Reflexive relation
binary relation over a set in which every element is related to itself
In mathematics, a binary relation
R
{\displaystyle R}
on a set
X
{\displaystyle X}
is reflexive if it relates every element of
X
{\displaystyle X}
to itself.
An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
Etymology
The word reflexive is originally derived from the Medieval Latin reflexivus ('recoiling' [cf. reflex], or 'directed upon itself') (c. 1250 AD) from the classical Latin reflexus- ('turn away', 'reflection') + -īvus (suffix). The word entered Early Modern English in the 1580s. The sense of the word meaning 'directed upon itself', as now used in mathematics, surviving mostly by its use in philosophy and grammar (cf. Reflexive verb and Reflexive pronoun).
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