Thread: Real Analysis - Functional Limits #3

Using the ε-δ characterization of continuity, prove that:

lim as x --> Pi of [[x]] = 3, where [[x]] denotes the greatest integer less than or equal to x.

Originally Posted by ajj86

Using the ε-δ characterization of continuity, prove that: lim as x --> Pi of [[x]] = 3, where [[x]] denotes the greatest integer less than or equal to x.

Just take note that: $\displaystyle \delta = \pi - 3\,,\,x \in \left( {\pi - \delta ,\pi + \delta } \right) \Rightarrow \quad \left\lfloor x \right\rfloor = 3$.