What is the set of all numbers, including all rational and irrational numbers?
We will use the definition of real numbers to answer this question.
Answer: Real number is the set of all numbers, including all rational and irrational numbers.
Any number that we can think of, except complex numbers, is a real number.
So, we can write the set of real numbers as, R = Q ∪ Q'. This indicates that real numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
For example, 3, 0, 1.5, 3/2, ⎷5, and so on.
The numbers that are neither rational nor irrational are not real numbers, like, ⎷-1, 2+3i, and -i. These numbers include in the set of complex numbers.
Therefore, the set of rational numbers and irrational numbers is contained in the set of real numbers.