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?
What is the "etymology" of the notation ":="?
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$\begingroup$
notation
math-history
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6The [notation](http://en.wikipedia.org/wiki/List_of_mathematical_symbols) usually stands for "by definition". – 2012-02-17
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1@Peter: I've seen "$def$" written above $=$ sign, is that the same or there are slight differences? – 2012-02-17
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0@Peter In maths it's them same, as far as I know. You can check the Wikipedia link, where they are put under the same name. – 2012-02-17
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6[ALGOL 58](http://en.wikipedia.org/wiki/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.) – 2012-02-17
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4I believe it was originally used in programming languages as a symbol for "is assigned as", but I have no documentation to justify the claim. – 2012-02-17
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5@Lazar: The sign you describe is symmetric, while := or =: allow to notationally distinguish that which is defined from the expression defining it. – 2012-02-17
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0I think the first time has been used in ALGOOL and after in PASCAL language – 2012-02-17
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4I 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." – 2012-02-17
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0@Stefan: Agreed, but I'd say that by convention we read from left to right, so unless stated otherwise, assigned object appears on the right, while the label on the left. But I agree that $:=$ is better than $=$, since $=$ may lead to confusion - "is it something that follows obviously, or is it a definition?." Even when one precedes the definition by, say, "let us define...", the equation with $=$ appearing on the next line leads to confusion if it is referenced later in the text (and the reader doesn't immediately refer to the line above it, but only to the equation). – 2012-02-17