Injective functions are not the same thing as injective correspondences, correct? Injective functions are a subset of the injective correspondences.
For example in $y^2 = x$, y is not a function of x, but this is still a correspondence between $\mathbb{R} \rightarrow \mathbb{R}$. Can we say that the correspondence, $C:X \rightarrow Y$ is injective? (Since, if $C(x_1) = C(x_2)$ then $x_1 = x_2$.) Can we say it is also a surjective correspondence since every y-value has at least one (mostly two) pre-images?
Or am I way off base applying these definitions to things that are not functions?
Last question. "Mappings" are, as the Wikipedia suggests, the same thing as functions. (For some reason I thought mappings were correspondences. In fact, it is in my old notes. My old notes are wrong, right? )