# Operators and functions

1. Jul 2, 2009

### SW VandeCarr

Is there a fundamental difference between operators and functions?

For example we could have F(x,y)=x+y or we could write SUM(x,y) where SUM is a defined operation in some program. Could operators be considered a particular type of function?

2. Jul 2, 2009

### Moo Of Doom

Yes. Any binary operation on $S$ is simpy a function from $S \times S \to S$. We use infix notation (that is, we write the function in between the operands as in x + y instead of +(x, y) ) out of convenience and familiarity.

3. Jul 3, 2009

### SW VandeCarr

Thanks Moo Of Doom. I was pretty sure of this, but math texts usually use these in terms in distinct ways.

Last edited: Jul 3, 2009
4. Jul 3, 2009

### HallsofIvy

Staff Emeritus
Moo of Doom talked about "operations". Your question was about "operators". Generally, an "operator" is a function defined on functions as opposed to functions on numbers.

5. Jul 3, 2009

### SW VandeCarr

Then SUM(x,y) would not be read as an operator on (x,y), but rather as an operation on (x,y)?

6. Jul 3, 2009

### HallsofIvy

Staff Emeritus
Yes, that is true. The original post was ambiguous.