What are Real numbers?

All numbers that can be expressed as the limit of a sequence of rational numbers. Every real number corresponds to a point on the number line.

all rational and irrational numbers are real numbers. i.e R=QUQ'

In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction4/3, and all the irrational numbers such as √2 (1.…, the square root of two, an irrational algebraic number) and π (3.…, a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced.