The collection of all rational and irrational numbers, represented by the letter R, is known as a real number. A real number can therefore be either rational or irrational.
The set of natural numbers N = {1, 2, 3, 4, 5, . . .}
The set of integers Z = {. . ., –3, –2, –1, 0, 1, 2, 3, . . .}
The set of rational numbers Q = {x: x = a/b; a, b ∈ Z and b ≠ 0}
The set of irrational numbers, denoted by T, is composed of all other real numbers.
Thus, T = {x : x ∈ R and x ∉ Q}, i.e., all real numbers that are not rational.
Some of the irrational numbers include √2, √3, √5, and π, etc.
Some of the apparent relations among these subsets are:
N ⊂ Z ⊂ Q, Q ⊂ R, T ⊂ R, N ⊄ T.
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