TITLE: Equal signs with fancy marks
QUESTION [8 upvotes]: Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions.
In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which implies the thesis", used when working backwards, or even the less common $\stackrel{!}{=}$ (for which it is difficult to infer a precise meaning, but it's something like "we are imposing this equality", or "this is an Ansatz").
It seems like the use of these symbols is not common in papers (apart from maybe the first ones for definitions); however, they seem useful to me as a way to convey more meaning than the usual equality symbols. For instance, in some sense the "?" superscript changes the set of "allowed operations": from $a=c$ and $b=d$ it follows that $a+b=c+d$, but the same implications wouldn't hold with $\stackrel{?}{=}$ signs.
Q1: has the use of these symbols ever been properly formalized?
Q2: are there contexts in which they are used in papers? Are they standard in your field? Are they used in lectures/seminars/papers?

REPLY [6 votes]: In a slightly different direction, $\overset{\mbox{(2.3)}}{\ge}$ (the overset should be in a smaller font using \tiny, but for some reason that wouldn't render here) is a nice way to indicate that the inequality uses $(2.3)$ - this is especially convenient with a long string of inequalities in display-math where it's otherwise hard work to figure out which inequality uses which previous calculation.