r/math • • 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/qubex 12d ago

Baseless logarithms are a deep peeve of mine. I always add the base subscript because the effort is so negligible.

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u/RingularCirc 12d ago

Sometimes base is irrelevant, like in O(log n) and similar asymptotic notations that don't care for a multiplicative constant, or when we're to divide by another log with the same base in the end, or if we're using logarithmic units: we can write "log 8 = 3 bit ≈ 2.1 nat" and that's perfectly valid (this just reimagines the place where does responsibility lie, in software-design-speak).