There is an interesting discussion of the reflexiveness of infinite wholes in the first of Galileo's Dialogues on Motion.
1580s, "reflective, capable of bending or turning back," from Medieval Latin reflexivus, from Late Latin reflexus (see reflect). Meaning "of the nature of a reflex" is from 1839 (implied in reflexively). Grammatical sense from 1837. Related: Reflexiveness; reflexivity.
Of or relating to a mathematical or logical relation such that, for any given element, that element has the given relation to itself. Equality in mathematics is a reflexive relation, since a = a for all a, whereas the relation of being 'less than' is not, since it is not true that a < a for any a.