Whether 0 is a natural number in elementary school textbooks

A natural number that is a non-negative integer (0,1,2,3,4......One of the reasons to think that natural numbers don't contain zeros is because people start learning numbers from "one, two, three." Instead of starting with "zero, one, two, three." At first, because it's very unnatural.

Natural numbers usually serve two purposes: they can be used for counting (e.g., "there are seven apples"), see cardinality; It can also be used for sorting (e.g. "This is the third largest city in the country"), see Ordinal.

The set of natural numbers is a countable, infinite set of supreme bounds. Mathematicians generally denote it in n. There are addition and multiplication operations on the set of natural numbers, and the result of adding or multiplying two natural numbers is still a natural number.

It can also be used for subtraction or division, but the results of subtraction and division may not always be natural numbers, so subtraction and division operations are not always true in the set of natural numbers.

Natural numbers are the most basic type of number system that people know. In order to make the system of numbers have a strict logical foundation, mathematicians in the 19th century established two theories about natural numbers: the ordinal number theory of natural numbers and the cardinal theory, so that the concepts, operations and related properties of natural numbers are strictly discussed.

The addition and multiplication operations of natural numbers can be defined in ordinal or cardinal theory, and the operations under both theories are the same.

Globally, there is still a debate about whether 0 is a natural number. In Chinese mainland, primary and secondary school textbooks before around 2000 generally do not include 0 in natural numbers, or refer to them as "expanded natural number series". In the new editions of primary and secondary school textbooks after around 2000, 0 was generally included in the natural number.

Count natural numbers. Historically, there have always been two domestic and foreign regulations on whether 0 is a natural number: one stipulates that 0 is a natural number, and the other stipulates that 0 is not a natural number. Since the founding of the People's Republic of China, our country's primary and secondary school textbooks have always stipulated that the set of natural numbers does not include 0.

At present, most of the foreign mathematical circles stipulate that 0 is a natural number, and for the convenience of international exchanges, the "National Standard" stipulates that the set of natural numbers includes 0. Therefore, in our newly published textbook, this treatment is carried out in accordance with the National Standards, and the original set of natural numbers is now called the set of positive integers. At the same time, we also use some mathematical symbols in accordance with the provisions of the national standards.

Elementary math 0 is a natural number.

0 is an integer between -1 and 1, the smallest natural number, and a rational number. Any number is summed or varied from 0, and its value does not change; The difference between the same two numbers is equal to 0, and the multiplication of other non-zero real numbers and 0 numbers is equal to 0; 0 divided by other non-zero real numbers is equal to 0, but 0 cannot be used as a divisor.

Natural numbers are numbers that are used to keep track of the number of items or to indicate the order of items. i.e. the numbers 0, 1, 2, 3, 4 ......The number indicated. Natural numbers are made up of 0, one after the other, forming an infinite group.

Natural numbers are controllable and infinite. It can be divided into even and odd numbers, composite numbers and prime numbers, etc.

Significance of Math 0:

0 is actually a very important number, although it means nothing, but the birth of this symbol is of epoch-making significance in the history of mathematics. In the early days of the development of mathematics, many ancient civilizations in ancient times did not have the concept of 0.

Because mathematics is the best and life, the things that can be seen in life are real quantities, 1 is 1, 2 is 2, so for a long time, everyone only had positive numbers.

Later, people began to realize the importance of zero, so some symbols for representing 0 began to appear, which meant that people began to understand numbers from concrete to abstract.

0 is a natural number, and 0 is an integer between -1 and 1, which is the smallest natural number and is also a rational number. 0 is neither positive nor negative, but the dividing point between positive and negative numbers. There is no reciprocal of 0, the opposite of 0 is 0, the absolute value of 0 is 0, the square of 0 is 0, the square root of 0 is 0, the cube root of 0 is also 0, 0 multiplied by any number is equal to 0, and the power of 0 of any number other than 0 is equal to 1.

0 cannot appear as a denominator or divisor, all multiples of 0 are 0, and 0 divided by any non-zero real number is equal to 0. If the divisor (denominator, posterior term) is 0 and the dividend is a non-zero positive number, the quotient does not exist, which is because multiplying any number by 0 will not result in a non-zero positive number, so it makes no sense to use 0 as the divisor (denominator, posterior term). However, some domains are defined as infinity ( ), so 0 is considered to give non-zero positive numbers.

Wikipedia states that natural numbers can refer to positive integers (1, 2, 3, 4...).It can also be a non-negative integer (0, 1, 2, 3, 4...).

For example, the former is usually used in number theory, while the latter is mostly used in set theory and computer science. One of the reasons to think that natural numbers don't contain zeros is because people (especially children) start learning numbers from one, two, and three. Instead of starting with "zero, one, two, three."

Start because it's unnatural. ......History and the qualitative nature of 0 are derived from the number of numbers. The ancient Greeks were the first to study its abstract properties, and the Pythagoreans regarded it as the basis of the universe.

Other ancient civilizations have also made great contributions to its research, especially India's acceptance of zero. Zero was used digitally by the Babylonians as early as 400 BC. The Mayans considered zero to be a number in 200 AD, but did not communicate with other civilizations.

