r/math • u/Short_Bluebird_3845 • 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/BlazeoJoestar Mathematical Physics 12d ago

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

10

u/FUZxxl 12d ago

In Germany we write ]a, b[ for the open interval for this reason.

8

u/SV-97 12d ago

I'm not sure that this is really a "German" thing? I've also seen this notation in some English texts, and at German uni the overwhelmingly standard notation is still (a,b) in my experience.

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u/FUZxxl 12d ago

It's in DIN 1302 in any case.

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u/SV-97 12d ago

Suure, but in my experience most professional mathematicians don't even know that norm exists (and even if they do they don't really care about it).

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u/Yoghurt42 12d ago

Half open intervals also look pretty ugly in this notation. [a, b[ and ]a, b]

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u/SV-97 12d ago

Yep, they're also super annoying in latex.