NUMBER SYSTEM( संख्या पद्धति)

                        NUMBER SYSTEM                          

What is Number (संख्या क्या होती है:)  .   

संख्या एक अंकगणितीय मान है जिसका उपयोग किसी वस्तु की मात्रा को दर्शाने के लिए किया जाता है। 

हम अपने दैनिक जीवन में संख्याओं का उपयोग कर रहे हैं, जैसे कि पैसा, समय, चीजें इत्यादि गिनना। 

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कुल अंकों की संख्या= 10.     ( 0,1,2,3,4,5,6,7,8,9)

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गणित की सभी संख्याएँ इन्ही अंकों के उपयोग से बनाई जाती हैं

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1• Natural Numbers/Counting Numbers( प्राकृतिक संख्या):  

 Numbers that start with 1,2,3……so on are called Natural Numbers. Zero, negative numbers, and decimals are not counted as natural numbers. 

N={ 1,2,3,4..............}

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2.Odd Numbers( विषम संख्याएं):  Those numbers that are not completely divisible by 2. 

{1,3,5,7,9,11,..........}

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3. Even Numbers( सम संख्याएं):  Those numbers that are completely divisible by 2. 

{2,4,6,8,10,...........}

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4.Prime Numbers (अभाज्य संख्याएं):

The numbers which have only two factors, one and the number itself, are called prime numbers.

(ऐसा नंबर जिसके केवल दो गुणनखंड होते हैं न दों से कम न दो से ज्यादा.)

For example:{ 2,3,5,7....}.

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5.Co-Prime Numbers ( सह अभाज्य संख्याएं):

The pair of numbers which do not have common factors except 1 are called Co-prime Numbers. For 

example, (3 , 5), (7, 11)  ,(5, 23) ,(8,17).etc.

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6. Twin Prime Numbers( जुड़वा अभाज्य संख्याएं):. 

 A prime number is called a twin prime if there exist another prime number differing Frome it by 2.

(ऐसी दो अभाज्य संख्याएं जिनके बीच का अंतर 2 आता हो तथा उनके बीच में एक composite numbe भी हो)

Ex:    (3,5), (5,7) ,(11,13).....etc.

Important Note

3-twin prime,  

5- twin prime.

(3,5) =pair of twin prime

Properties of Twin Primes

• (2,3) are not considered as twin primes, since there is no composite number in between them and the difference between the two primes is not equal to 2.
• 5 is the only prime number that is available in two different pairs
• Every prime pair other than (3,5) is in the form of (6n-1, 6n+1), where n is any natural number.
• The sum of each prime pair apart from (3,5) is divisible by 12.

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7. Composite Numbers(मिश्रित संख्याएं) The numbers which have more than two factors are called composite numbers.

ऐसा Number जिसके कम से कम तीन factor होते है)

For example: 4,6,8,10,12,14,15, etc. are composite numbers.

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8. Whole Numbers(पूर्णांक).

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

W={0,1,2,3,4......................

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9. Integers:-(पूर्ण संख्याएं) The numbers which are positive and negative, including 0 are termed Integers. -3,-2,-1,0,1,2,3,4,5 are integers.

I,or Z={....... -3,-2-,1,0,1,2,3................   }

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10• Rational Numbers ( परिमेय संख्याएं): 

The Rational Numbers are those Numbers that can be written in the form of  p/q .

P and q are integers. where the value of q is not equal to zero.

Ex. 2/3  0/5 ,  5......etc

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Types of decimal Numbers 

11. Terminating decimal: 

it has a finite number of digits after the decimal point. Ex: 1.23,  3.5, 7.01,   9.87 . etc.

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12. Non-Terminating but Repeating: 

A decimal that never ends, but repeats one or more numbers after the decimal point. for example : i.e 0. 5555......, 0.171717......, 0.15222222... These numbers are also written in the form of p/q.

0.777777....= 

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13. Non- Terminating non Repeating :(Irrational  Numbers)( अपरिमेय संख्याएं)

Decimal numbers that neither end nor have any repetitive digits (or group of digits).

Examples:

•1.010010001...

• π 3.141592...

•√3 = 1.7320508...

.√2 = 1.4142135...

•0.125125125.... = 

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N<W<I<Q<R

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 A CARDINAL NUMBER 

A cardinal number is a number that says how many of something there are, such as one, two, three, four, five. 

AN ORDINAL NUMBER 

An Ordinal Number is a number that tells the position of something in a list, such as 1st, 2nd, 3rd, 4th, 5th etc. Most ordinal numbers end in "th" except when the final word is: one → first (1st)