Graph (Function)

set-theory

Definition

Graph (Function)

Let $f:X\to Y$ be a (possibly partial) function. The graph of $f$ is the set of input-output pairs

$${\Gamma }_f=\{(x,y)\in X\times Y\mid f(x)\text{ is defined}\wedge f(x)=y\}$$

Example:

• $f:\mathbb{N}\to \mathbb{N},n\mapsto n^2,{\Gamma }_f=\{(0,0),(1,1),(2,4),\dots \}$