Answer to Question #177918 in Real Analysis for Nikhil Singh

Question #177918

Prove or disprove the following statement

‘ Every strictly increasing onto function is invertible'


1
Expert's answer
2021-05-07T09:04:01-0400

Let F: R "\\to" R be any strictly increasing into function.


We show that F is bijective.

To this end, let x,y "\\in" R with x "\\ne" y then so we assume x<y, so that F(x)<F(y) implies F(x) "\\ne" F(y). That is f is injective, and since F is onto by the hypothesis, it is bijective and thus Invertible.


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