# Is there a name for functions that can not be described by sets?

Functions are usually (though not always) defined as a relation, which is a set of ordered pairs. In this sense, functions are merely sets. However, some ''functions" can only be described by proper classes, and not sets. A familiar example of this is the power set function $\mathcal{P}(X)$. Is there a name for these kinds of "functions", or are they just called functions as well, or is there perhaps not a standard terminology for them?

• I've seen/heard "class function" used before. – Hayden Jan 7 '15 at 20:41

Class function, as Hayden points in the comments, is the common term for describing a collection of ordered pairs which is not [necessarily] a set, and if $\langle x,y\rangle$ and $\langle x,z\rangle$ are both in this collection, then $y=z$.