What's "the most right" symbol to use for "defined to be equal to"? What's the most used symbol for "defined to be equal to", at least in your experience (and I'm sure there are a lot of experienced people here)? Also, which one do you think is the "the most right" of them, in the sense of making the most amount of sense (no pun intended)? The ones I frequently see in literature, papers and articles on the Web are '$\equiv$', '$:=$' and '$=_{def}$'. The first one I come across a lot, though for me it's still "reserved" for modular arithmetic. The second one seems like it's come straight out of some programming language and the last one I frequently see in philosophy papers on logic and the like. What are your thoughts on this?
 A: $$:=$$ is the commonest symbol to denote "is equal by definition."
Note that $$\equiv$$ is used to denote an algebraic identity: this means that the equation is true for all permitted values of its variables. Rarely, however, it may denote a definition, so it's best to use this symbol only for congruences or identities.
In short: $$:=$$ is the most widespread (presumably as it's the easiest to typeset) "by definition" symbol .
Other symbols used to denote a definition include $$\stackrel{\triangle}= \quad , \stackrel{\text{def}}= \quad, \stackrel{\cdot}= \quad .$$
Whilst there's no amibguity in the latter three symbols, you try typing \stackrel{\triangle}= every single time you make a definition, as opposed to the much-shorter :=. You'll then see why the latter of these two is most widespread in this context.
A: One advantage of $:=$ is that it's assymetric, meaning you can distinguish the thing being defined and the definition.
A: All of the above. The most common one however is $ := $. The symbol $\equiv$ is usually used to denote a logical equivalence. The symbol $\stackrel{\mathrm{def}}=$ should just be exiled along with $\div$.
Ultimately, the symbol you choose is a matter of personal preference. I personally use $:=$.
