**1.1. The Real Number System**

A **number** means something you can count, just like counting the number of coins one has or the number of students in a class. These are *natural numbers* which are normally used for counting and sometimes called *counting numbers *

**1.1.1. Natural Numbers**

Natural numbers start from 1 to infinity ∞. Natural numbers are numbers you will use when counting things. For instance if you have to count the number of Oranges, you will start from 1.

Natural Numbers (N) 1,2,3,4,5,6,7,8,9,10,11,…………

**1.1.2. Whole Numbers**

Whole numbers start from 0 to infinity ∞. Whole numbers are Natural Numbers together with a zero.

Whole Number ( N0 ): 0,1,2,3,4,5,6,7,8,….

**1.1.3. Integers **

Integers are Whole Numbers plus negatives.

Integers (Z): …-4,-3,-2,-1,0,1,2,3,4,…

**1.1.4. Rational Numbers**

Rational Numbers are all numbers of the form *a/b*, where both *a* and *b* are integers. *b* cannot be zero. Rational numbers include fractions.

Fractions can be numbers which are smaller than 1, i.e 1/2 ; 1/4 and 4/7. These are called *proper fractions. *Fractions can also be numbers bigger than 1 and they are called *improper fractions*), i.e. 4/2 ; 5/3 ; 7/2.

**1.1.5. Irrational Numbers**

Irrational Numbers cannot be expressed as ratio of integers. As decimals they never repeat or terminate.

**1.1.6. The Real Numbers**

The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.

**1.1.7. Non Real Numbers ( Imaginary Numbers)**

Not all numbers are real numbers. For instance all square roots of the negative numbers are imaginary numbers or non real numbers. For example √-2 , √-4, √-1 and √-22.