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# Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1]

## Alternation (formal language theory)

In formal language theory and pattern matching, alternation is the union of two sets of strings or patterns.

## Associative property

In mathematics, the associative property is a property of some binary operations.

## Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

## Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

## Class (set theory)

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.

## Commutative property

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

## Complement (set theory)

In set theory, the complement of a set refers to elements not in.

## Disjoint union

In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.

## Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

## Empty set

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

## Existential quantification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".

## Finite set

In mathematics, a finite set is a set that has a finite number of elements.

## Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Index set

In mathematics, an index set is a set whose members label (or index) members of another set.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## 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.

## List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

## Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

## Naive set theory

Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.

## 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").

## Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Symmetric difference

In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection.

## Universe (mathematics)

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.

## References

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