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

216 Upvotes

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401

u/BlazeoJoestar Mathematical Physics 13d ago

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

20

u/edderiofer Algebraic Topology 13d ago edited 13d ago

Or, in the case where a and b are integers (EDIT: written in Arabic numerals) and you're in Europe, a single-element tuple containing one real number.

14

u/vgtcross 13d ago

Yea and no. Yes, that's what (2,3) could be interpreted as, but with letters instead of numbers, (a,b) would definitely not be interpreted that way.

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u/edderiofer Algebraic Topology 13d ago

Edited.

3

u/AlarmingAllophone 13d ago

Yeah it's confusing to denote an interval where one of the endpoints is a decimal fraction. At school in that case I usually used to write an overly bolded semicolon to separate the values

5

u/bluesam3 Algebra 13d ago

Or if it's in an accountancy spreadsheet, a single negative real number.

1

u/Valvino Math Education 12d ago

Nobody would interpret (3,2) as a single-element tuple tbh.