Increasing sequence

A sequence of real numbers $x_n$ such that for all $n=1,2,\ldots,$ the inequality $x_n<x_{n+1}$ is satisfied. Such a sequence is sometimes called a strictly-increasing sequence, the term "increasing sequence" being reserved for sequences that for all $n$ merely satisfy the inequality $x_n\leq x_{n+1}$. Such sequences are also known as non-decreasing sequences. All non-decreasing sequences which are bounded from above have a finite limit, while all those not bounded from above have an infinite limit, equal to $+\infty$.

Comments

See also Decreasing sequence.