powerpoint
- 1. The Set of Real Numbers By: Zenaida S. Allarse
- 2. Historically, whole numbers were used hundreds of years before negative integers were introduced. As trading became more common, two distinctly different uses of whole numbers were needed, one to indicate credit and the other one to indicate debit. Many of these ideas of opposites, like north and south, up and down, east and west, profit and gain, above and below sea level, and so on, paved the way to the development of positive and negative integers, also known as signed number. In algebra, a good grasp of signed numbers is necessary
- 3. The Set of Real Numbers At an early age, elementary school pupils learned how to use the set of counting numbers, {1, 2, 3, . . .} This set is called the set of Natural numbers/ set of positive whole numbers . Later, the idea of numbers was extended to include zero “0” forming the set of whole numbers , {0, 1, 2, 3, . . .} Still later, the set of counting numbers, zero, and negative numbers were combined forming the set of integers , {. . . – 3, – 2, – 1, 0, 1, 2, 3, . . .}
- 4. However, not all numbers can be expressed in any of these forms. Such numbers which cannot be expressed as a quotient of two integers are called Irrational Numbers. These are the non repeating and nonterminating decimals.The set of rational and irrational numbers form the set of real numbers. There are also numbers which can be expressed in the form a/b, where a and b are integers and b=0. These are called Rational Numbers ( Integers, simple fractions, mixed numbers, finite decimals, or repeating decimals, whether positive or negative, are all rational numbers.
- 5. POINTS TO REMEMBER: The Real Number System is divided into two categories: Rational and Irrational. Rational Numbers : Numbers, such as ½ and –3/1 that can be written as a ratio of two integers. Irrational Numbers : Real numbers, such as square root of 2 or , that are not rational.
- 6. Rational Numbers: Includes integers, whole numbers, natural numbers, and numbers written as the ratio of two integers. Integers: {. . . – 3, – 2, – 1, 0, 1, 2, 3, . . .} Whole Numbers: {0, 1, 2, 3, . . .} Natural Numbers: {1, 2, 3, . . .}
- 8. Importance of Real Number in our life The Meaning of Numbers are very crucial in our life but at the same time we completely fail to recognize its importance. Our day starts with numbers and it ends with numbers. Every minute of our life revolve around numbers and they hold the potential to change our lives too. Start to work on the meaning of numbers and what you have a real truth that surround and influence our lives. We remain ignorant for most part of our lives and when the truth come bare in front of us we cannot help but think that how such facts remained hidden from us for much part of our lives. Numbers and their meaning is subject to our interpretation and how skillfully we play around with them determines how successful we become in our lives.