In a word, R\Q stands for irrational number set.
Generally speaking, a real number set is a set that usually contains all rational numbers and irrational numbers, and is usually represented by the capital letter R. In the18th century, calculus was developed on the basis of real numbers. But the real number set at that time was not precisely defined. It was not until 187 1 that German mathematician Cantor put forward the strict definition of real numbers for the first time. Any set that is not empty and has an upper bound (included in R) must have an upper supremum.
The set of rational numbers, that is, the set of all rational numbers, is represented by the bold letter Q, and the set of rational numbers is a subset of the set of real numbers. The set of rational numbers is an infinite set with no maximum and minimum.
Extended data:
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. Represents any rational number):
1, the commutative law of addition: a+b = b+a.
2. The associative law of addition: A+(B+C) = (A+B)+C.
3. There is an addition unit of 0, so 0+a = a+0 = a..
4. For any rational number A, there is an addition inverse element, which is recorded as -a, so that a+(-a)=(-a)+a=0.
5. The commutative law of multiplication: ab=ba
6. Multiplicative associative law; ABC
7. Distribution law of multiplication: a(b+c)=ab+ac.
8. The unit of multiplication is 1, so for any rational number A, there is1× a = a×1= a.
9. For rational number A which is not 0, there is a multiplication inverse 1/a, so1/a× a = a×1/a =1.
0a=0 Description: A number multiplied by 0 equals 0.
Any set that is not empty and has an upper bound (included in R) must have an upper supremum.
Let A and B be two sets contained in R. For any X belonging to A and Y belonging to B, there is X.
Any set that conforms to the above four axioms is called a real number set, and the elements of a real number set are called real numbers.
References:
Baidu encyclopedia-rational number set
References:
Baidu encyclopedia-real number set