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In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R.
For example, if X is a set of distinct numbers and x R y means "x is less than y", then the reflexive closure of R is the relation "x is less than or equal to y".
Definition
The reflexive closure S of a relation R on a set X is given by
In words, the reflexive closure of R is the union of R with the identity relation on X.
See also
References
- Franz Baader and Tobias Nipkow, Term Rewriting and All That, Cambridge University Press, 1998, p. 8