• 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
  • Thumbnail for Equivalence relation
    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
  • Thumbnail for Relation (mathematics)
    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
  • Thumbnail for Symmetric difference
    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