What is the measurement of natural numbers, and what is the counting method of natural numbers

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 using axiomatic methods).

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 the successor to 0. 0 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.

Cardinality theory defines natural numbers as the cardinality of finite sets, and this theory proposes that two finite sets that can establish a one-to-one correspondence between elements have a common quantitative characteristic, which is called cardinality. In this way, all single-element sets {x}, {y}, {a}, {b}, etc., have the same cardinality, denoted as 1. Similarly, any set that can be set up with two fingers has the same cardinality, denoted as 2, and so on.

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

Natural numbers play a big role in daily life, and people use them extensively. Natural numbers are the earliest numbers in human history, and natural numbers have a wide range of applications in counting and measurement. People also often use natural numbers to number or order things, such as city bus routes, house numbers, zip codes, etc.

Natural numbers are integers (natural numbers include positive integers and zeros), but integers are not all natural, for example: -1 -2 -3....It's an integer and not a natural number. Natural numbers are infinite.

The set of all non-negative integers is called a set of non-negative integers (i.e., a set of natural numbers).

When counting objects, the number that is counted is called a natural number. Natural numbers have two meanings: quantity and order, and are divided into cardinal numbers and ordinal numbers. Basic unit: 1 Counting unit: one, ten, hundred, thousand, thousand, ......

In short, a natural number is an integer greater than or equal to 0.

The counting method of natural numbers is decimal notation.

Decimal notation is a rate of ten between every two adjacent units of counting. The decimal system is an outstanding creation of the Chinese people and is of great significance in the history of mathematics in the world.

The counting method of natural numbers is decimal notation. If the digit is full of 10, it will be 1, and if it is a digit full of 10, it will be 1 to the 10th digit, which is called "decimal notation".

Any natural number can be expressed as an·10n+an-1·10n-1+......A1·10+A0. 10 is called the carry base a0, a1,..., an is 1,2 ,..., 9, 0, one of the 10 numbers.

Nature of Natural Numbers:

1. Transitivity: Let n1, n2, and n3 all be natural numbers, if n1> n2, n2> n3, then n1>n3.

2. Trimisformity: For any two natural numbers n1 and n2, there is only one of the following three relations: n1> n2, n1=n2 or n1

3. The principle of minimum numbers: there must be a minimum number in any non-empty subset of a set of natural numbers. A set of numbers with properties is called a linear order set. It is easy to see that the set of rational numbers and the set of real numbers are linear order sets.

But neither of these sets of numbers has the property 5, for example, the set of all numbers of the form nm (m>n, m, n are natural numbers) is a nonempty subset of the set of rational numbers, and this set does not have a minimum number; The open interval (0,1) is a non-empty subset of the set of real numbers, and it also does not have a minimum number.

The counting method of natural numbers is decimal notation.

Decimal notation is relative to binary notation, is the most used counting method (commonly known as "every decimal one"), its fixed return marketing meaning is: "every two adjacent counting single band between the rate of ten is ten", which digit is full of 10 into 1, if it is a full 10 to the ten digit into 1 is called "decimal notation".