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.
Extended data:
First, the addition theorem
1. For any element A and B belonging to the set R, their addition a+b can be defined, and a+b belongs to R. ..
2. Addition has a constant of 0, a+0=0+a=a (so there is a reciprocal).
3. Addition has commutative law, A+B = B+A. ..
4. Addition has an associative law, (a+b)+c=a+(b+c).
Second, the completeness theorem
1. Any set that is not empty and has an upper bound (included in R) must have an upper supremum.
2. 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 satisfies the axioms of addition, multiplication, completeness and order is called a real number set, and the elements of a real number set are called real numbers.
Baidu encyclopedia-real number set
Baidu encyclopedia -R