How to write good math proofs?

>>9104236
You pretty much have to be a grammar nazi when it comes to constructing a proof.

There are 2 barriers you face when writing the proof.
1) Is it a correct proof?
2) Is it communicated in an understandable manner?

It's like programming, to an extent.

Make sure you include all of the necessary dependencies (all of the mathematical machinery you are using).

Make sure your notation is adequately defined (many people use the same symbols for different things and different symbols for the same thing).

Sometimes small "toy" examples are useful for illustrating your construction by showing how the machinery works together.

Aim for zero ambiguity in the words you use. Prefer latin words over Germanic ones (assuming you write in English). Never write anything in the first person. Don't use parentheses (use commas instead, or footnotes in extreme cases). Use "iff" when giving a definition instead of "if." Use quantifiers ([math]\forall \exists[/math]) only when the symbols you are introducing will not be used outside the formula using them. Put quantifiers on the beginning of formulas to keep them consistent with left-to-right reading. Use [math]\cdots[/math] as rarely as possible. [math]\Rightarrow [/math] meas "if ... then" and not "then" which must be written in plain letters. Don't fallback to [math]\left( \varepsilon,\, \delta \right)[/math] when you have theorems that can avoid introducing new symbols (it starts getting confusing above seven symbols). Write numbers in plain letters unless they are considered as mathematical objects or measures.