I'm not really sure if this is the right place to ask this, but given the seemingly large concentration of mathematicians, and the tangentiality to TeX, I'll just ask here: what are the mathematical typesetting requirements regarding things like blackboard bold, bold calligraphic, and sans-serif; Are there situations where one would need all of the above in addition to their non-bold variants inside the same equation? Or is there only a requirement for the above so that the whole equation is then very bold/sans-serif?
Clarification: Are there situations where one would need all of the following inside the same equation (possibly non-existent mark-up, I hope you get the idea): $$ A {\cal A} {\boldcal A} {\frak A} {\boldfrak A} {\bb A} {\bbb A} {\sf A} {\sfb A} etc. $$
Best Answer
I have seen (and write) documents with four or more fonts in the same equation.
The idea behind is to visually differentiate the signification of symbol. for exemple : mathitalic for variable, sans-serif for matrix, fraktur for ideals and so on.
For example :
$$\mathfrak p=\big(\mathsfup P\big)\coloneq\big((p)\big)$$denotes a prime ideal in a matrix ring who's engendrate by a single element.