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

Example of Extension of Mapping

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

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

Let $h: \R \to \R$ be the mapping defined as:

$\forall x \in \R: \map h x = x^2$

Then $h$ is a extension 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