4
$\begingroup$

Possible Duplicate:
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

  • 0
    Technically speaking, $=$ and $\equiv$ are not operators, they are relations.2013-08-23

4 Answers 4

5

Since your professor was referring to engineering students, then it's likely they were referring to the identity symbol, which is used in an expression to mean the left and right hand sides are true for all values. So $\cos^2\theta +\sin^2\theta \equiv 1 $ since it's true for all $\theta$ whereas $\cos\theta = 1$ since it's true only for some.

  • 0
    A special case of that, function identically equal to a value (zero here) can be written as $f(x)\equiv 0$.2011-09-13
3

There's the obvious meaning: Congruence modulo an integer, i.e. "$a \equiv b \pmod c$" (read: "$a$ is congruent to $b$ modulo $c$") which means $c \mid(b-a)$ ("$c$ divides $b-a$").

As someone else has mentioned it's also occasionally used to indicate equality of functions by writing $f(x) \equiv g(x)$, but why not just write $f=g$ then?!

  • 0
    This is correct but from what I remember it was not used in this context. Could it mean something else , something simpler? Or may be our professor could be wrong :(2011-09-13
2

It's used for various things in various contexts. The one about "defined to be equal" is often rendered as ":=". I haven't seen "$\equiv$" used for that. It's certainly used for congruence with respect to a modulus; e.g. $44\equiv62 \pmod 6$, etc. It's used for identities like $(x+1)^2 = x^2+2x+1$ when one wants to say that that is true for all values of $x$.

However, the variety of different uses that this symbol temporarily has in more advanced work has probably never been tabulated.

1

The "≡" operator often used to mean "is defined to be equal."