Classification of Numbers in Mathmatics

Classification of Numbers:

To classify the various kinds of numbers  that we deal in algebra. The counting numbers or natural numbers are the numbers,

i.e  N={1,2,3,4,…}. The three dots, called an ellipsis, indicates the pattern continues indefinitely. As their name implies, these numbers

Often used to count things. For example, there are 26 alphabet; there are 100 cents in a dollar. The whole numbers are the numbers

i.e W={0,1,2,3,4,5,…}. The whole numbers  are also counting numbers with 0. The integers are the numbers

i.e Z={ …,-3,-2,- 1,0,1,2,3,… }. These numbers are very useful. These numbers are used in many situations. E.g if your checking

account has $10 in it and you write a check for $15, you can represent the current balance as -$5.

It must notice that the counting numbers are included among the whole numbers . Every time we expand a number system. Such as

From the whole numbers to the integers, we do so in order to be able to handle new, and usually more complicated problems. Thus

The integers allow us to solve problems requiring both positive and negative counting numbers, such as profit /loss, height

above/below sea level, temperature above/below 0°F, and so on. But integers alone are not sufficient for all

problems. What part of a dollar is 38 cents? Or what part of pound is 5 ounces? We are unable to give answer by using integers  .

To answer these type of questions we enlarge number system to include rational numbers. For example 38/100 answers the

question  “ what part of a dollar is 38 cents?”  and 5/16 answers the question “what part of a pound is 5 ounces?.”

RATIONAL NUMBER:

Rational number is a number that can b expressed as a quotient a/b of two integers, The integer  “a” is called the

numerator, and the integer “b” is called “ denominator” it can not be zero ( 0 ).

Examples of rational numbers are following.        3/4, 5/2, 0/6, - 2/3   etc. since a/1 = a for any integer a., it allows rational numbers contain the integers

Special case .

Sher Afzal Ranais

Author & Editor

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