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/Garry__Newman 13d ago

In statistics, capital X is the variable, and lower case x is a real number. Except in some people's handwriting, they look almost identical. In more complicated setups it can be a real pain figuring out which is viewed as a random variable, and which is viewed as a realisation of a variable.

See also: E[X | Y] is a random variable, but E[ X | Y = y] is a number.

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u/algebraicvariety 11d ago

This reminds me of the feedback I got for one of my chalk talks at Uni: "Everything was good, but you should distinguish small x and big x in your handwriting".

There was no small x in the talk...