www.ddhw.org---据说这世界是彩色的？
传统的自然数是不包括0，因为自然数就是用来数东西的，从1开始比较直观。 近代的说法包括0，这样在集合论里会方便一些。 通常用下面的记号可以避免歧义， N0={0,1,2...} N*={1,2,3....} 这个对数学定理没什么影响，没什么变化，这是个芝麻小问题，算不上是数学问题。 |
俺的感觉也是把0放在自然数中会比较方便。从整数的近代定义来看，从0 （0对应于空集{}，1对应于{{}}，2对应于{{},{{}}}，......）出发也很合理、自然。事物都在变化，科学也在发展，教科书与时俱进是理所当然的。 |
报道最后援引的说法称把0规定为自然数是国际标准。请问是否存在这样的国际标准？在国际上进行数学讨论的时候，在0是否自然数会对讨论结果有影响的时候，是特意说明还是有一个默认的定义？ |
In mathematics, the natural numbers are the ordinary whole numbers used for counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively (see English numerals). A later notion is that of a nominal number, which is used only for naming. Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics. There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition first appearing in the 19th century. Some authors use the term "natural number" to exclude zero and "whole number" to include it; others use "whole number" in a way that excludes zero, or in a way that includes both zero and the negative integers. |
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