Real Square Function is neither Injective nor Surjective
Jump to navigation
Jump to search
Example of Mapping which is Not an Injection nor a Surjection
Let $f: \R \to \R$ be the real square function:
- $\forall x \in \R: \map f x = x^2$
Then $f$ is neither an injection nor a surjection.
Proof
Consider the real square function:
From Real Square Function is not Injective:
- $f$ is not an injection.
From Real Square Function is not Surjective:
- $f$ is not a surjection.
$\blacksquare$
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 5$. Induced mappings; composition; injections; surjections; bijections: Exercise $6$