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# Parity of zero

Zero is an even number. 

## Abstract algebra

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

## Abstraction (mathematics)

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.

## Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## All Things Considered

All Things Considered (ATC) is the flagship news program on the American network National Public Radio (NPR).

## Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Arthur Cayley

Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.

## Associative property

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

## École normale supérieure (Paris)

The École normale supérieure (also known as Normale sup', Ulm, ENS Paris, l'École and most often just as ENS) is one of the most selective and prestigious French grandes écoles (higher education establishment outside the framework of the public university system) and a constituent college of Université PSL.

## 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).

## 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.

## Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.

## Bit-reversal permutation

In applied mathematics, a bit-reversal permutation is a permutation of a sequence of n items, where n.

## Calendar date

A calendar date is a reference to a particular day represented within a calendar system.

## Casino

A casino is a facility which houses and accommodates certain types of gambling activities.

## Charleston Gazette-Mail

The Charleston Gazette-Mail is the only daily morning newspaper in Charleston, West Virginia.

## Christian Goldbach

Christian Goldbach (March 18, 1690 &ndash; November 20, 1764) was a German mathematician who also studied law.

## Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

## Complex question

A complex question, trick question, multiple question or plurium interrogationum (Latin, "of many questions") is a question that has a presupposition that is complex.

## Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

## Computer

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

## Computer monitor

A computer monitor is an output device which displays information in pictorial form.

## Concept image and concept definition

In mathematics education, concept image and concept definition are two ways of understanding a mathematical concept.

## Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.

## Convention (norm)

A convention is a set of agreed, stipulated, or generally accepted standards, norms, social norms, or criteria, often taking the form of a custom.

## Cooley–Tukey FFT algorithm

The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm.

## 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.

## Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

## Counting

Counting is the action of finding the number of elements of a finite set of objects.

## Cycle (graph theory)

In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself.

## 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.

## Deborah Loewenberg Ball

Deborah Loewenberg Ball is an educational researcher noted for her work in mathematics instruction and the mathematical preparation of teachers.

## Definition

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).

## Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

## Degree (graph theory)

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice.

## Deseret News

The Deseret News is a newspaper published in Salt Lake City, Utah, United States.

## Distance (graph theory)

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them.

## 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.

## Education in England

Education in England is overseen by the United Kingdom's Department for Education.

## Empty product

In mathematics, an empty product, or nullary product, is the result of multiplying no factors.

## 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.

## Equivalence class

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

## Even and odd ordinals

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

## 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".

## Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

Fourth Grade (also called Grade Four, equivalent to Year Five in Britain) is a year of elementary education in some countries.

## Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

## Gasoline

Gasoline (American English), or petrol (British English), is a transparent, petroleum-derived liquid that is used primarily as a fuel in spark-ignited internal combustion engines.

The Graduate Management Admission Test (GMAT ()) is a computer adaptive test (CAT) intended to assess certain analytical, writing, quantitative, verbal, and reading skills in written English for use in admission to a graduate management program, such as an MBA.

The Graduate Record Examinations (GRE) is a standardized test that is an admissions requirement for most graduate schools in the United States.

## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

## Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

## Handshaking lemma

In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree (the number of edges touching the vertex).

## Heute

heute (German for 'today') is a television news program on the German channel ZDF.

## Ideal (ring theory)

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

## 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.

## Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

## 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).

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

## 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 (computer science)

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.

## Integer factorization

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

## Internet

The Internet is the global system of interconnected computer networks that use the Internet protocol suite (TCP/IP) to link devices worldwide.

## Isabelle (proof assistant)

The Isabelle theorem prover is an interactive theorem prover, a Higher Order Logic (HOL) theorem prover.

## Jewish World Review

Jewish World Review is a free, online magazine updated Monday through Friday (except for legal holidays and holy days), which seeks to appeal to "people of faith and those interested in learning more about contemporary Judaism from Jews who take their religion seriously." It carries informational articles related to Judaism, dozens of syndicated columns written mostly by politically conservative writers, both Jewish and Gentile, advice columns on a number of issues, and cartoons.

## Johann Heinrich Lambert

Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.

## Lemma (mathematics)

In mathematics, a "helping theorem" or lemma (plural lemmas or lemmata) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.

## Leopold Kronecker

Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Limit ordinal

In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Logical framework

In logic, a logical framework provides a means to define (or present) a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to a type inhabitation problem in the framework type theory.

## Maryland

Maryland is a state in the Mid-Atlantic region of the United States, bordering Virginia, West Virginia, and Washington, D.C. to its south and west; Pennsylvania to its north; and Delaware to its east.

## Mathematical induction

Mathematical induction is a mathematical proof technique.

## Mathematical proof

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

## Mathematics education

In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.

## Möbius function

The classical Möbius function is an important multiplicative function in number theory and combinatorics.

