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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , NUMBER SYSTEM, A Mathematical symbol represented by a set of, digits is called a number., Numbers are everywhere in our daily life for, counting, measuring, labeling, ordering and coding., , Number System, , Page 1
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , Natural Numbers :, They are denoted by N., N = { 1, 2, 3 }, All positive integers are natural numbers., , Whole numbers :(0 & all N), They are denoted by W., W= { 0, 1, 2, 3… }, , INTEGERS :, They are denoted by I., I = { …..,-3, -2, -1, 0, 1 , 2, 3,….., , Number System, , }, , Page 2
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , Rational numbers :, They are called by Q., Q, , Irrational numbers :, , Number System, , Page 3
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , Real numbers : Real numbers include both, rational as well as irrational numbers., Positive or negative, large or small, whole, numbers or decimal numbers are all real, numbers., e.g.= 1, 13.79, -0.01, etc., Imaginary numbers : An imaginary number is, a complex number that can be written as a real, number multiplied by the imaginary unit ‘i’, which is defined by its properly, Note : Zero (0) is considered to be both real and, imaginary number., Prime number : A prime number is a natural, number greater than 1 and is divisible only by 1, and itself., e.g.2, 3, 5, 7, 11, 13, 17 ,19 etc., Note :- 2 is the only even prime number., Number System, , Page 4
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , Composite Numbers : A number, other than 1,, which is not a prime number is called a, composite number ., E.g. 4, 6, 8, 9, 10, 12, 14, 15 etc., Note :, 1. 1 is neither a prime number nor a composite, number., 2. there are 25 prime numbers between 1 and 100., 3. 15 prime numbers between 1 and 50, 4. 10 prime numbers between 50 and 100, To find whether a number is prime or notTo check whether the number is prime or not,, 1 We take an integer larger than the square root, of the number. Let the number be ‘k’. 2 Test the, divisibility of the given number by every prime, number less than ‘k’., , Number System, , Page 5
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , 3. If it is not divisible by any of them, then the, given number is prime otherwise it is a composite, number., E.g.= Is 881 a prime number ?, Sol- The appropriate square root of 881 is 30., Prime number less than 30 are 2, 3, 5, 7, 11, 13,, 17,19, 23,29., 881 is not divisible by any of the above, numbers, so it is a prime number., Co-prime numbers : Two numbers are, co-prime of their HCF is 1., E.g. (2,3), (3,4) , (5,7), (3,13) etc., , Even numbers : The number which is, divisible by 2 is called even number., E.g. – 2, 4, 6, 8……………., Odd numbers – The number which is not, Number System, , Page 6
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HIMANSU STUDY POINT, , Telegram link- https://t.me/Hstudypoint, , divisible by 2 is called odd number., e.g.= 3, 5, 7, 9………….., Consecutive numbers : A series of numbers, in which the succeeding number is greater then, the preceding number by 1 is called a series of, consecutive numbers., i.e., Difference between two consecutive, numbers is 1., , Number System, , Page 7
