I am a little confused by the definitions of these different types of functions:
I think the definition of a surjection is pretty clear in that each element of x is mapped to some value of y.
But I'm a little confused about the difference between an injection and a bijection. An injection maps an element of x to at most one y and a bijection maps an element of x to exactly one y. Does this mean that an injection can have an element of x that does not map to any element of y whereas a bijection always has exactly one mapping?
And then, does this mean that all bijections are injections and all injections and bijections are surjections? Or can a function only be one of the three?