Definition:Operation

Definition
An operation is an object, identified by a symbol, which can be interpreted as a process which, from a number of objects, creates a new object.

Comment
It can be seen that, in the same way that a mapping can be seen as a way of "transforming" one element into to another, an operation does the same thing, just with a larger number of operands.

In fact, as we have just defined it, we see that an operation is a generalisation of the concept of the mapping, or (if you like) a mapping is just an operation with only one operand.

There is another way to view an operation. Instead of viewing it as the act of combining two things in a certain way to get a third, we can look upon it as doing something to the first thing with the second to turn it into the third.

Thus, $\map \circ {a, b}$ can be interpreted as $\map {\circ_b} a$, where $\circ_b$ is defined as the mapping which performs "$\circ_b$" on a single operand.

For example, take the statement "$1 + 2 = 3$", where the symbol $+$ represents the familiar binary operation of addition of numbers. Thus, we can either view $+$ as being the operation that takes $1$ and $2$ and maps them onto $3$, or we can say that we take $1$, and then we do something to it: we "add $2$", and this turns the $1$ into $3$.

In the case of addition, in a certain sense the first interpretation comes to mind more easily than the second, but if we take the statement "$3 - 2 = 1$", it's more natural to think of this as "doing something" to $3$, that is, to take $2$ off it, to change it into something smaller, that is, $1$.

Both interpretations are equally valid, but depending on the circumstances, one may be more appropriate than the other.