A symmetric relation is a type of binary relation. Formally, a binary relation R over a set X is symmetric if: ∀ a , b ∈ X ( a R b ⇔ b R a ) , {\displaystyle...
4 KB (385 words) - 06:02, 19 August 2024
mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...
31 KB (4,436 words) - 19:07, 29 October 2024
other's bills, the relation is antisymmetric. Partial and total orders are antisymmetric by definition. A relation can be both symmetric and antisymmetric...
4 KB (589 words) - 16:30, 24 January 2024
simultaneously reflexive, symmetric, and transitive – in other words, equivalence relations – (sequence A000110 in the OEIS), those that are symmetric and transitive...
17 KB (2,092 words) - 16:24, 29 September 2024
asymmetric, anti-symmetric, left-unique, or right-unique, then so is R. A relation is reflexive, irreflexive, symmetric, asymmetric, anti-symmetric, connected...
36 KB (3,758 words) - 19:49, 25 October 2024
of) quasi-reflexivity. Symmetric for all x, y ∈ X, if xRy then yRx. For example, "is a blood relative of" is a symmetric relation, because x is a blood...
22 KB (2,177 words) - 16:30, 29 September 2024
a symmetric polynomial if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), ..., Xσ(n)) = P(X1, X2, ..., Xn). Symmetric polynomials...
21 KB (3,833 words) - 01:08, 26 January 2024
{\displaystyle x=y.} A relation R {\displaystyle R} is coreflexive if and only if its symmetric closure is anti-symmetric. A reflexive relation on a nonempty set...
10 KB (1,334 words) - 01:01, 10 September 2024
Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...
16 KB (2,441 words) - 17:45, 28 September 2024
less-than-or-equal relation is an example of a relation that is neither symmetric nor asymmetric, showing that asymmetry is not the same thing as "not symmetric". The...
6 KB (835 words) - 11:12, 17 October 2024