Bijection/Examples/Real Cube Function
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Example of Bijection
Let $f: \R \to \R$ be the mapping defined on the set of real numbers as:
- $\forall x \in \R: \map f x = x^3$
Then $f$ is a bijection.
Proof
A direct application of Integer Power Function is Bijective iff Index is Odd.
$\blacksquare$
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Composition of Functions