Reflexivity

Basic idea

A relation is reflexive if every element is related to itself. One of the three defining properties of an equivalence relation (with symmetry and transitivity).

Key formulas

• $\forall a \in X.\; R(a,a)$
• Equivalently: $\Delta_X \subseteq R$, where $\Delta_X = \{(a,a) : a\in X\}$

A binary relation R over a set X is reflexive if it relates every element of X to itself.

Siblings

• AntiSymmetry
• Transivity