Antisymmetric relation and Equivalence relation

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Difference between Antisymmetric relation and Equivalence relation

Antisymmetric relation vs. Equivalence relation

In mathematics, a binary relation R on a set X is anti-symmetric if there is no pair of distinct elements of X each of which is related by R to the other. In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

Asymmetric relation

In mathematics, an asymmetric relation is a binary relation on a set X where.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Order theory

Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Reflexive relation

In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Symmetric relation

In mathematics and other areas, a binary relation R over a set X is symmetric if it holds for all a and b in X that a is related to b if and only if b is related to a. In mathematical notation, this is: Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.

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Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

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