CHAPTER 1:REAL NUMBERS
Introduction to Real Numbers Real Numbers Real numbers constitute the union of all rational and irrational numbers. Any real number can be plotted on the number line. Euclid’s Division Lemma Euclid’s Division Lemma states that given two integers a and b , there exists a unique pair of integers q and r such that a = b × q + r a n d 0 ≤ r < b . This lemma is essentially equivalent to : dividend = divisor × quotient + remainder In other words, for a given pair of dividend and divisor, the quotient and remainder obtained are going to be unique. Euclid’s Division Algorithm Euclid’s Division Algorithm is a method used to find the H.C.F of two numbers, say a and b where a> b. We apply Euclid’s Division Lemma to find two integers q and r such that a = b × q + r a n d 0 ≤ r < b . If r = 0, the H.C.F is b, else, we apply Eucl...