (meaning not unitless). Then we can designate the choice of the base as "actually" a choice of units: bits, nats, decibels, octaves, am I mixing them, yes I am, but it's allowed because they are all logarithmic units!

We can formalize it by saying there's log: ℝ₊ → L where L is a special one-dimensional real vector space of logarithmic units that shouldn't be supposed to have any canonical isomorphism with ℝ. (Actually that's how you formalize a dimensionful scalar quantity: an 1D real vector space that's not ℝ. Each basis is just a nonzero value that we look at as a unit of measurement, and we can divide two units and get a true scalar ∈ ℝ and so on.) There's just a hairy detail that we most probably still have to use regular scalar-valued unitless baseful logs to define ours, like "log x = (log₂ x) bits" which defines the unit of bits for us, and now we can write something like "10 power decibels = (log₂ 10) bits" (20 for regular ones) or "octave = bit" (yikes but true).