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I tend to write proofs in the style of a paragraph or essay, using words (if-then) for the "logic" and reserving symbols (e.g. $\in, \subseteq$ etc.) for the "mathematics." (On the other hand, within definitions and/or set-builder notation, when terseness is especially desirable, I sometimes use logical symbols such as $\forall$ and $\rightarrow$.)

I also try to keep things in the order "Premise $\rightarrow$ Conclusion," so for example I would never say "Thus $P$ follows because $Q$ and $Q'$." Instead, I would say "Since $Q$ and $Q'$, it follows that $P$." Similarly I never say "We will show that $A$ if $B$," but always "We will show that if $B$, then $A$."

I am currently experimenting with writing statements that I am talking "about" but not assuming to be true in angled brackets, as in: "Assume $x \in (0,\infty)$. Our goal is to show that $\langle x^2 \in (0,\infty)\rangle$."

What do you do to facilitate proof clarity?

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closed as not constructive by Henning Makholm, rschwieb, martini, froggie, Per Manne Nov 25 '12 at 20:37

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

As it stands, your question is too broad for this site. I suggest you edit the question to be a reference request. For example, you might find Leslie Lamport's "How to Write a Proof" interesting. research.microsoft.com/en-us/um/people/lamport/pubs/… –  Austin Mohr Nov 25 '12 at 20:37