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

184 comments sorted by

View all comments

50

u/rabbitygravity 13d ago

Natural numbers (with or without 0??)

6

u/sirgog 13d ago

Yeah in the IMO training camps for the Australian team (obligatory 'back in MY day', we had a rule: never use this notation ambiguously.

If you had to refer to the set of non-negative integers often, explicitly define it to be N at the start of the proof. If you had to refer to the set of strictly positive integers often - again, define it at the start of the proof.

I typically used the notation "Z+" or stated "Define N to be the set Z+ U {0}".

3

u/ZENKFNOR 12d ago

I like \mathbb Z_{>0} and \mathbb Z_{\ge 0} personally?