In mathematics, r stands for a set of real numbers. Because the English word of real number is real number, the set of real numbers is represented by R; Real numbers can be intuitively regarded as a one-to-one correspondence between finite decimals and infinite decimals, and between real numbers and points on the number axis, but the whole of real numbers can not be described only by enumeration.

A real number set is a set that contains all rational numbers and irrational numbers, and is usually represented by the capital letter R.

Addition theorem of r set;

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).

Multiplication theorem of r set;

1. For any element A and B belonging to the set R, you can define their products A and B, and A and B belong to R. ..

2. The constant of multiplication is 1, and a is 1 = 1 A = A (so there is a reciprocal besides 0).

3. Multiplication has a commutative law, a b = b a ..

4. Multiplication has an associative law, (a b) c = a (b c).

5. Multiplication has a distribution ratio to addition, that is, A (B+C) = (B+C) A = AB+A C.