I'm wondering whether or not starting a sentence with a display occasion should be avoided in all situations. In general I would say it should be avoided (maybe not quite like the plague, but quite severely!), but sometimes two sentences are linked very closely. Consider for example the following.
TL;DR. Basically, the final one isn't acceptable to me because it doesn't make grammatical sense (
=, to me, is the verb to equal, in various forms). The second is perhaps idea, but I don't want to overuse colons, as I find this unpleasant visually (just looks fairly amateurish to me). The first seems a little strange starting a sentence with an equation, but the sentences are closely linked...
My concern with the latter two are the following. For the second, I don't want to overuse colons. I find in maths writing they're thrown about all over the place, usually in a grammatically incorrect way. The issue with the third is that it's just not a grammatically sound sentence: it has two clauses (equations should be read like sentences), not linked by any words or punctuation.
I certainly wouldn't start a new idea with an equation, display or otherwise, but here the two sentences are extremely tightly linked.
I inadvertently used a similar thing twice in asking this question! When I say "Consider for example the following.", a fullstop is required, because it's the end of the sentence. Similar with when I say "... latter two are the following.". I could use a colon, but then I have to have a long list without fullstops (since they are 'stronger' than colons).
You may read this and think "does it really matter", and maybe no it doesn't that much, but I take great pride in my work and and slightly OCD about grammatical, particularly punctuation, structure. Your comments and feedback would be most appreciated!