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When should I use $=$ and $\equiv$?

I heard about this in our calculus class years ago. I was actually not in that class when the processor explained this. 95% of engineering student do not know about this operator. Trying to recall, what did it mean? And is it used standard in Math classes? I think it means approximately equal to.

I am not 100% sure about the syntax.

Edit: Originally I asked for === operator

  • 1
    "Approximately equal to" is $\approx$. ===, I've seen in some programming languages...2011-09-13
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    this is not a programming question by the way.2011-09-13
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    Maybe it means "is defined to be equal" like "≡", except they didn't have "≡" on a typewriter.2011-09-13
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    @xpda Thanks I corrected the question. I meant to ask ≡.2011-09-13
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    "I was actually not in that class when the *processor* explained this." That's a curious typo. :-)2011-09-13
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    It is often used in the form $f(x) \equiv g(x)$ to say $f(x) = g(x)$ for all $x$, as opposed to $f(x) = g(x)$ for some specific $x$.2011-09-13
  • 5
    When used in the sense of @Theo's comment, I think it is common to read it like: "$f(x)$ is *identically equal to* $g(x)$".2011-09-13
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    I read it as "identically equal to" ... and I think of the symbol as "=" with an emphatic underscore.2011-09-13
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    See also [this question](http://math.stackexchange.com/questions/29523/why-do-they-use-equiv-here).2011-09-13
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    Technically speaking, $=$ and $\equiv$ are not operators, they are relations.2013-08-23

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