Sometimes I struggle in choosing notations for a mathematical paper. There are probably no explicit rules, but unwritten conventions. In a discussion, is it proper to use different typographical variants of the same letter to denote different variables?
For example, is it acceptable to use an italic K (𝐾), an upright K (K), a blackletter K (𝔎) and a calligraphic K (𝒦) for four different variables in one section?
Answer
Enhancing on some of the other answers: while this is OK, and I have done this and worse in extremis (one of my papers is known as "the one with the four types of arrow"), your paper will be difficult to read.
You need to be aware of the fact that many readers will have a hard time tracking the differences between symbols. I recommend:
- Doing everything in your power notationally to avoid this situation in the first place
- If you must, first choose things that are easy to tell apart: e.g. capital vs. lowercase vs. mathcal. Upright vs. italic or symbol vs. symbol-bar are much harder to tell apart at a glance.
- Most important, in any symbol-heavy paper, include a "cheat sheet" table up front that gives the definitions of all important symbols or symbol-classes
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