[JadeNB]

> I think this #1 item should really be termed Consistency, because above all, notation must not contradict itself.

This is a good goal, but I'm not sure it's the primary goal; the phrase 'abuse of notation' exists precisely to describe its breakage, with even the best mathematicians and expositors engaging in it, and I think insisting on no abuse of notation leads us rapidly to the style of impenetrable Principia-style logic, or of modern formal proofs—both of which have their place (at least the latter …), but neither of which should govern all mathematical discourse.

As with all writing, I think that part of being a good mathematical writer is knowing the rules so that you can figure out when to break them unintentionally, rather than stumbling into it accidentally.

[riazrizvi]

Great point. It is bad to nitpick consistency when you are in the initial stages of developing a model outline, and looking to capture the most important points. What's the right term for this notational quality? Precedence?