Preorder - Wikipedia
Consider a homogeneous relation {\displaystyle \,≤ \,} on some given set {\displaystyle P,} so that by definition, {\displaystyle \,≤ \,} is some subset of {\displaystyle P× P} and the notation {\displaystyle a≤ b} is used in place of {\displaystyle (a,b)∈ \,≤ .} Then {\displaystyle \,≤ \,} is called a preorder or quasiorder if it is reflexive and transitive; that is, if it satisfies:
Reflexivity: {\displaystyle a≤ a} for all {\displaystyle a∈ P,} and Transitivity: if {\displaystyle a≤ b{\text{ and }}b≤ c{\text{ then }}a≤ c} for all {\displaystyle a,b,c∈ P.}