Let's give a quick review of all the subsets that combine to be the real numbers.
Natural numbers: Those which are used for counting, {1,2,3, ... }.
Whole numbers: The set of Natural numbers as well as the number 0, this is { 0,1,2,3,... }.
Integer numbers: The set of Whole numbers and the opposites of the Natural numbers, { ... -2, -1, 0, 1, 2 ... }.
Rational numbers: All numbers that can be written in the form ab where a and b are integers and b ≠0. Notice that this set includes Natural, Whole, and Integer numbers as subsets.
Irrational numbers: These are all the numbers that cannot be written in the form ab.
Looking at their definitions, we can notice that Rational and Irrational numbers are disjoint sets. This means that they have no common elements. At the same time, all the rest of subsets composing the Real Numbers, are subsets of the Rational Numbers. Therefore, by combining the Rational and Irrational numbers, we obtain the Real numbers. The diagram below helps to illustrate this idea.
