Number System - Basics 1

Tuesday, April 25, 2006

Prehistoric men didn't had any method to count quantities, as someone said "Necessity is Mother of invention", holds true for this, they slowly evolved a method with which one can distinguish between quantities, count them, but not limited only to these. The earliest number system known in use was somewhere around 30,000 BC, used by Stone age people as Tally marks.

The system was limiting, large numbers cannot be represented, then evolved Roman Number system, which also had limiting factors, zero was known but didn't have any existence.

Finally the evolution of Number system which we are using today, the Numerals from 0 - 9 of base 10, evolved. Life became easy and peaceful. This evolution was not an easy one, each species of human being from every corner of the world has contributed in every stage, in every level, the Greeks, the Indians, the Egyptians and many others.

Classification of Numbers:
1) Natural Numbers: All the positive numbers from 1 to infinity. {1, 2, 3, ...}

2) Whole Numbers: All the natural numbers with an introduction of 0. {0, 1, 2, ...}

3) Integers: Numbers including whole numbers and negative numbers. {..., -2, -1, 0, 1, 2, ...}

4) Rational Numbers: A number which can be expressed as a fraction p/q where q <> 0 (not equal / non-zero) and the number is terminating or recurring(periodic). {5/2 = 2.5}

5) Irrational Numbers: A number which cannot be expressed as a fraction p/q where q<> 0, irrational numbers have decimal expansions which are not terminating nor periodic. 2^1/2 (root 2)

6) Real Numbers: All the above numbers collectively known as real numbers. These numbers can be plotted on a number line.

7) Imaginary Numbers: Some numbers cannot be expressed such as square root of a negative number -1^1/2. Imaginary number is denoted by i. In other words those are not real numbers. {i = -1^1/2}

8) Complex Numbers: A combination of real numbers and imaginary numbers is known as complex number. {5 + 2i}

*TIP: Don't expect a direct question like, "Is the following number a rational or irrational number". CAT doesn't ask such silly questions. But the understanding of the above is crucial, questions will contain terms like rational number, real number, integer, which you need to consider while marking your answers.