# Trivial Chain

Hey there. I was looking around but could not find it: what is the number of chains in a “degenerate” interval of a poset? Thank you!

1. I assume that by “degenerate” interval you mean the trivial interval, namely $[x, x]$, for \$x\$ in a poset. In this case, there is only one possible chain contained in $[x, x]$, namely $C = {x}$.
In this case, there is only one possible chain contained in $[x, x]$, namely $C = \{x\}.$
(Recall that a chain $C$ is a subset of a poset where any two elements in $C$ are related, or “comparable.”)