Parity of zero

zero is an even number0 is evenevenevenness of zerozero is even
Zero is an even number.wikipedia
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Parity (mathematics)

even numberodd numberparity
In other words, its parity—the quality of an integer being even or odd—is even.
In particular, zero is an even number.

0

zerozero function0 (number)
Zero is an even number.
Zero is an even number because it is divisible by 2 with no remainder.

Singly and doubly even

singly evendoubly evenSingly even number
Multiples of 4 are called doubly even, since they can be divided by 2 twice.
This definition applies to positive and negative numbers n, although some authors restrict it to positive n; and one may define the 2-order of 0 to be infinity (see also parity of zero).

Integer

integersintegralZ
In other words, its parity—the quality of an integer being even or odd—is even.

Multiple (mathematics)

multiplemultiplesinteger multiple
This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 × 2.

2

bracetwo2 (number)
This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 × 2.

Identity element

identityneutral elementleft identity
Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined.

Group (mathematics)

groupgroupsgroup operation
Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined.

Natural number

natural numberspositive integerpositive integers
Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined.

Recursive definition

inductive definitionrecursively definedinductively defined
Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined.

Graph theory

graphgraphsgraph-theoretic
Applications of this recursion from graph theory to computational geometry rely on zero being even.

Computational geometry

computational geometergeometric algorithmssearch space
Applications of this recursion from graph theory to computational geometry rely on zero being even.

Mathematics education

mathematics educatorMathematicsAlgebra I
Researchers in mathematics education propose that these misconceptions can become learning opportunities.

Number

number systemnumericalnumbers
Studying equalities like 0 × 2 = 0 can address students' doubts about calling 0 a number and using it in arithmetic.

Arithmetic

arithmetic operationsarithmeticsarithmetic operation
Studying equalities like 0 × 2 = 0 can address students' doubts about calling 0 a number and using it in arithmetic.

Abstraction (mathematics)

abstractabstractionAbstraction in mathematics
Evaluating the parity of this exceptional number is an early example of a pervasive theme in mathematics: the abstraction of a familiar concept to an unfamiliar setting.

Mathematical proof

proofproofsprove
The standard definition of "even number" can be used to directly prove that zero is even.

Number line

Numbers can also be visualized as points on a number line.

Counting

inclusive countinginclusivecount
Starting at any even number, counting up or down by twos reaches the other even numbers, and there is no reason to skip over zero.

Multiplication

productmultipliermultiplying
With the introduction of multiplication, parity can be approached in a more formal way using arithmetic expressions.

Definition

definitionsdefineddefine
The precise definition of a mathematical term, such as "even" meaning "integer multiple of two", is ultimately a convention.

Convention (norm)

conventionconventionalconventions
The precise definition of a mathematical term, such as "even" meaning "integer multiple of two", is ultimately a convention.

Triviality (mathematics)

trivialnontrivialnon-trivial
Unlike "even", some mathematical terms are purposefully constructed to exclude trivial or degenerate cases.

Christian Goldbach

GoldbachGoldbach, ChristianGold'''bach
Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime.