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Allen TALLENTEX 2018 (Class 5 to 11) |

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**NATURAL NUMBERS**

The numbers 1, 2, 3, 4…. Are called natural numbers, their set is denoted by N. Thus N* = *{1, 2, 3, 4, 5….}

**WHOLE NUMBERS**

The numbers 0, 1, 2, 3, 4…… Are called whole numbers, their set is denoted by W.

Thus W = {0, 1, 2, 3, 4….}

**INTEGERS**

The numbers …– 3, –2, –1, 0, 1, 2, 3….are called integers and their set is denoted by I & Z

- Set of positive integers denoted by I
and consists of {1, 2, 3…}, also known as set of natural numbers.^{+} - Set of negative integers denoted by I
and consists of {…– 3, – 2, – 1}^{–} - Set of non-negative integers is {0,1,2, 3…} also known as set of whole numbers
- Set of non-positive integers is {…– 3, – 2, – 1, 0}

**RATIONAL NUMBERS**

All numbers of the form p/q where p and q are integer and q ¹ 0, are called rational. Thus

it may be noted that every integer is a rational number it can be written as p/1. Examples are 1/3, – 4/9 and 57

The rational numbers are precisely the real numbers with decimal expansions that are either

- Terminating (ending in an infinite string of zeros), for example 3/4
*=*.75000…*=*.75

**or** - Non- Terminating Repeating (ending with a block of digits that repeats over and over).

For example 23/11 *= *2.090909… *= *2.09. The bar indicates the block of repeating digits.

**IRRATIONAL NUMBERS**

Real numbers that are not rational are called irrational numbers. They are precisely the real numbers with decimal expansions that are non-terminating non-repeating. Their set is denoted by Q^{c} (i.e. complementary set of Q)

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