Right Inverse Mapping/Examples/Real Part of Complex Number
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Example of Right Inverse Mapping
Let $f: \C \to \R$ be the mapping:
- $\forall z \in \C: \map f z = \map \Re z$
From Real Part as Mapping is Surjection, $f$ is a surjection.
Hence it has a right inverse $g: \R \to \C$ which, for example, can be defined as:
- $\forall x \in \R: \map g x = x + i$
This right inverse is not unique.
For example, the mapping $h: \R \to \C$ defined as:
- $\forall x \in \R: \map h x = x - i$
is also a right inverse.
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Exercise $\text{Q}$