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$$:=$$ is the commonest symbol to denote "is equal by definition." Note that $$\equiv$$ is used to denote an algebraic identity: this means that the equation is true for all permitted values of its variables. Rarely, however, it may denote a definition, so it's best to use this symbol only for congruences or identities. In short: $$:=$$ is the most widespread (presumably as it's the easiest to typeset) "by definition" symbol . Other symbols used to denote a definition include $$\stackrel{\triangle}= \quad , \stackrel{\text{def}}= \quad, \stackrel{\cdot}= \quad .$$ Whilst there's no amibguity in the latter three symbols, you try typing \stackrel{\triangle}= every single time you make a definition, as opposed to the much-shorter :=. You'll then see why the latter of these two is most widespread in this context. (责任编辑:) |
