Answer to Question #310416 in Real Analysis for Nikhil

Question

All strictly monotonically decreasing sequences are convergent.

True or false with full explanation

Answer 1

Consider $x_n=-n,n\geq 1$

The sequence is obviously strictly monotonically decreasing, and

$\underset{n\rightarrow \infty}{\lim}x_n=-\infty$

Thus it is not convergent.

The statement is false.