Increasing sequence

A sequence \(u_1\), \(u_2\), … is called increasing if \(u_n \le u_{n+1}\) for all \(n\ge 1\) (so \(u_1\le u_2\le u_3\le \cdots\)).

It is called strictly increasing if \(u_n < u_{n+1}\) for all \(n\ge 1\).

See also decreasing sequence.