- #1

Phys12

- 351

- 42

Let A and B be sets and f:A->B. The function f is said to be onto if, for each b ϵB, there is at least one a ϵ A for which f(a)=b. In other words, f is onto if R(f)=B. A function which is onto is also called a surjection or a surjective function.

However, what I don't understand is why does there need to be

*at least one*a ϵ A? Shouldn't there be only one since it's a function and a function by definition, for a given image, cannot have 2 pre-images?