Restriction/Mapping/Examples/Restriction of Square Function on Natural Numbers

Example of Restriction of Mapping

Let $f: \N \to \N$ be the mapping defined as:

$\forall n \in \N: \map f n = n^2$

Let $S = \set {x \in \N: \exists y \in \N_{>0}: x = 2 y} = \set {2, 4, 6, 8, \ldots}$

Let $g: S \to \N$ be the mapping defined as:

$\forall n \in \N: \map g n = n^2$

Then $g$ is a restriction of $f$.

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Graphs and functions