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  2. Reflexive relation - Wikipedia

    en.wikipedia.org/wiki/Reflexive_relation

    An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.

  3. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    A relation that is reflexive, symmetric, and transitive. It is also a relation that is symmetric, transitive, and serial, since these properties imply reflexivity. Orderings: Partial order A relation that is reflexive, antisymmetric, and transitive. Strict partial order A relation that is irreflexive, asymmetric, and transitive. Total order

  4. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

  5. Equivalence relation - Wikipedia

    en.wikipedia.org/wiki/Equivalence_relation

    A reflexive and symmetric relation is a dependency relation (if finite), and a tolerance relation if infinite. A preorder is reflexive and transitive. A congruence relation is an equivalence relation whose domain X {\displaystyle X} is also the underlying set for an algebraic structure , and which respects the additional structure.

  6. Uniformly convex space - Wikipedia

    en.wikipedia.org/wiki/Uniformly_convex_space

    The unit sphere can be replaced with the closed unit ball in the definition. Namely, a normed vector space is uniformly convex if and only if for every < there is some > so that, for any two vectors and in the closed unit ball (i.e. ‖ ‖ and ‖ ‖) with ‖ ‖, one has ‖ + ‖ (note that, given , the corresponding value of could be smaller than the one provided by the original weaker ...

  7. Reflexive closure - Wikipedia

    en.wikipedia.org/wiki/Reflexive_closure

    A relation is called reflexive if it relates every element of to itself. For example, if X {\displaystyle X} is a set of distinct numbers and x R y {\displaystyle xRy} means " x {\displaystyle x} is less than y {\displaystyle y} ", then the reflexive closure of R {\displaystyle R} is the relation " x {\displaystyle x} is less than or equal to y ...

  8. Similarity (geometry) - Wikipedia

    en.wikipedia.org/wiki/Similarity_(geometry)

    Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.

  9. Tolerance relation - Wikipedia

    en.wikipedia.org/wiki/Tolerance_relation

    In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence , except that the assumption of transitivity is dropped. [ 1 ]