Of course, 0 is a special number, different from any other number. For example, 0 is the boundary between positive and negative numbers, and 0 multiplied by any number equals 0, especially 0 is the most special. If we ignore these characteristics and only pay attention to the apparent consistency between 0 and integer and even number, it may mislead students and make it difficult for them to study mathematics further. Will leave hidden dangers, not worth the loss. Historically, there have been two views at home and abroad about whether 0 is a natural number: one thinks that 0 is a natural number, and the other thinks that 0 is not a natural number. Since the founding of the People's Republic of China, textbooks for primary and secondary schools in China have always stipulated that natural numbers do not include 0. At present, most foreign mathematicians stipulate that 0 is a natural number. In order to facilitate international communication, the national standard of People's Republic of China (PRC) (GB3 100-3 102-93), quantity and unit (1 1-2.9) were promulgated on 1993. Therefore, in the revision of mathematics textbooks for primary and secondary schools in recent years, the researchers and compilers of the textbooks are all revised according to the above national standards. That is, there is no object, which is represented by 0. 0 is also a natural number.
The definitions of "divisible number" and "divisor and multiple" in Book 10 of Nine-year Compulsory Education and Six-year Mathematics in Primary School have not changed. The textbook has such a statement on page 54: "Because 0 can also be divisible by 2, 0 is also an even number". By analogy, 0 can be divisible by all non-zero natural numbers. According to the definition of divisor multiple, 0 is a multiple of any nonzero natural number, and any nonzero natural number is a divisor of 0. However, considering that the research on factorization factor, greatest common divisor and least common multiple is generally limited to the range of non-zero natural numbers, such as least common multiple, 0 is excluded. Therefore, page 50 of Book 10 of Nine-year Compulsory Education and Six-year Primary School Mathematics clearly points out: "For convenience, when we learn divisor and multiple in the future, the number we say generally does not include 0". This avoids some unnecessary troubles. But some past statements must be corrected. For example, the conclusion that "the smallest multiple of a natural number is itself" and "the divisor of a natural number is limited" must be corrected.
In elementary school mathematics, we know that numbers divisible by 2 are called even numbers, usually called even numbers; Numbers that are not divisible by 2 are called odd numbers, usually called odd numbers. Is 0 technical or even? At that time, we discussed odd and even numbers, generally referring to the range of natural numbers. 0 is not a natural number, so it is not mentioned. So can this problem be studied? Our answer is: we can study, we should study. We should not only study the only integer 0 in mathematics that is not a natural number, but also extend the concept of even and odd numbers to negative integers after learning algebra in middle school. The standard of judgment is also very simple. Everything that is divisible by 2 is even, and everything that is not divisible by 2 is odd. The so-called divisibility means that the quotient should be an integer with no remainder. Obviously, because 0 ÷ 2 = 0 and the quotient is an integer 0, 0 is an even number. Similarly, in integers, -2, -4, -6, -8,-10, -360, -2578 and so on. Are even numbers; And-1, -3, -5, -7, -249,-1683 are all odd numbers.
Historically, there have been two views on whether 0 is a natural number in mathematics circles at home and abroad: one thinks that 0 is a natural number, and the other thinks that 0 is not a natural number. Since the founding of the People's Republic of China, textbooks for primary and secondary schools in China have always stipulated that natural numbers do not include 0. At present, most foreign mathematicians stipulate that 0 is a natural number. In order to facilitate international communication, the national standard of People's Republic of China (PRC) (GB3 100-3 102-93), quantity and unit (1 1-2.9) were promulgated on 1993. Therefore, in the revision of mathematics textbooks for primary and secondary schools in recent years, the researchers and compilers of the textbooks are all revised according to the above national standards. That is, there is no object, which is represented by 0. 0 is also a natural number.
The definitions of "divisible number" and "divisor and multiple" in Book 10 of Nine-year Compulsory Education and Six-year Mathematics in Primary School have not changed. The textbook has such a statement on page 54: "Because 0 can also be divisible by 2, 0 is also an even number". By analogy, 0 can be divisible by all non-zero natural numbers. According to the definition of divisor multiple, 0 is a multiple of any nonzero natural number, and any nonzero natural number is a divisor of 0. However, considering that the research on factorization factor, greatest common divisor and least common multiple is generally limited to the range of non-zero natural numbers, such as least common multiple, 0 is excluded. Therefore, page 50 of Book 10 of Nine-year Compulsory Education and Six-year Primary School Mathematics clearly points out: "For convenience, when we learn divisor and multiple in the future, the number we say generally does not include 0". This avoids some unnecessary troubles. But some past statements must be corrected. For example, the conclusion that "the smallest multiple of a natural number is itself" and "the divisor of a natural number is limited" must be corrected.