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# Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd. [1]

64 relations: Abstract algebra, Binary number, Bishop (chess), Chess, Clarinet, Combinatorial game theory, Commutative ring, Computer, Configuration space (mathematics), Coset, Cubic crystal system, Cyclic permutation, Decimal, Divisibility rule, Division (mathematics), Divisor, Error detection and correction, Euclidean space, Even and odd functions, Even and odd ordinals, Finite group, Flight number, Friedrich Fröbel, Fundamental frequency, GF(2), Goldbach's conjecture, Harmonic, Harmonic series (music), House numbering, Ideal (ring theory), Identity (mathematics), If and only if, Index of a subgroup, Information theory, Integer, Integer factorization, Kayles, Knight (chess), Lattice (group), Localization of a ring, Mathematical proof, Mathematics, Megaminx, Modular arithmetic, Monad (philosophy), Mutilated chessboard problem, Numeral system, Organ stop, Parity bit, Parity function, ... Expand index (14 more) »

## Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Bishop (chess)

A bishop (♗,♝) is a piece in the board game of chess.

## Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

## Clarinet

The clarinet is a musical-instrument family belonging to the group known as the woodwind instruments.

## Combinatorial game theory

Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.

## Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

## Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

## Configuration space (mathematics)

T^3/S_3, is the above orbifold. --> In mathematics, a configuration space (also known as Fadell's configuration space) is a construction closely related to state spaces or phase spaces in physics.

## Coset

In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, then Only when H is normal will the set of right cosets and the set of left cosets of H coincide, which is one definition of normality of a subgroup.

## Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

## Cyclic permutation

In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

## Divisibility rule

A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.

## Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

## Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

## Error detection and correction

In information theory and coding theory with applications in computer science and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of digital data over unreliable communication channels.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

## Even and odd ordinals

In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers.

## Finite group

In abstract algebra, a finite group is a mathematical group with a finite number of elements.

## Flight number

In the aviation industry, a flight number or flight designator is a code for an airline service consisting of two-character airline designator and a 1 to 4 digit number.

## Friedrich Fröbel

Friedrich Wilhelm August Fröbel or Froebel (21 April 1782 – 21 June 1852) was a German pedagogue, a student of Pestalozzi who laid the foundation for modern education based on the recognition that children have unique needs and capabilities.

## Fundamental frequency

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform.

## GF(2)

GF(2) (also F2, Z/2Z or Z2) is the '''G'''alois '''f'''ield of two elements.

## Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

## Harmonic

A harmonic is any member of the harmonic series, a divergent infinite series.

## Harmonic series (music)

A harmonic series is the sequence of sounds&mdash;pure tones, represented by sinusoidal waves&mdash;in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency.

## House numbering

House numbering is the system of giving a unique number to each building in a street or area, with the intention of making it easier to locate a particular building.

## Ideal (ring theory)

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.

## Identity (mathematics)

In mathematics an identity is an equality relation A.

## 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 of a subgroup

In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively half of the elements of G lie in H. The index of H in G is usually denoted |G: H| or or (G:H).

## Information theory

Information theory studies the quantification, storage, and communication of information.

## 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").

## Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

## Kayles

In combinatorial game theory, Kayles is a simple impartial game.

## Knight (chess)

The knight (♘ ♞) is a piece in the game of chess, representing a knight (armored cavalry).

## Lattice (group)

In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.

## Localization of a ring

In commutative algebra, localization is a systematic method of adding multiplicative inverses to a ring.

## Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

## Mathematics

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

## Megaminx

The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

Monad (from Greek μονάς monas, "singularity" in turn from μόνος monos, "alone"), refers in cosmogony (creation theories) to the first being, divinity, or the totality of all beings.

## Mutilated chessboard problem

The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book Critical Thinking (1946).

## Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

## Organ stop

An organ stop (or just stop) is a component of a pipe organ that admits pressurized air (known as wind) to a set of organ pipes.

## Parity bit

A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd.

## Parity function

In Boolean algebra, a parity function is a Boolean function whose value is 1 if and only if the input vector has an odd number of ones.

## Parity of a permutation

In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.

## Parity of zero

Zero is an even number.

## Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

## Prime ideal

In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.

## 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.

## Quotient

In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.

## Remainder

In mathematics, the remainder is the amount "left over" after performing some computation.

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

## Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

## Thue–Morse sequence

In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far.

## United States Numbered Highway System

The United States Numbered Highway System (often called U.S. Routes or U.S. Highways) is an integrated network of roads and highways numbered within a nationwide grid in the contiguous United States.

## Wind instrument

A wind instrument is a musical instrument that contains some type of resonator (usually a tube), in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at or near the end of the resonator.

## References

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