In mathematics, a relation \(R\) on a set \(X\) is transitive if, for all elements \(a, b, c\) in \(X\), whenever \(R\) relates \(a\) to \(b\) and \(b\) to \(c\), then \(R\) also relates \(a\) to \(c\). Each partial order as well as each equivalence relation needs to be transitive.
\((a \, R \, b \; \text{and} \; b \, R \, c) \implies\) \(a \, R \, c \; \forall \; a, b, c \in X \; | \; R\) is a homogeneous relation over a set \(X\).
Bibliography
“Transitive Relation.” 2022. Wikipedia, June. https://en.wikipedia.org/w/index.php?title=Transitive_relation&oldid=1094090871.