The Evolution of the Number System

The Development of the Number System

1. Evolution of the Number System IMMANUEL JOHN ISAAC X STD A C.S. Academy an adventure through the world of numbers

2. Name: Sample: Approx. first appearance: Babylonian numerals 3100 BC Chinese numerals, Japanese numerals, Korean numerals Unknown Egyptian numerals 3000 BC Roman numerals 1000 BC DIFFERENT TYPES OF NUMERALS

3. Name: Sample: Approx. first appearance: Greek numerals After 100 BC Chinese rod numerals 1st century Hindu-Arabic Numerals 1st century John Napier's Location arithmetic 1617

4. The number system we have today, commonly called Hindu-Arabic Numerals, has evolved so much and come through a long route and mostly from some far away lands, outside of Europe. It came about because human beings wanted to solve problems and mainly, wanted to know the quantity of a particular thing. So they started creating numbers to solve these problems.

5. In Olden Days, The "Counting Numbers" satisfied people for a long time. Counting through fingers

6. The "Counting Numbers" satisfied people for a long time. Counting through Symbols

7. The "Counting Numbers" satisfied people for a long time. Zero Dog(s) Two Dogs Counting through Sticks

8. Though humans have always understood the concept of nothing or having nothing, the concept of zero is relatively new. They wanted to find some number to represent a nil value. So they found 0 to represent a nil value. Some people say that Zero was invented independently by the Babylonians, Mayans and Indians. Discovery of 0

9. Many mathematicians of different era has suggested for symbolizing ‘NOTHING’. Then they introduced the symbol “0” for symbolizing nothing, to the world and made complicated things easier. Indian texts used a Sanskrit word Shunye or shunya to refer to the concept of void. In mathematics texts this word often refers to the number zero . But even now people are not sure whether zero was discovered by A ryabhatta or Brahmagupta , an indian mathematician. Discovery of 0

10. But still it was not easier. So people started to find number systems. NUMBER SYSTEM: A number system is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

11. Natural numbers The natural numbers are those used for counting and ordering. Natural numbers are represented by ℕ. Example: 1, 2, 3, 4, 5, 6, 7

12. Whole numbers Whole number is collection of positive numbers and zero . Example: 0, 1, 2, 3, 4, 5, 6, 7

13. Integers An integer is a number that can be written without a fractional component. Integers are represented by ℤ, standing for the German word Zahlen. Example: 21, -4, are integers, while 9.75, 5½, and √2 are not.

14. Rational numbers: A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q ≠0. Since q may be equal to 1, every integer is a rational number. Rational numbers are represented by ℚ. It was thus denoted in 1895 by Peano . Example: ⅛, ⅔.

15. Irrational numbers: An irrational number is any number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals. Example: √5, √3, √6.

16. Real numbers: A real number is a number which includes natural, whole, integers, rational and irrational numbers. Real numbers are represented by . Example: 1, -4, ⅔, √3.

17. Imaginary numbers: An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i , which is defined by its property i 2 = −1. The square of an imaginary number bi is −b 2 . Example: 5i is an imaginary number, and its square is −25.

18. Complex numbers: A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation x 2 = −1, that is, i 2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers are represented by ℂ.