1, rational number refers to a number that can be expressed as the ratio of two integers, where the denominator is not zero. For example, 1/2, -3/4 and 5/6 are all rational numbers. The mathematical set of q includes all rational numbers, which can be expressed as q={a/b|a, b∈Z, b≠0}, where z stands for integer set.
2. Rational number is one of the basic concepts in mathematics, and it is also widely used in real life. For example, rational numbers can be used to represent fractions, ratios, percentages, etc. It is one of the important tools in mathematics. In the fields of science and engineering, rational numbers are also widely used.
3. the set of rational numbers, that is, the set composed of all rational numbers, is represented by the bold letter q. Rational number set is a subset of real number set, and it is an infinite set with a hole, and there is no maximum and minimum. A set of rational numbers is a field, that is, four operations can be performed in it (except that 0 is a divisor). For these operations, the following algorithms hold (a, b, c, etc. All represent arbitrary rational numbers).
4. The interior of the rational number set is an empty set, which is equivalent to that the rational number set has no interior point. The definition of the interior point is as follows: for the element Q in the set Q, if there is a neighborhood U(q) that makes this neighborhood completely contained in the set Q, then Q is called the interior point of Q, that is, all points in this neighborhood belong to the set Q.
The difference between irrational numbers and rational numbers
1, the concept is different: rational numbers are collectively called integers and fractions, positive integers and fractions are collectively called positive rational numbers, and negative integers and fractions are collectively called negative rational numbers. So the number set of rational numbers can be divided into positive rational numbers, negative rational numbers and zero. Irrational number, also known as infinite acyclic decimal. Simply put, an irrational number is an infinite cyclic decimal with 10 as the base, such as pi and root number 2.
2. Different nature: the nature of rational number is the ratio of integer A to integer B, for example, 3 to 8, usually the ratio of A to B. The essence of irrational number is a number composed of integer ratio or fraction.
3. Different ranges: Rational number set is an extension of integer set. In the set of rational numbers, four operations can be performed: addition, subtraction, multiplication and division. Irrational number refers to a number that cannot be expressed as the ratio of two integers within the real number range.