One of the ideas: Why should we classify 0 as a natural number?

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, People's Republic of China (PRC) national standard (GB 3 100-3 102-93), quantity and unit (1 1-2.9) was promulgated in 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.

Thinking 2: Is the smallest number "1" or "0"?

0 is the smallest natural number, so is the smallest number "1" or "0"? It is clear to all that before 0 is classified as a natural number, the minimum number of digits is 1. So, now that 0 has become a natural number, is the smallest number still 1 This is a question raised by many teachers. I think the smallest number is 1.

Because, 0 means there is no object, which is a symbol indicating vacancy in notation. For example, 3005, "0" means that ten digits, hundreds digits and all numbers are empty. Although this adjustment classifies "0" as a natural number, the concepts of several numbers have not changed. The definition of "several digits" is as follows: "A number represented by only one significant digit is called a number, and a number represented by only two significant digits, in which the first digit on the left is a significant digit and is called a double digit ..." Assuming that 0 is also counted as a number, is the smallest double digit "10" or "00"? What are the smallest three and four digits?

On page 98 of "Nine-year Compulsory Education and Six-year Primary School Mathematics Teachers' Teaching Book", there is such a statement: "Usually, in natural numbers, numbers containing several numbers are called numbers. For example, 2, a number containing a number, is called a number; 30 Numbers containing two digits are called two digits; 405 is a three-digit number, called three digits ... but it should be noted that generally speaking, 0 is not a number.

The so-called maximum and minimum digits are usually within the range of non-zero natural numbers. So the maximum number of digits is 9 and the minimum number of digits is1; The maximum two digits are 99, and the minimum two digits are10; The largest three digits are 999, and the smallest three digits are 100 ... "

To sum up, although "0" is the smallest natural number, it cannot be called "one digit", let alone the smallest digit.

Thinking 3: Is the counting unit of natural numbers still "1"?

As we all know, 0 is the smallest natural number. 1 add 0 to 1, 1 add 2 to 2, 1 add 2 to 3, ... If this continues, you can get any natural number. According to the order of natural numbers, the latter natural number is more than the previous natural number 1. So any natural number is a combination of several 1, so 1 is the unit of natural number. 0 can be regarded as a natural number consisting of 0 1