Number Systems Includes Rational Numbers , Irrational Numbers, Rationalization Of Denominator

MATHEMATICS Chapter 1: Number Systems(1) NUMBER SYSTEMS 01 Number Systems 1. Numbers 1, 2, 3., which are used for counting are called natural numbers. The collection of natural numbers is denoted by N. Therefore, N = {1, 2, 3, 4, 5, }. 2. When 0 is included with the natural numbers, then the new collection of numbers called is called whole number. The collection of whole numbers is denoted by W. Therefore, W = {0, 1, 2, 3, 4, 5, }. 3. The negative of natural numbers, 0 and the natural number together constitutes integers. The collection of integers is denoted by I. Therefore, I = {, -3, -2, -1, 0, 1, 2, 3, }. 4. The numbers which can be represented in the form of p/q, where q 0 and p and q are integers are called rational numbers. Rational numbers are denoted by Q. If p and q are co-prime, then the rational number is in its simplest form. 5. All-natural numbers, whole numbers and integer are rational number. 6. Equivalent rational numbers (or fractions) have same (equal) values when written in the simplest form. 7. Rational number between two numbers x and y =. 8. There are