What is the union of the set of irrational numbers and the set of rational numbers called?

The union of the set of irrational numbers and the set of rational numbers is known as the set of real numbers. This is because the real numbers include all numbers that can be found on the number line, encompassing both rational numbers (which can be expressed as fractions of integers, such as 1/2, -3, or 5) and irrational numbers (which cannot be expressed as exact fractions, such as the square root of 2 or π).

Rational numbers and irrational numbers together form the complete set of numbers used in typical mathematical calculations and representations of continuous quantities. Therefore, the term "real numbers" effectively captures this entire range of numeric values.

The other options reflect different subsets of numbers. Natural numbers refer specifically to positive integers starting from 1, and whole numbers include 0 and all natural numbers. Imaginary numbers represent a different realm of numbers involving the square root of negative one, which do not interact with the concept of rational and irrational numbers in the context of describing the overall number system.