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Zero is an even number. In other words, its ''parity''—the quality of an integer being even or odd—is even. The simplest way to prove that zero is even is to check that it fits the definition of "even": it is an integer multiple of 2, specifically . As a result, zero shares all the properties that characterize even numbers: 0 is divisible by 2, 0 is neighbored on both sides by odd numbers, 0 is the sum of an integer (0) with itself, and a set of 0 objects can be split into two equal sets. Zero also fits into the patterns formed by other even numbers. The parity rules of arithmetic, such as , require 0 to be even. 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. Applications of this recursion from graph theory to computational geometry rely on zero being even. Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all.〔 "By the same test zero surpasses all numbers in 'evenness.'"; "Thus, the integer is the most 'even.'〕 Among the general public, the parity of zero can be a source of confusion. In reaction time experiments, most people are slower to identify 0 as even than 2, 4, 6, or 8. Some students of mathematics—and some teachers—think that zero is odd, or both even and odd, or neither. Researchers in mathematics education propose that these misconceptions can become learning opportunities. Studying equalities like can address students' doubts about calling 0 a number and using it in arithmetic. Class discussions can lead students to appreciate the basic principles of mathematical reasoning, such as the importance of definitions. 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. ==Why zero is even== The standard definition of "even number" can be used to directly prove that zero is even. A number is called "even" if it is an integer multiple of 2. As an example, the reason that 10 is even is that it equals . In the same way, zero is an integer multiple of 2, namely so zero is even.〔: Lemma B.2.2, ''The integer 0 is even and is not odd''. Penner uses the mathematical symbol ∃, the existential quantifier, to state the proof: "To see that 0 is even, we must prove that and this follows from the equality ."〕 It is also possible to explain why zero is even without referring to formal definitions.〔 discuss this challenge for the elementary-grades teacher, who wants to give mathematical reasons for mathematical facts, but whose students neither use the same definition, nor would understand it if it were introduced.〕 The following explanations make sense of the idea that zero is even in terms of fundamental number concepts. From this foundation, one can provide a rationale for the definition itself—and its applicability to zero. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「parity of zero」の詳細全文を読む スポンサード リンク
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