A real sequence ( x n ) n ∈ N {\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }} is called increasing, if x n + 1 ≥ x n {\displaystyle {}x_{n+1}\geq x_{n}} holds for all n ∈ N {\displaystyle {}n\in \mathbb {N} } .
