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I like the idea of using the compound symbol ":=" for "is defined to be". So, you can say something like "For x∈A, y := 2x". When I take math notes, it helps a lot using this shorthand. I'm able to remove some ambiguity between what is and is not a definition.

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I definitely agree with the use of ":=", but "=" simply doesn't mean the same thing. For example, the similar statement "For x∈A, y = 2x" could even be interpreted as using y to define x.

I don't understand -- you say "=" and ":=" are not the same thing, but give an example where they act the same?

Practically speaking, using ":=" removes any doubt when quickly skimming over old notes. It is nice to be able to easily separate what is defined and what is asserted in each of dozens of statements.

I'm working on improving that section; would be great if you could chime in here:

https://github.com/Jam3/math-as-code/issues/17

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