Mathematically, a value is a quantity, and a number is an abstract concept, which is used for counting, marking or measuring.

2. Different roles:

A numerical value is how much a quantity is represented by a number, which is called the numerical value of this quantity. For example, "3" of "3 grams" means a certain value only if the number is written on the number of digits.

Number is a simple symbolic record form (or measure) of the level of things with the same quality or property. A series of symbols representing numbers, including numbers and operation symbols, are collectively called the numeration system. In mathematics, the definition of number is extended to include abstract concepts such as fraction, negative number, irrational number, transcendental number and complex number.

At first, people only thought that the number of a certain part was a number, but later, with the need, the concept of number gradually expanded; For example, Pythagoras believed that numbers must be represented by the ratio of integers to integers. Later, it was found that irrational numbers could not be expressed in this way, which caused the first mathematical crisis. However, people gradually accepted the existence of irrational numbers and expanded the concept of numbers.

Extended data:

Natural numbers play a great role in daily life, and people use them widely. Natural numbers are the earliest numbers in human history, which are widely used in counting and measurement. People often use natural numbers to mark or classify things, such as bus routes, house numbers, postal codes, etc.

Whether "0" is included in natural numbers is controversial. Some people think that natural numbers are positive integers, that is, counting from 1; Others think that natural numbers are non-negative integers, that is, counting from 0. There is no consensus on this issue. However, in number theory, the former is often used; In set theory, the latter is often used. The textbooks of primary and secondary schools in China classify 0 as a natural number.

Natural numbers are integers, but integers are not all natural numbers.

For example,-1, -2, -3, ... are integers, not natural numbers.

In short, natural numbers are integers greater than or equal to 0.

The set of all nonnegative integers is called the nonnegative integer set (i.e. natural number set).