1.1 Revision

The concept of a set is fundamental in all branches of mathematics. Recall that a set is a well defined collection of distinct objects which are called its elements. The sets are usually denoted by A, B, C , . . . X, Y, Z and the elements by a, b, c, . . x, y, z. If a is an element of a set A, we write a ∈ A and read "a belongs to set A" and if a is not an element of a set A, we write a ∉ A and read "a does not belong to set A".

1.2 Some Important Sets of Numbers

Following notations will be used for sets of numbers:

Set of Natural Numbers : N = {1, 2, 3, . . .}

Set of Whole Numbers : W = {0, 1, 2, 3, . . .}

Set of Integers : Z = {0, ±1, ±2, ±3, . . }

Set of Positive Prime Numbers : P = {2, 3, 5, 7, 11, . . . }

Set of Odd Numbers : O = {±1, ±3, ±5, . . . .}

Set of Even Numbers : E = {0, ±2, ±4, ±6, . . . .}

Set of Rational Numbers : Q = {x|x = p/q ; p, q ∈ Z, q ≠ 0}

Set of Irrational Numbers : Q' = {x|x ≠ p/q ; p, q ∈ Z, q ≠ 0}

Set of Real Numbers : R = Q U Q'

Also, Z⁺ and Z^¯ will, respectively, denote the set of all positive and negative integers. Likewise R⁺ and R¯ will denote the set of all positive and negative real numbers, respectively.