## Möbius inversion formula

In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius.

## Mental chronometry

Mental chronometry is the use of response time in perceptual-motor tasks to infer the content, duration, and temporal sequencing of cognitive operations.

## Millisecond

A millisecond (from milli- and second; symbol: ms) is a thousandth (0.001 or 10−3 or 1/1000) of a second.

## Milwaukee Journal Sentinel

The Milwaukee Journal Sentinel is a daily morning broadsheet printed in Milwaukee, Wisconsin.

## 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).

## Multiple (mathematics)

In science, a multiple is the product of any quantity and an integer.

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

## Multiplication table

In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.

## Multiplicative function

In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1).

## 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").

## New South Wales

New South Wales (abbreviated as NSW) is a state on the east coast of:Australia.

## NPR

National Public Radio (usually shortened to NPR, stylized as npr) is an American privately and publicly funded non-profit membership media organization based in Washington, D.C. It serves as a national syndicator to a network of over 1,000 public radio stations in the United States.

## Null graph

In the mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an "empty graph").

## Number

A number is a mathematical object used to count, measure and also label.

## Number line

In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by \mathbb.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Numeral (linguistics)

In linguistics, a numeral is a member of a part of speech characterized by the designation of numbers; some examples are the English word 'two' and the compound 'seventy-seventh'.

## 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.

## Numerical cognition

Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics.

## Odd–even rationing

Odd–even rationing is a method of rationing in which access to some resource is restricted to half the population on any given day.

## Odds and evens

Odds and evens, also known as swords, choosies, pick, odds-on poke, or bucking up, is a hand game played between two people, used to decide an issue.

## Ordinal number

In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.

## Orientation (vector space)

In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.

## Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

## Parity (mathematics)

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

## 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.

## Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

## Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

## Point in polygon

In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Port and starboard

Port and starboard are nautical and aeronautical terms for left and right, respectively.

## Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

## Primary education

Primary education and elementary education is typically the first stage of formal education, coming after preschool and before secondary education (The first two grades of primary school, Grades 1 and 2, are also part of early childhood education).

## 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.

In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.

## Proposition bet

In gambling, a "proposition bet" (prop bet, prop, novelty, or a side bet) is a bet made regarding the occurrence or non-occurrence during a game (usually a gambling game) of an event not directly affecting the game's final outcome.

## Recursive definition

A recursive definition (or inductive definition) in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set (Aczel 1978:740ff).

## Reflexive relation

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

## Reform mathematics

Reform mathematics is an approach to mathematics education, particularly in North America.

## Ring (mathematics)

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

## Roulette

Roulette is a casino game named after the French word meaning little wheel.

Second grade (corresponding to Year 3 in the UK) is a year of primary education in Canada and the US.

## Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

## Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

## Singly and doubly even

In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not.

## Sperner's lemma

In mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which is equivalent to it.

## Standardized test

A standardized test is a test that is administered and scored in a consistent, or "standard", manner.

## Stanislas Dehaene

Stanislas Dehaene (born May 12, 1965) is a French author and cognitive neuroscientist whose research centers on a number of topics, including numerical cognition, the neural basis of reading and the neural correlates of consciousness.

## Subgroup

In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.

## Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

## Successor function

In mathematics, the successor function or successor operation is a primitive recursive function S such that S(n).

## Successor ordinal

In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α.

## Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

## The Guardian

The Guardian is a British daily newspaper.

Third grade (equivalent to Primary 4 in the UK) is a year of primary education in many countries.

Traditional mathematics (sometimes classical math education) was the predominant method of mathematics education in the United States in the early-to-mid 20th century.

## Triangulation (geometry)

In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.

## Triviality (mathematics)

In mathematics, the adjective trivial is frequently used for objects (for example, groups or topological spaces) that have a very simple structure.

## United States

The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.

## University of Michigan

The University of Michigan (UM, U-M, U of M, or UMich), often simply referred to as Michigan, is a public research university in Ann Arbor, Michigan.

## University of Nottingham

The University of Nottingham is a public research university in Nottingham, United Kingdom.

## University of South Florida

The University of South Florida, also known as USF, is an American metropolitan public research university in Tampa, Florida, United States.

## Valuation (algebra)

In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field.

## Vehicle registration plate

A vehicle registration plate, also known as a number plate (British English) or a license plate (American English), is a metal or plastic plate attached to a motor vehicle or trailer for official identification purposes.

## Vertex (graph theory)

In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

## Year One (education)

Year One is an educational year group in schools in many countries including England, Wales, Australia and New Zealand.

## Year Six

Year 6 is an educational year group in schools in many countries including England, Wales, Australia and New Zealand.

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

## 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

## 2

2 (two) is a number, numeral, and glyph.

## References

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