# 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.

**Explanation:**

The set of real numbers, which is denoted by R, is the union of the set of rational numbers (Q) and the set of irrational numbers (Q').

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.

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