Ask Xueba to explain what natural numbers are

Non-negative integers. Natural numbers can be positive integers (1, 2, 3, 4) or non-negative integers (0, 1, 2, 3, 4). 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, three." Instead of starting with "zero, one, two, three." To start, because that'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.

Share. History.

Natural numbers start by counting. The original notation of natural numbers was to represent each object with a symbol, the ancient Babylonian numerals.

For example|||It can be used to represent four apples, or four stones, or four cows. This representation is reflected in the notation of ancient Babylon (c. 2000 BC).

Numbers can be positive integers (1, 2, 3, 4) or negative integers (0, 1, 2, 3, 4). In number theory the former is usually the former, while set theory and computer science are the majority of the latter. One of the reasons to think that numbers don't contain zeros is because we (especially children) start learning numbers by " , three.

In the beginning, it is not made up of "zero, three, three." At first, because that's not always the case.

Numbers usually have two functions: they can be counted (e.g., "there are seven apples"), see cardinal numbers; It can also be sorted (e.g. "This is the third city in the country"), see Ordinal Numbers.

The set of natural numbers is a countable, upper bound set of poor. Mathematicians generally use n to express it. There are additions 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 is also possible to subtract or divide, but the result of subtraction and division may not always be natural numbers, so subtraction and division operations are not always possible in the natural number set.

The number of pieces used to measure things or the order of things. i.e. digital 0, 1, 2, 3, 4 ,......The number represented. The number that represents the number of objects is called a natural number, and the natural number starts from 0 (including 0), one after the other, forming an infinite collective.

Natural numbers are Arabic numerals ranging from 0 to an infinite number.

Like are all natural numbers, and natural numbers are infinite.

Non-decimals, fractions, negative numbers.

Every number is a natural number.

1 to countless are natural trees.

Integers above 0, except for decimal fractions.

1. Natural numbers refer to the number that represents the number of objects, that is, starting from 0, 0, 1, 2, 3, 4, ,......One after the other, forming an infinite collective, i.e., non-negative integers.

2. The set of natural numbers is a set of all non-negative integers, which is often represented by n. There are endless numbers of natural numbers.

3. [Pinyin] zì rán shù

4. [English translation] natural number

5. General concepts.

6. Natural numbers are markers of the common characteristics of all equivalent finite sets.

1. The natural number refers to the number that represents the number of infiltrated bodies, that is, starting from 0, 0, 1, 2, 3, 4, ,......One after the other, forming an infinite collective, i.e., non-negative integers.

2. The set of natural numbers is a set of all non-negative integers, which is often represented by n. There are endless numbers of natural numbers.

3. [Pinyin] zì rán shù

4. [English translation] natural number

5. General concepts.

6. The natural number is the mark of the common feature of all the equivalent clusters of Lingmin.

Natural numbers are used to measure the number of pieces of things or to represent the order of things. i.e. digital 0, 1, 2, 3, 4 ,......The number represented.

The number that represents the number of objects is called a natural number, and the natural number starts from 0 and follows one after the other to form an infinite collective. Natural numbers are orderly, infinite. It is divided into even and odd numbers, composite numbers and prime numbers, etc.

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Natural numbers are a mathematical concept, which refers to a series of positive integers, starting from 1, each number is greater than the previous number by 1, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc. Natural numbers can also be represented by the English letter n, i.e., n=. Natural numbers are the most basic number concepts in mathematics, and they can be used to represent the number of objects, such as 3 apples.

Natural numbers can also be used to represent a period of time, such as 24 hours in a day, which can be expressed by 24. Natural numbers can also be used to represent a range, such as 1 to 100, which can be expressed from 1 to 100.

A natural number is a number of things that are used to measure things or to represent the order of things.

i.e. digital 0, 1, 2, 3, 4 ,......The number represented. Natural numbers start with 0 and follow each other to form an infinite collective. Natural numbers are orderly, infinite.

It is divided into even and odd numbers, composite numbers and prime numbers, etc. A set of natural numbers is a set of all non-negative integers, often denoted by n. There are endless numbers of natural numbers.

Natural numbers are markers of the common characteristics of all equivalent finite sets. The orderliness of natural numbers means that natural numbers can start from 0 and be arranged in a sequence without repeating or omitting: 0, 1, 2, 3, ,...This sequence is called a natural sequence.

A natural number set is an infinite set, and the natural number series can be written endlessly.

Nature of Natural Numbers:

1. Orderliness. The orderliness of natural numbers means that natural numbers can start from 0 and be arranged in a sequence without repeating or omitting: 0, 1, 2, 3, ,...This sequence is called the natural dust answer sequence.

A set of elements is countable if it can establish a one-to-one correspondence with a natural sequence or a part of a natural sequence, otherwise it is said to be uncountable.

2. Infinity. A natural number set is an infinite set, and the natural number series can be written endlessly. Pimin.

For infinite sets, the concept of "number of elements" is no longer applicable, and comparing the number of elements in a set by counting them is only applicable to finite sets. In order to compare the number of elements of two infinite sets, the German mathematician Cantor, the founder of set theory, introduced a one-to-one correspondence method. This approach is obviously applicable to finite sets, and in the 21st century, it has been extended to infinite sets, that is, if there is a one-to-one correspondence between the elements of two infinite sets, the two sets are considered to have the same number of elements.

3. Tri-fidality: For any two natural numbers n1 and n2, there is only one of the following three relations: n1>n2, n1=n2 or n1.

Natural number: The concept of natural number refers to the number of pieces used to measure something or to express the number of parts of a thing. i.e. digital 0, 1, 2, 3, 4 ,......The number represented. Natural numbers start from 0 and follow each other to form an infinite collective.

A natural number is just an integer that is not less than 0 (that is, 0 and a positive integer), so there are an infinite number of natural numbers, which are usually represented by n. The number of natural numbers is unlimited.

Ordinal number theory is the work of the Italian mathematician GPiano brought it up. He summarized the properties of natural numbers and gave the following definition of natural numbers in axiomatic terms:

The set of natural numbers n is the set of the following conditions: n has an element in it, denoted as 1. Each element in n can find an element in n as its successor.

1 is not the successor of any element. Different elements have different successors. (Inductive axioms) any subset of n m, if 1 m, and as long as x is in m it can be deduced that x's successor is also in m, then m = n.

Natural number, i.e. ......

Formula: Number sequence 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ,......n, which is called a natural sequence.

The general formula for natural sequences is an=n.

The first n terms of the natural series and sn=n(n+1) 2. sn=na1+n(n-1)/2

The natural sequence is essentially an equal difference sequence, with the first term a1 = 1 and the tolerance d = 1.