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Which of the following notation is a correct definition of the square function?

  1. $f(x) \triangleq x^2$
  2. $f(x) := x^2$
  3. $f(x) = x^2$
  4. $f(x) \equiv x^2$

While this question is similar to The meaning of various equality symbols, the aforementioned question and its answers do not address the usage if these symbols in the context of function definition.

Robbo
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1 Answers1

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Different authors use different conventions. Unless you have a particular reason you need to do something fancier, just write $f(x)=x^2$ -- that's what the vast majority of written mathematics does.

hmakholm left over Monica
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  • $=$ my get confusing when defining predicates as in $P(x) = (x=0)$. – Robbo Aug 28 '18 at 13:53
  • @Robbo: Mathematical notation does not usually use $=$ between things that have truth values (rather than denote objects). So one would typically write that definition as $P(x)\Leftrightarrow x=0$ or $P(x)\equiv x=0$. Not because it's a definition (though some authors also use $\equiv$ for definitions), but because it's asserting that two propositions have the same truth value, not that two expressions evaluate to the same object. – hmakholm left over Monica Aug 28 '18 at 14:06