Given some set $T$ and an indexed family $({\nequiv{n}}\subseteq T \times T)_{n \in\mathbb{N}}$ of equivalence relations, a \emph{chain} is a function $c : \mathbb{N}\to T$ such that $\All n, m. n < m \Ra c (m)\nequiv{n} c (n+1)$.
Given some set $T$ and an indexed family $({\nequiv{n}}\subseteq T \times T)_{n \in\mathbb{N}}$ of equivalence relations, a \emph{chain} is a function $c : \mathbb{N}\to T$ such that $\All n, m. n \leq m \Ra c (m)\nequiv{n} c (n)$.