Best practices in notation

Question

I have already read A Primer of Mathematical Writing, by Steven Krantz which gives extremely good advice about writing mathematics. But I would like to collect some more specific suggestion about notation. I know that there are many different possible and equally correct notations and that it is a matter of taste and that therefore this question is likely to be very subjective. However, I am sure that there are some choices that are agreeably better than others.

To make only an example, I personally feel that ":" is preferable to "|" to express "such that", because "|" is used to mean "divisible" as well, and that $\mathbb{N}_0$ is neater than $\mathbb{N}^{>0}$.

So my question is: can you point out some "officially recognized"choices of notation that are agreeably better than other ones in terms of clarity? Even better, can you recommend some references on this topic?

Answer 1

One good resource is Florian Cajori's A History of Mathematical Notation, which will at the least give you a glimpse of the sheer variety of ways of notating things. Volume I is available online.

Added later: My looking up Cajori's book on Amazon prompted Amazon's recommendation engine to tell me about Mathematical Notation: A Guide for Engineers and Scientists by Scheinerman$^2$. (It also reminded me of another very nice book on the history of notation: Enlightening Symbols by Joseph Mazur.)

Answer 2

I don't necessarily believe that these sources are better, but I can try to answer your question about what's "official."

1. ISO, the International Organization for Standardization, has an official set of mathematical symbols. See http://www.ise.ncsu.edu/jwilson/files/mathsigns.pdf . I believe they may have had physicists in mind more than mathematicians, but that's what there is.

2. Bourbaki's notations are of course hugely influential. And the more time you've spent in France, the more likely you are to think of them as "official." They are responsible for the hilarious $\subsetneq$, and I believe they may also be the reason mathematicians in France and some other countries began referring to the number $0$ as "positive" (as well as "negative").