# 0的奇偶性

0是一个偶数。来证明0是偶数的最简单的方法是检查0是否符合偶数的定义：若某数是2的整数倍数，那么它就是偶数。因为0＝0×2，所以0为偶数。除此以外，0还满足偶数的所有性质：0可以被2整除；与0相邻的两个数字都是奇数；0可以被等分成两份。

0还满足其它一些由偶数构建出来的一些模型，例如在算术运算中的一些奇偶规则：偶数－偶数＝偶数。

2-2=0
-3+3=0
4×0＝0

## 参考

1. ^ Penner 1999，第34页: 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 k (0 = 2k), and this follows from the equality 0 = 2 ⋅ 0."
2. ^ Ball, Lewis & Thames（2008, p. 15） 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.
3. ^ Compare Lichtenberg（1972, p. 535） Fig. 1
4. ^ Lichtenberg 1972，第535–536页 "...numbers answer the question How many? for the set of objects ... zero is the number property of the empty set ... If the elements of each set are marked off in groups of two ... then the number of that set is an even number."
5. ^ Dickerson & Pitman 2012, p. 191.
6. ^ Lichtenberg 1972，第537页; compare her Fig. 3. "If the even numbers are identified in some special way ... there is no reason at all to omit zero from the pattern."
7. ^ Caldwell & Xiong 2012, pp. 5–6.
8. ^ Gowers 2002，第118页 "The seemingly arbitrary exclusion of 1 from the definition of a prime … does not express some deep fact about numbers: it just happens to be a useful convention, adopted so there is only one way of factorizing any given number into primes." For a more detailed discussion, see Caldwell & Xiong（2012）.
9. ^ Partee 1978，第xxi页
10. ^ Stewart 2001，第54页 These rules are given, but they are not quoted verbatim.