Rational number:
Rational number is the collective name of integer (positive integer, 0, negative integer) and fraction, and it is the set of integer and fraction. Integers can also be regarded as fractions with a denominator of 1 Real numbers that are not rational numbers are called irrational numbers, that is, the fractional part of irrational numbers is infinite cyclic numbers. It is one of the important contents in the field of number and algebra.
Real number:
Is the floorboard of rational numbers and irrational numbers. Mathematically, real number is defined as the real number on the sum axis, which is a general term for rational number and irrational number. Mathematically, a real number is defined as the number corresponding to a point on the number axis. Real numbers can be intuitively regarded as one-to-one correspondence between finite decimals and infinite decimals, and between real numbers and points on the number axis.
Natural number:
A number 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, one by one, forming an infinite group. Natural numbers are ordered and infinite. Divided into even and odd numbers, composite numbers and prime numbers.
Positive integer:
Like an integer, a positive integer is a countable infinite set. In number theory, positive integers, namely 1, 2, 3 ...; But in set theory and computer science, natural numbers usually refer to non-negative integers, that is, the set of positive integers and 0.
Integer:
All integers form an integer set, which is a number ring.
Orderliness:
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, which 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.
Infinite:
Natural number set is an infinite set, and the sequence of natural numbers can be written endlessly. For infinite sets, the concept of the number of elements is no longer applicable, and comparing the number of elements in a set by numbers is only applicable to finite sets.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.