Prime numbers
It can only be divided by one or itself i.e., a prime number has no factors other than 1 and itself. e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, are examples of prime numbers..
Prime factors
They are prime numbers which are factors of a given number. e.g., Prime factors of 42 = 2 x 3 x..
Rational and Irrational Numbers
Introduction - The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecuti..
Introduction
The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecutive intege..
Illustrative Examples
Example 1: - 01. If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not tru..
Illustrative Examples
The following are the Illustrative Examples: If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not true. Prove by P.M.I , n < 2 n for all n ..
Questions on Number theory
Question 1 - Question: Define an even number. Answer: A number which is divisible by 2 is called an even number..
Basic number theory question and answers
Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..
Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..Real Numbers
The union of the set of rational numbers and irrational numbers forms the set of real numbers. (i) For every real number, there is a corresponding point on the number line. (ii) For every point on the number line, there exists a real..
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