Natural numbers are numbers used to measure the number of things or to indicate the order of things. That is, the numbers represented by the numbers 0, 1, 2, 3, 4, ... representing the number of objects are called natural numbers, and natural numbers start from 0 and form an infinite group one by one. Natural numbers have the properties of beginning, order and infinity. Divided into even and odd numbers, composite numbers and prime numbers.
Natural numbers are what we often call positive integers and 0, and integers contain natural numbers, so natural numbers must be integers and non-negative integers. Natural numbers are integers, but not all integers are natural numbers. For example,-1, -2, -3 are integers instead of natural numbers, and natural numbers are infinite.
Properties of natural numbers
1, orderly
The orderliness of natural numbers means that natural numbers can be arranged into a series starting from 0 without repetition or omission: 0, 1, 2, 3, … This series is called natural number series. If the elements of a set can establish a one-to-one correspondence with a natural sequence or a part of a natural sequence, we say that the set is countable, otherwise it is uncountable.
2. infinity
Natural number set is an infinite set, and the sequence of natural numbers can be written endlessly. For infinite sets, the concept of "number of elements" is no longer applicable, and comparing the number of elements in a set by counting is only applicable to finite sets. In order to compare the number of elements in two infinite sets, the German mathematician Cantor, the founder of set theory, introduced a one-to-one correspondence method.
3. Transferability
Let n 1, n2 and n3 all be natural numbers, if n1>; N2, n2 & gtN3, then n1>; n3 .