Surjection/Examples/Non-Surjection

Examples of Mappings which are Not Surjections

Arbitrary Mapping on Sets

Let $A = \set {a, b, c}$.

Let $B = \set {1, 2, 3}$.

Let $f \subseteq {A \times B}$ be the mapping defined as:

$f = \set {\tuple {a, 2}, \tuple {b, 1}, \tuple {c, 1} }$

Then $f$ is not a surjection.

Square Function is Not Surjection

Let $f: \R \to \R$ be the real square function:

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

Then $f$ is not a surjection.

$2 x + 1$ Function on Integers Not Surjection

Let $f: \Z \to \Z$ be the mapping defined on the set of integers as:

$\forall x \in \Z: \map f x = 2 x + 1$

Then $f$ is not a surjection.