Editing Reflexive relation (section)

== Etymology ==
[[File:Arithmetices principia Properties of equality.png|thumb|242x242px|[[Giuseppe Peano|Giuseppe Peano's]] introduction of the reflexive property, along with symmetry and transitivity.]]
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]]'').<ref>{{Cite web |title=reflexive {{!}} Etymology of reflexive by etymonline |url=https://www.etymonline.com/word/reflexive#etymonline_v_37000 |access-date=2024-12-22 |website=www.etymonline.com |language=en}}</ref><ref>''[[Oxford English Dictionary]]'', s.v. “[[doi:10.1093/OED/7005855243|Reflexive (''adj.'' & ''n.''), Etymology]],” September 2024.</ref> 

The first explicit use of "reflexivity", that is, describing a relation as having the property that every element is related to itself, is generally attributed to [[Giuseppe Peano]] in his ''[[Arithmetices principia, nova methodo exposita|Arithmetices principia]]'' (1889), wherein he defines one of the fundamental properties of [[Equality (mathematics)|equality]] being <math>a = a</math>.<ref>{{Cite book |last=Peano |first=Giuseppe |author-link=Giuseppe Peano |url=https://books.google.com/books?id=z80GAAAAYAAJ |title=Arithmetices principia: nova methodo |date=1889 |publisher=Fratres Bocca |pages=XIII |language=la |archive-url=https://archive.org/details/arithmeticespri00peangoog/page/n18/mode/2up |archive-date=2009-07-15}}</ref><ref name=":0">{{Cite journal |last=Russell |first=Bertrand |author-link=Bertrand Russell |date=1903 |title=Principles of Mathematics |url=https://doi.org/10.4324/9780203864760 |journal=[[Routledge]] |doi=10.4324/9780203864760|isbn=978-1-135-22311-3 |url-access=subscription }}</ref> The first use of the word ''reflexive'' in the sense of mathematics and logic was by [[Bertrand Russell]] in his ''[[Principles of Mathematics]]'' (1903).<ref name=":0" /><ref>''[[Oxford English Dictionary]]'', s.v. “[[doi:10.1093/OED/4192548146|Reflexive (''adj.''), sense 7 - ''Mathematics and Logic'']]”, "'''1903–'''", September 2024.</ref>