Is the equals sign an operator?

[Sque]

Hello. I have recently seen on some site what the equals sign is an operator too, for example as the plus sign. And I know that = is an operator in programming, but I'm interested only in the mathematical definition of this sign. Generally, operators are formally any map from a set to a set. And If we map a set into itself, don't we use the equals sign? I mean: 1=1,2=2,(y+2)/(y+2)=11=1,2=2,(y+2)/(y+2)=1, etc.

 

[Dr.Peterson]

Hello. I have recently seen on some site what the equals sign is an operator too, for example as the plus sign. And I know that = is an operator in programming, but I'm interested only in the mathematical definition of this sign. Generally, operators are formally any map from a set to a set. And If we map a set into itself, don't we use the equals sign? I mean: 1=1,2=2,(y+2)/(y+2)=1, etc.

What programming language are you referring to? In some languages, "=" is a comparison operator (whose value is a Boolean); in others it is an assignment "operator", which may or may not be what one would normally think of as an operator. (In C, its output is the value just assigned, so you can string together a = b = 1.)

In math, the use in a mapping, like f(x) = x^2, could be thought of as an assignment; but that is not really operating on something, but more like an arrow in a mapping definition, x -> x^2, which is not part of the function itself. I don't see how you call 1=1 a mapping.

The normal use of "=" in math is as a comparison. One could stretch the idea and treat it as a binary operator whose result is true or false (as in programming); but I don't think that is standard way to think of it.

Can you show us the site you refer to, and in what sense they say it is an operator?

 

[HallsofIvy]

Of course, you can think of "=" as an operator in the sense that "A= B" maps the pair (A, B) to either "true" or "false".