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What does := mean?

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    For future reference, the [table of mathematical symbols](http://en.wikipedia.org/wiki/Table_of_mathematical_symbols) at wikipedia is fairly extensive and has a number of further references.2011-03-06

2 Answers 2

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It is borrowed from computer programming: it means that the item on the left hand side is being defined to be what is on the right hand side. For example, $y := 7x+2$ means that $y$ is defined to be $7x+2$.

This is different from, say, writing $1 = \sin^2(\theta) + \cos^2(\theta)$ where we are saying that the two sides are equal, but we are not defining "1" to be the expression "$\sin^2(\theta) + \cos^2(\theta)$".

Basically, some people think that there should be notational difference between saying "I define blah to be equal to blankety" and saying "blah is equal to blankety". So they use := for the first and = for the latter. Usually, it is clear from context which of the two uses of the equal sign is intended (often because of signal words like "Let", "We define", etc.)

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    lthough entities can have the same number and be numerically equal in value but not numerically identical, identical (so its a little confusing as to what '=' means in a total order, particular if multi-imensional. where both orders are numerical,particularly when$\equiv$which is defined as the identity symbol is often used for the weaker 'equal in value' between two events whose values in the domain rank are numerically equal yet are not numerically identical events (and particularly given that $\equiv $ is often defined as 'identity'as above not just equivalence or congruence2017-10-12
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I think the Bourbaki used it first.. not sure.. I know physicists use $\equiv$

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    @Ruslan Interestingly, Apple's new Swift programming language uses `?` to represent optional (possibly-nil) values, and `!` to indicate non-optional (definitely-not-nil!) values. So, there, `!` is the symbol for negation *and* emphasis!(!)2014-11-18