### Mathematics for Class 9 and 10

**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.