The SlugMath Wiki is under heavy development!
Def/Extension of functions
Definition of Extension of a function: Suppose that $X$ and $Y$ are sets, and $S$ is a subset of $X$. Suppose that $f \colon S \rightarrow Y$ is a function. An extension of $f$ to $X$ is a function $\tilde f \colon X \rightarrow Y$ such that: $$\forall s \in S, \tilde f(s) = f(s).$$ Under this condition, we say that $\tilde f$ extends $f$.
This definition logically relies on the following definitions and statements: Def/Function
To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Functions