A real sequence ( x n ) n ∈ N {\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }} is said to tend to − ∞ {\displaystyle {}-\infty } , if for every s ∈ R {\displaystyle {}s\in \mathbb {R} } , there exists some N ∈ N {\displaystyle {}N\in \mathbb {N} } . such that
