A [[Real sequences|sequence of reals]] $(a_{n})$ is 'increasing' if$a_{1}\leq a_{2} \leq a_{3}\dots$A sequence $(a_{n})$ is 'decreasing' if$a_{1} \geq a_{2} \geq a_{3} \dots$ A sequence is (strictly) monotonic if it's (strictly) increasing or (strictly) decreasing. ### Properties - [[Monotone Bounded Real Sequence is Convergent]]. - [[Subsequence of Convergent Sequence Converges to Same Limit]] and [[Monotonic Subsequence Theorem]] so [[Bolzano-Weierstrass Theorem (Sequential Compactness of The Reals)]]. - [[If a subsequence of a monotonic sequence converges then the sequence converges]].