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12 relations: Antisymmetric relation, Binary relation, Connex relation, Equivalence relation, Euclid's Elements, First-order logic, Mathematics, Natural number, Quasitransitive relation, Reflexive relation, Set (mathematics), Symmetric relation.
Antisymmetric 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.
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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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Connex relation
In mathematics, a binary relation R on a set X is called a connex relation if it relates all pairs of elements from X in some way.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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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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Quasitransitive relation
Quasitransitivity is a weakened version of transitivity that is used in social choice theory or microeconomics.
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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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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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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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