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