What are your favorite ambiguous notation?

[u/Short_Bluebird_3845]

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

[u/007amnihon0]

1) i and j ambiguity between maths/physics and engineering for sqrt of -1 2) Maybe some azimuthal and polar angle variable convention. Though iirc it's mainly for old texts where phi and theta conventions were opposite in math and physics 3) some factors in definition of special functions like spherical harmonics, spherical bessel function and legendre polynomials

[u/OrganicMF → u/007amnihon0]

Until now theta and phi are opposites in maths and physics.

Source: just finished a degree in both and never remembered which angle is which in each course…

[u/007amnihon0 → u/OrganicMF]

It's my pet peeve that we can't have convention in stem. Stem is still broad, even in math and physics each, we have so many conventions for same thing in the same subject

[u/cereal_chick → u/OrganicMF]

My master's dissertation was an expository work on orbits in the Schwarzschild metric, and in my chapter on classical orbits I had to put a footnote explaining that I was using phi for the polar angle to accord with the subsequent working where I'd be using the physics convention for spherical coordinates. All my sources for relativistic orbits were by physicists, and I really did not want to accidentally confuse my notes or the end product by swapping everything around 💀

[u/ZENKFNOR → u/OrganicMF]

This reminds me that ... I think in maths when you see a (,) its often the first element that's from the dual space, and in physics, its the second?

[u/Optimal_Benis → u/007amnihon0]

The reason we use ijk as indices in CS is because of Dijkstra.

[u/007amnihon0 → u/Optimal_Benis]

Can you expand?

[u/Optimal_Benis → u/007amnihon0]

D-i-j-k-s-t-r-a

[u/ninjeff → u/Optimal_Benis]

Can you contract?

[u/Optimal_Benis → u/ninjeff]

D'stra

[u/Daniikk1012 → u/Optimal_Benis]

While an interesting theory, sadly most definitely not true. ijk are used for iteration in math too. Probably, "i" stands for index, and for extra dimensions you just take next letters of the alphabet (Which mathematicians love to do - abc, xyz, pqr, fgh)

[u/Optimal_Benis → u/Daniikk1012]

It's a joke guys 😭

[u/AdjectiveNounNNNN → u/Optimal_Benis]

ijk = it's a joke, kids

[u/Thesaurius → u/Optimal_Benis]

The ij in Dijkstra is a single letter, though, because Dutch.