Prove that the Greatest Integer Function

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

3. Prove that the Greatest Integer Function

f: \mathbf{R} \rightarrow \mathbf{R}

, given by

f(x)=[x]

, is neither one-one nor onto, where

[x]

denotes the greatest integer less than or equal to

x