Symmetric closure
In mathematics, the symmetric closure of a binary relation R on a set X is the smallest symmetric relation on X that contains R.
For example, if X is a set of airports and xRy means "there is a direct flight from airport x to airport y", then the symmetric closure of R is the relation "there is a direct flight either from x to y or from y to x". Or, if X is the set of humans and R is the relation 'parent of', then the symmetric closure of R is the relation "x is a parent or a child of y".
Definition
The symmetric closure S of a relation R on a set X is given by
In other words, the symmetric closure of R is the union of R with its converse relation, RT.
gollark: Not really.
gollark: I did patch *some* of the bugs.
gollark: We were just discussing how broken rednet is.
gollark: Hi.
gollark: Or, because of the `nMessageID` thing (this is very insidious) send a *table* so that (due to reference equality) *the relay won't flag it as a message it's already seen*.
See also
References
- Franz Baader and Tobias Nipkow, Term Rewriting and All That, Cambridge University Press, 1998, p. 8
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