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Number system, natural numbers to real numbers

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a short story discribing number system from natural numbers to real numbers

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Number system, natural numbers to real numbers

1. 1. In ancient times, early man use to keep animals…
2. 2. He faced many problems regarding the taking care of them…
3. 3. As GOD has given him Brain to utilize it, so He found a way of keeping an eye on his animals…
4. 4. Every night, he used to keep a stone with him , correspondence to one animal…
5. 5. 2 stones for 2 animals… 3 stones for three animals…
6. 6. AND SO ON…
7. 7. This one to one correspondence gave birth to many mathematical symbols. Some of these symbols are now called as NUMBERS.
8. 8. These numbers/symbols, are collectively called counting numbers. And mathematically they are called Natural Numbers.
9. 9. The collection of numbers 1,2,3,4,5… is called as the set of NATURAL NUMBERS, as these numbers are used naturally for counting… The symbol used for natural numbers is
10. 10. People from different localities and different countries used different symbols to denote the numbers…
11. 11. MORE TO KNOW
12. 12. MORE NUMBER SYSTEMS
13. 13. Babylonian numerals were written in CUNEIFORM, using a wedge-tipped REED STYLUS to make a mark on a soft CLAY tablet which would be exposed in the SUN to harden to create a permanent record.
14. 14. This system first appeared around 3100 BC. It is also credited as being the first known POSITIONAL NUMERAL SYSTEM, in which the value of a particular digit depends both on the digit itself and its position within the number
15. 15. Human’s need for numbers seems to be fulfilled here…
16. 16. BUT its just the beginning… His Need doesn't end. NEED is the MOTHER of INVENTIONS and DISCOVERIES
17. 17. One morning, he found no animal in the shed… He was amazed to see the empty shed…
18. 18. Suddenly a question came into his mind… No animal = no stone No stone = what symbol?
19. 19. Here he realized the need for “symbolizing NOTHING” for the first time… NO ANIMALS
20. 20. Many mathematicians of different era has suggested for symbolizing nothing but ARYABHATTA, The INDIAN Mathematician was the first who Introduced the Symbol “0” for symbolizing nothing, to the world and made complicated things easier.
21. 21. By the 9th century AD, The number system consists of one more member namely “0”… The set of numbers 0,1,2,3,4,5… is called as the set of WHOLE NUMBERS. Is used for representing the set of whole numbers
22. 22. But HUMAN NEEDS DOESN’T FULFILLED HERE. AS FAR AS THE HE DEVELOPED THE SENSE OF TRADE, HE FOUND SOME OR THE OTHER WAYS OF EXCHANGE OF GOODS AND SERVICES.ONE OF THE WAY HE ADOPTED IS THE BARTER SYSTEM
23. 23. The history of bartering dates all the way back to 6000 BC. Introduced by Mesopotamia tribes, bartering was adopted by Phoenicians. Phoenicians bartered goods to those located in various other cities across oceans. Babylonian's also developed an improved bartering system. Goods were exchanged for food, tea, weapons, and spices. At times, human skulls were used as well. Salt was another popular item exchanged. Salt was so valuable that Roman soldiers' salaries were paid with it. In the Middle Ages, Europeans traveled around the globe to barter crafts and furs in exchange for silks and perfumes. Colonial Americans exchanged musket balls, deer skins, and wheat. When money was invented, bartering did not end, it become more organized.
24. 24. Due to lack of money, bartering became popular in the 1930s during the Great Depression. It was used to obtain food and various other services. It was done through groups or between people who acted similar to banks. If any items were sold, the owner would receive credit (borrow) and the buyer's account would be debited (lending). INFACT MONEY WASN’T ENOUGH
25. 25. This system of credits and debits introduced the concept of borrowing in trade. If I have nothing and I am borrowing money from someone, it means I have a negative balance. And, if I have a lot and someone else is borrowing from me, I have positive balance…
26. 26. The positives and negatives in mathematics refer to positive numbers and negative numbers. These numbers are symbolized as …-4,-3,-2,-1 etc.
27. 27. The collection of natural numbers, zero and natural numbers with –ve sign (called as negative numbers) is defined as the set of integers… This symbol used for the set of integers…
28. 28. With the flow of time, the social relationships of people improved. People started sharing goods with each other. This sharing habit raise a question in mathematics.
29. 29. Once, a boy was eating an apple. He gave a part of the apple to his sister.  How much apple has he eaten? And how much part his sister received?
30. 30. Note that, part of the whole is called as FRACTION. Thus, the sister had a fraction of the Apple and the boy also had another fraction of the same Apple… Sister’s portion Boy’s portion
31. 31. = ?
32. 32. =? =?
33. 33. The number written at the above part of the fraction is called as NUMERATOR and the number written below the bar is called as DENOMINATOR. NUMERATOR DENOMINATOR
34. 34. … -327, -243, -137, -91, -86, -44, -30, -23, -5, -4, 0, 2,10, 34, 62, 97, 129, 294,892… A handful of integers are written in the box above. Let us choose any two of them and write them in the form of a fraction… Eg: __ __ , etc…
35. 35. A fraction in which numerator and denominator are chosen from the set of integers, denominator non zero, is called a RATIONAL NUMBER… And, the collection of all such rational numbers is called as the set of RATIONAL NUMBERS.
36. 36. We observe that any number can also be written in the form of a decimal number. Further, A decimal number can be categorized as follows… DECIMAL NUMBERS TERMINATING NON-TERMINATING RECURRING DECIMALS NON- RECURRING DECIMALS
37. 37. TERMINATING Eg: 4.5, 3.0, 22.75, 984.60, 2019.25 etc… A number whose decimal representation terminates. NON-TERMINATING A number whose decimal representation does not terminates… Eg: 7.333…, 6.494949…, 87.126126…, 3.142345667543277889665430045664… 78.909090…, 79.12356635679879… etc 3.142345667543277889665430045664…, 79.12356635679879… 7.333…, 6.494949…, 87.126126…,78.909090… RECURRING NON-RECURRING
38. 38. DECIMAL NUMBERS TERMINATING NON-TERMINATING RECURRING DECIMALS NON- RECURRING DECIMALS Terminating decimals and non-terminating recurring decimals together called as RATIONAL NUMBERS. And Non-Terminating Non-Repeating decimals are called IRRATIONAL NUMBERS.
39. 39. RATIONA L NUMBERS (Q) IRRATION AL NUMBERS (QC ) REAL NUMBERS (R) ALTOGETHER
40. 40. PREPARED BY : RICHA BHARDWAJ