Notation – Difference Between := and =

notation

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 (:=).

Best Answer

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

  1. $A \triangleq B$
  2. $A \equiv B$
  3. $A \stackrel{\mathrm{def}}{=} B$
  4. $A := B$

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 x := 5 and compare x = 5. However in C you assign x = 5 and compare x == 5. (It should be noted that in C this syntax has caused untold confusion and a few famous bugs.)

My favorite (meaning "most awful") example is in PHP and javascript where one can do a "strict compare" with x === 5. Finally, some languages have ridiculous vagaries like distinguishing which comparision operator is used based on the type of variable (usually strings being different from numerics), with syntaxes like .eq. and related.

Related Question