Definition#

Let \(\rho\) be a relation on a set \(S\). We say that \(\rho\) is transitive if, whenever \(a \rho b\) and \(b \rho c\), we also have \(a \rho c\).

Example#

On \(\mathbb{Z}\), the relations \(\leq\) and \(\lt\) are both transitive.

Source#

Gregory T. Lee. Abstract Algebra. 1st ed. Springer Cham, 2018. pp. 6.