# What is the “etymology” of the notation “:=”?

I've noticed that sometimes people use ":=" to set variables, like "With $f(x):=x^{2}$, we have $f(1) = 1$." This is also the variable definition operation in Mathematica. My question is, did Mathematica come first and then people started using ":=" or vice versa? And when was the first documented use of such notation?

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The notation usually stands for "by definition". –  Pedro Tamaroff Feb 17 '12 at 20:46
ALGOL 58 used the ":=" notation to set variables back in the late 1950s, so it clearly pre-dates Mathematica. (I do not claim this is the first major use of the notation.) –  Arthur Fischer Feb 17 '12 at 20:51
I believe it was originally used in programming languages as a symbol for "is assigned as", but I have no documentation to justify the claim. –  JavaMan Feb 17 '12 at 20:56
@Lazar: The sign you describe is symmetric, while := or =: allow to notationally distinguish that which is defined from the expression defining it. –  Stefan Walter Feb 17 '12 at 20:57
I read the question and for a split second I thought of posting an answer that says "I think it came from programming languages." So if someone asks about the Riemann hypothesis, and someone else responds with a complete proof in the comments section, I'll post an answer that says "I think that's a conjecture due to Bernhard Riemann." –  Michael Hardy Feb 17 '12 at 21:59

For what it's worth, Dijkstra preferred to use $:=$ for assignment (which is actually its use in ALGOL), and if I am reading that opinion right, did not see the need for a "definitional" equality symbol (probably because if you write proofs in his favored style, "definitional" equality is explicitly signaled in words between formulas).