The modern idea was proposed by the Indian scholar Brahmagupta in 628 A.D. and spread to Europe by the Arabs. Europeans were initially still resistant to zero as a number, believing that zero was not a "natural" number. At the end of the 19th century, setists gave a more rigorous definition of natural numbers.

According to this definition, it is more convenient to include zeros (corresponding to empty sets) in natural numbers. Logicians and computer scientists accept the definition of set theorists. Other mathematicians, mainly number theorists, follow tradition and keep zero out of natural numbers.

In addition, in Japan, Asia, textbooks from elementary school to high school still have "natural numbers start with 1". Let's add a paragraph from the former Fengyue Dancer netizens:**People's Education Forum:

With the successive use of the nine-year compulsory education primary school mathematics textbook (trial revised version), we have received letters and calls from some primary school mathematics teachers, parents and students, asking whether 0 is a natural number. The answer is as follows: Historically, there have always been two views on whether 0 is a natural number or not

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, China's primary and secondary school textbooks have always stipulated that natural numbers do not include 0At present, most of the foreign mathematical circles stipulate that 0 is a natural number.

In order to facilitate international exchanges, the National Standards of the People's Republic of China (GB 3100 3102-93) promulgated in 1993 "Quantities and Units" (page 311) stipulates that natural numbers include 0Therefore, in the revision of primary and secondary school mathematics textbooks in recent years, our textbook research and compilation staff have revised them according to the above-mentioned national standards. That is, there is no object, which is represented by 0.

0 is also a natural number. However, in the "divisible" part of the elementary school level, the natural number 0 is still not considered, so 0 is not included in concepts such as divisors and multiplesAlso, in general, we don't say that the number 0 is a few digits, so the smallest single digit is 1

In the study of numbers, there are different definitions and schools of thought as to whether 0 is a natural macro and destroyer. According to some definitions and schools, 0 is considered to be part of the natural number, while according to other definitions and schools, 0 is excluded from the natural number.

In traditional Piano axiomatic mathematics, natural numbers are a sequence of positive integers starting from 1: 1, 2, 3, 4, 5, ,..By this definition, 0 is not a natural number.

However, in some modern mathematical and computer science, there is also a definition of 0 that incorporates 0 into the set of natural numbers. According to this definition, a natural number is a sequence of integers starting from 0: 0, 1, 2, 3, 4, ,..According to this definition, 0 is a part of the natural number.

So, the exact answer to this question depends on the definition and school of thought you are going to use.

The natural number of 0 belongs to the natural number.

In mathematics, natural numbers are one of the most basic number systems. The natural number is determined by ......Infinitely extended, it is our most common integer. However, there are different opinions and controversies as to whether the number 0 is a natural number.

Some scholars believe that a set of natural numbers should include 0 because it is a special element in a set of integers.

0 stands for no quantity, and has important applications in counting, metricizing, and representing numbers. In addition, 0 is one of the important components in most mathematical formulas and equations. Therefore, the inclusion of 0 in the category of natural numbers can more completely describe the nature, laws and characteristics of the integer system.

Other scholars take a different view, arguing that 0 should not be counted as a natural number. This is because natural numbers are always defined starting from 1 and working backwards, and natural numbers are usually used in the case of counting length, age, or other similar delays;

0 has no such characteristic. In addition, 0 is often excluded from most studies of natural numbers, and therefore should not be classified as natural numbers.

In fact, there is no absolute standard for the definition of a natural number, which has led to a debate about whether 0 is a natural number. But in any case, whether 0 is considered a natural number or not, it does not have much impact on the basic properties and operations of the natural number set.

In practice, zero-related issues are usually handled in a special way. For example, in computer programming, programmers generally treat 0 as a special value of an integer; In statistics and physics, 0 is usually excluded from the sample data, or used as a reference value to judge changes in other values, etc.

To sum up, although there is controversy about whether 0 is a natural number, it does not affect the establishment and application of basic mathematical principles. We need to flexibly apply and define the concept of natural numbers according to specific situations, and continue to deepen our knowledge and understanding of mathematical laws and phenomena in practice.

0 is a natural number.

Historically, there have always been two views in the mathematical circles at home and abroad on whether 0 is a natural number: one believes that 0 is a natural number, and the other believes that 0 is not a natural number. In the decades after the founding of the People's Republic of China, primary and secondary school textbooks have always stipulated that natural numbers do not include zero.

However, most of the foreign mathematical circles stipulate that 0 is a natural number. In order to facilitate the flow of international cross-mold shouting, the National Standard of the People's Republic of China (GB 3100-3102-93) "Quantity and Unit" (page 311) promulgated in 1993 stipulates that natural numbers include 0. Infiltration.

In the earliest stages of human history, due to the need for measurement, it was used to express the number of numbers. First there is the number one, and then add one one after another, and it is obtained.

Two, three, four, etc., collectively referred to as "natural numbers". Natural numbers are part of integers, i.e. "positive integers".

Natural numbers can also be described in axiomatic terms (see "Piano's axioms" on page 1727). Since the number 0 is so commonly used, in modern mathematics it is often attributed to a natural number as well, so the set of natural numbers n is the union of the set of integers n+ = and .