about number theory

Question 1 - Question: Define an even number. Answer: A number which is divisible by 2 is called an even number..

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..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the types of compl..

A prime number is one that has only two factors namely 1 and itself. and a composite number has factors besides 1 and itsel..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the types of compl..

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..

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..

Such numbers have only 1 as common factor even though they may be composite numbers e.g., 21 and 32 are prime to each other. We generally write (21, 32) = 1, which means 21 and 32 are prime to each other i.e., they have only one factor in common viz., ..

The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..