What Is a Natural Number?

Natural number refers to the number of things used to measure things or the number that represents the order of things. That is, the numbers represented by the numbers 0, 1, 2, 3, 4 ... Natural numbers start with 0, one after the other, forming an infinite collective. Natural numbers are ordered and infinite. Divided into even and odd numbers, composite and prime numbers.

Natural numbers refer to the number of objects, that is, starting from 0, 0, 1, 2,

Natural number set is the whole

Natural numbers are everything equivalent

This proposition is called Piano's Axiom of Arithmetic, which declares the set of natural numbers

Existence.

Among them, the injectable stated in Article 2

Called Successor Mapping is what we are used to in life. "

".

The third one claims that the existence of a number is the starting point of a natural number, it is not a successor to any number.

The fourth is the well-known inductive hypothesis, which makes the establishment of mathematical induction in natural number sets, and is also a limitation on the form of natural number sets. Because even a finite set, there exists a ring map that satisfies the second item (self-injective), any infinite set satisfies the second and third items, and only a natural number set can satisfy all the four items.

From Article 4, we can use mathematical induction:

To prove propositions related to natural number sets.

1.Can define natural numbers

1. Natural numbers are the most widely used in "number series", because in all numbers, the serial numbers of the items form a natural number series.

The general formula of any series can be regarded as: a fixed quantitative relationship between the number of each item in the series and its serial number.

2. To find out how many angles can be formed by n rays, the first n terms and formula of natural number series are applied

The first ray and other rays form (n-1) angles, the second ray and other remaining rays form (n-2) angles, and so on to obtain the formula

1 + 2 + 3 + 4 + + n-1 = n n-1 / 2

3. When finding n points on a straight line, how many line segments are formed, the first n terms and formulas of the natural number series are also applied.

The first point and other points form (n-1) line segments, the second point and the remaining points form (n-2) line segments, and so on.

1 + 2 + 3 + 4 + + n-1 = n n-1 / 2

Any natural number can be substituted into the following formula, and the equation always holds: