Join and meet, the Glossary

Table of Contents

1. 24 relations: Associative property, Binary operation, Binary relation, Cambridge University Press, Commutative property, Complete lattice, Completeness (order theory), Directed set, Duality (order theory), Empty set, Family of sets, Idempotence, Infimum and supremum, Iterated binary operation, Lattice (order), Mathematics, Order theory, Partial function, Partially ordered set, Power set, Semilattice, Subset, Total order, Upper and lower bounds.

2. Binary operations
3. Binary relations

Associative property

In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result.

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Binary operation

In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. Join and meet and binary operation are binary operations.

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Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. Join and meet and binary relation are binary relations.

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Complete lattice

In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Join and meet and complete lattice are lattice theory.

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Completeness (order theory)

In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). Join and meet and completeness (order theory) are order theory.

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Directed set

In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation \,\leq\, (that is, a preorder), with the additional property that every pair of elements has an upper bound. Join and meet and directed set are binary relations and order theory.

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Duality (order theory)

In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. Join and meet and Duality (order theory) are order theory.

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Empty set

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Family of sets

In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class.

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Idempotence

Idempotence is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application.

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Infimum and supremum

In mathematics, the infimum (abbreviated inf;: infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists. Join and meet and infimum and supremum are order theory.

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Iterated binary operation

In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Join and meet and iterated binary operation are binary operations.

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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. Join and meet and lattice (order) are lattice theory.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Order theory

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

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Partial function

In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to.

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Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. Join and meet and Partially ordered set are binary relations and order theory.

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Power set

In mathematics, the power set (or powerset) of a set is the set of all subsets of, including the empty set and itself.

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Semilattice

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Join and meet and semilattice are lattice theory.

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Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

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Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. Join and meet and total order are order theory.

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Upper and lower bounds

In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of. Join and meet and upper and lower bounds are order theory.

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See also

Binary operations

• Absorbing element
• Barrel shifter
• Binary operation
• Blaschke sum
• Cap product
• Circular convolution
• Commutator
• Composition of relations
• Courant bracket
• Cup product
• DE-9IM
• Demonic composition
• Elvis operator
• Exponentiation
• Ext functor
• Function composition
• Icosian calculus
• Identity element
• Inverse element
• Iterated binary operation
• Join and meet
• Light's associativity test
• Logic alphabet
• Logical connectives
• Logical consequence
• Lulu smoothing
• Magma (algebra)
• Mean operation
• Minkowski addition
• Modular multiplicative inverse
• Null coalescing operator
• Operations on numbers
• Relational operator
• Tor functor
• Wreath product

Binary relations

• Accessibility relation
• Ancestral relation
• Apartness relation
• BIT predicate
• Binary operations
• Binary relation
• Category of relations
• Comparability
• Congruence relation
• Converse relation
• Countable Borel relation
• Covering relation
• Dependence relation
• Directed set
• Equality (mathematics)
• Equipollence (geometry)
• Equivalence class
• FNP (complexity)
• Inequalities
• Join and meet
• Partially ordered set
• Quotient by an equivalence relation
• Rational consequence relation
• Reflexive closure
• Separoid
• Symmetric closure
• TFNP
• Transitive closure

References

[1] https://en.wikipedia.org/wiki/Join_and_meet

Also known as Directed supremum, Join (lattice theory), Join (mathematics), Join (order theory), Meet (Mathematics), Meet (lattice theory), Meet (order theory), Meet and join.