We say that a sequence { a n } {\displaystyle \{a_{n}\}} converges to a number L {\displaystyle L} if for all ϵ > 0 {\displaystyle \epsilon >0} there exists an N ∈ N {\displaystyle N\in \mathbb {N} } such that for all n ∈ N {\displaystyle n\in \mathbb {N} } with n ≥ N {\displaystyle n\geq N} we have | a n − L | < ϵ {\displaystyle |a_{n}-L|<\epsilon } .