**Definition**: A given [[Real sequences|sequence]] $(a_{n})$ is a Cauchy Sequence iff:$\forall \epsilon>0,\quad \exists N\in \mathbb{N} \quad \text{ s.t. } \quad \forall m,n \geq N, \quad |a_{n} -a_{m}|<\epsilon $ See **Property** [[Real Cauchy Sequences are Bounded]]. **Remark** A sequence is [[Convergence|convergent]] iff it's *Cauchy* by [[General Principle of Convergence]].