Reflexivity
Reflexivity
A dyadic relation R is called reflexive if xRx holds for all x within a certain previously fixed domain which must include the field of R (cf. logic, formal, 8). In the propositional calculus, the laws of reflexivity of material implication and material equivalence (the conditional and biconditional) are the theorems,
p ? p,
p = p,
expressing the reflexivity of these relations. Other examples of reflexive relations are equality, class inclusion, ? (see logic, formal, 7); formal implication and formal equivalence (see logic, formal, 3); the relation not greater than among whole numbers, or among rational numbers, or among real numbers; the relation not later than among instants of time; the relation less than one hour apart among instants of time.
A dyadic relation R is irreflexive if xRx never holds (e.g., the relation less than among whole numbers). — A.C.