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Is there any consensus about when to use inline math mode and when it is more appropriate to use display math mode when writing in latex (in formal math writing)?

When writing, I feel that it is often easier to read display math mode, but sometimes doing that breaks up the flow of the sentence, expecially when defining variables or functions.

For example

Define $f: \mathbb{R}^2 \to \mathbb{R}$ by $f(x,y) = \frac{27x^3 - 5}{2xy} + \cos x $.

vs.

Define $f: \mathbb{R}^2 \to \mathbb{R}$ by $$f(x,y) = \frac{27x^3 - 5}{2xy} + \cos x .$$

Peter_Pan
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    In this particular example, I would avoid words, (generally use as little text as possible) and write this instead: $$$$Let $f:\Bbb R^2\to\Bbb R^2$, $$f(x,y)\color{red}{:=}\frac{27x^3-5}2xy+\cos x$$ Quite often, text is redundant and can be replaces by symbols. Then some of our dilemmas disappear. I think the tag proof-writing shouldn't be associated with literal writing, but on deduction problems etc. – PinkyWay Jun 13 '20 at 22:23
  • I like a few words (not too many). The result seems very subjective. Go with what you like. – lcv Jun 13 '20 at 23:44
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    I'm not an expert but older math books (Courant- Hilbert, Schwartz theorie des distributions, even more recently V I Arnold) where written in a much more colloquial fashion. Trying to build a dialogue. I must say I liked that. It's probably because of the Bourbaki's school that a much more terse style became popular. I find that very "mechanic" and unpleasant. I think recently the style is getting again more relaxed (still of course keeping the proper level of rigor). For example the books by Terence Tao are written in a very pleasant and fluent way. – lcv Jun 13 '20 at 23:52
  • Did you know there’s actually a TeX SE? Anyways, your question asks if a consensus exists, and the answer is unequivocally no. – gen-ℤ ready to perish Jun 14 '20 at 06:26
  • @gen-zreadytoperish, I also-thought of Tex SE, but, when you click _this question belongs to another SE, there are Physics SE and, I think, meta and stackoverflow. – PinkyWay Jun 14 '20 at 06:41
  • @lcv, I feel more comfortable reading symbols, especially if people are, I'm not saying illiterate, but less into languages and grammar (lack of commas makes things even more exausting). It's much easier to follow a proof written in more symbols because, usually, people tend to be economical and save paper and "compress" the sentences. Not to mention if we have to read a foreign paper... However, a text can have some advantages-it can make paper more interesting and exciting, so to say and we agree on that part. – PinkyWay Jun 14 '20 at 06:52
  • @gen-zreadytoperish I had thought about TeX SE but decided it was a question for mathematicians esp. since TeX SE tends to be about how to format, not when – Peter_Pan Jun 14 '20 at 20:16
  • @Icv thanks for your response. Sometimes I feel that mathematicians trade readability for a sense of rigour when they opt to keep the use of english to a minimum. – Peter_Pan Jun 14 '20 at 20:19
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    I must point out that the codomain of $f$ as you’ve defined it is actually $\Bbb R$; the output isn’t ordered pairs – gen-ℤ ready to perish Jun 14 '20 at 21:40
  • @gen-zreadytoperish ah yes, obvious point. Thanks. – Peter_Pan Jun 14 '20 at 21:50
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    This would be better on meta.math.se I like inline when the equations are simple and there are words around them. Display is better with complicated equations because they are not squashed by text. I use display for a derivation with no words as well because I find it easier to follow. In your example I would use inline. – Ross Millikan Jun 14 '20 at 22:09
  • Just curious- was this written using Latex? Latex works on here, right? – Radial Arm Saw Jul 09 '20 at 21:29

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