What term describes the set that includes both rational and irrational numbers?

The term that describes the set that includes both rational and irrational numbers is "Real numbers."

Real numbers encompass a broad spectrum of numbers, which includes all the numbers that can be found on the number line. This includes rational numbers, which are those that can be expressed as the quotient of two integers (like 1/2 or -3), and irrational numbers, which cannot be expressed as a simple fraction and have non-repeating, non-terminating decimals (such as the square root of 2 or pi).

By contrast, integer numbers are a subset of real numbers that include all whole numbers, both positive and negative, but do not include fractions or decimal values. Whole numbers are even more restricted, consisting only of non-negative integers (0, 1, 2, ...). Complex numbers, on the other hand, include real numbers and imaginary numbers and are used in advanced mathematics, but they do not solely define the set of numbers that includes both rational and irrational elements. Therefore, the term "Real numbers" is the comprehensive category that accurately captures the entire set being referenced.