Reflexive relation
A binary relation where every element relates to itself.
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A reflexive relation is a binary relation on a set where every element is related to itself. It is one of the three properties, along with symmetry and transitivity, that define an equivalence relation. An example is the relation 'is equal to' on the set of real numbers, since every real number is equal to itself.
Quick Facts
- Field
- Mathematics
- Known for
- Reflexive property of binary relations
- First explicit use
- Giuseppe Peano in Arithmetices principia (1889)
Facts from the source article.
Background
The word 'reflexive' derives from Medieval Latin reflexivus ('recoiling' or 'directed upon itself') from around 1250 AD, from classical Latin reflexus- ('turn away', 'reflection') plus the suffix -īvus. It entered Early Modern English in the 1580s, with the sense of 'directed upon itself' surviving in mathematics, philosophy, and grammar. The first explicit use of 'reflexivity' to describe a relation where every element is related to itself is generally attributed to Giuseppe Peano in his Arithmetices principia (1889), where he defines one of the fundamental properties of equality as a = a. The first use of the word 'reflexive' in the sense of mathematics and logic was by Bertrand Russell in his Principles of Mathematics (1903).
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Sources
Compiled from Wikipedia and the sources listed below. Text from Wikipedia is available under CC BY-SA 4.0; this entry is adapted from it.
- Wikipedia: Reflexive relation (CC BY-SA 4.0).
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