Function/R/Strictly increasing/Definition/Injective/Exercise

A function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x),$

is called strictly increasing if for all ${}x_{1},x_{2}\in \mathbb {R}$ satisfying ${}x_{1}<x_{2}$, also ${}f(x_{1})<f(x_{2})$ holds. Show that a strictly increasing function ${}f$ is injective.

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