First, all natural numbers are integers.

1, the definition of natural number and integer

Natural numbers refer to positive integers, including infinite acyclic numbers such as 1, 2 and 3. Integers include positive integers, negative integers and 0. Therefore, all natural numbers are integers.

2. The connection between natural numbers and integers

There is a close relationship between natural numbers and integers. Natural numbers are part of integers, because integers include all rational numbers and irrational numbers, and natural numbers are part of rational numbers. Therefore, all natural numbers are integers.

Second, the application of natural numbers and integers

1, mathematics field

In the field of mathematics, natural numbers and integers are widely used. Natural numbers are the basis of mathematics and one of the most basic elements in mathematics. Integer plays an important role in mathematics and is widely used in algebra, geometry and other fields.

2. Natural science field

Natural numbers and integers also play an important role in the field of natural science. Natural numbers are indispensable elements in physics, chemistry, biology and other disciplines. Integers are widely used in the fields of quantum mechanics and electromagnetism in physics.

Properties of natural numbers and integers

First, the nature of natural numbers.

1, countability: natural numbers are countable, that is, poor, and can be enumerated one by one.

2. Infinity: The natural number is infinite, with no end, and it can be listed all the time.

3. Continuity: natural numbers are continuous without interruption, such as 1, 2, 3, 4 … are all continuous natural numbers.

4. Discretization: Natural numbers are discrete, that is, there are no overlapping parts. For example, 1, 3, 5, 7 ... are discrete natural numbers.

Second, the nature of integers

1, countability: integers are countable, that is, poor, and can be enumerated one by one.

2. Infinity: Integer is infinite, with no end, and it can be listed all the time.

3. additivity: the addition of integers satisfies the closure, that is, the result of the addition of two integers is still an integer.

4. Multiplication: Integer multiplication satisfies closure, that is, the result of multiplication of two integers is still an integer.

5. Orderliness: Integers can be compared according to their size and satisfy transitivity, antisymmetry and completeness.