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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.

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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!

For real examples that I'm interested in, see the following links: Example 1; Example 2; Example 3. For the second example, I added the words "Specifically, we have" to try to help.

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  • $\begingroup$ Not starting a sentence with a display is a good rule of thumb, but one that may occasionally be violated. Here, how about just changing the sentence: "We calculate $f(x) = \dotsc = x^3 - 2x^2 + a\,.$"? $\endgroup$ – Daniel Fischer Dec 7 '17 at 16:42
  • $\begingroup$ So this was really a dummy example. I didn't want to clog up the question with lots of pictures, but actually I've added examples as links to SE-hosted pictures. I've just added some links with some further examples, which should hopefully explain better. (Probably should've done this at the start; apologies.) $\endgroup$ – Sam T Dec 7 '17 at 16:53
  • $\begingroup$ Of course it was a dummy example, but the strategy of changing the sentence often works. In example 3, you could write "… coupling to obtain the lower bound $\mathbb{P}_{\mathcal{G}}(\dotsc) \geqslant \dotsc = (\dotsc)\,.$" [Don't forget the full stop to end the sentence.] $\endgroup$ – Daniel Fischer Dec 7 '17 at 17:12
  • $\begingroup$ (Sorry, I wasn't suggesting you didn't realise it was dummy =P) -- and yes, I agree, that would help (and often would) :) -- and don't worry, I won't forget the last fullstop, very important! $\endgroup$ – Sam T Dec 7 '17 at 17:16
  • $\begingroup$ Do you think, though, that I should strive to make sure I never have one of the first two version (ie fullstop or colon)? It happens quite a few times in my paper, and to me it seems a little unnecessary to work so hard to remove them. This is, however, my first paper, so I appreciate the input of seasoned professionals like yourself! :) $\endgroup$ – Sam T Dec 7 '17 at 17:19

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