I am sorry if this is quite elementary question. But I always think, that why we use $:=$ at some places, instead of $=$. Is there any fundamental difference between these two? Before reading Terry Tao's blog (4 months ago), I had never seen a symbol like this (:=).
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Some authors like to distinguish the assertion "A is equal to B" from "define A as an object equal to B".
In math, the first one is always $A=B$ (I've never seen anything else, at least). But for definitions, I've seen
Often the triple equal sign is used for strong notions of equivalence (such as in binary relations) or with the "mod" symbol.
In computer programming, we are typographically limited of course. The assignment operator is usually distinguished from the comparison operator, and this is done in different ways depending on the language. For example in Pascal you assign
Modern programming languages use