Set includes rational numbers and irrational numbers.

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Presentation transcript:

Set includes rational numbers and irrational numbers. You need to understand the definition of each set of numbers and whether or not the sets are CLOSED under certain operations. That means: when you perform an operation on a specific set of numbers, and the answer remains within that set, it is CLOSED under that operation. To prove that a set is NOT CLOSED under an operation, you need to find only one counterexample. 1. Give a counterexample to show why the set of integers is not closed under division. 2. Give a counterexample to show why the set of irrational numbers is not closed under multiplication. Real Numbers Set includes rational numbers and irrational numbers. Rational Numbers Irrational Numbers Any number you can write in the form In decimal form it either terminates or repeats. Cannot be expressed in the form Decimal forms are non-repeating or non-terminating. Integers Whole Numbers Natural Numbers

3. The irrational numbers are closed under multiplication. These are Practice Exam type questions {mainly 42-47}. 3. The irrational numbers are closed under multiplication. . True B. False For questions 4-5, classify each number as rational or irrational. 4. 5. A. Rational A. Rational B. Irrational B. Irrational 6. Answer each part. A. What is an irrational number? B. Explain why is an irrational number. 7. In each part, provide an example of the statement. A. The sum of two rational numbers is rational. B. The product of a rational number and an irrational number is irrational. 8. Answer each part. A. Write as the product of a rational and an irrational number. B. Give an example where the product of two irrational numbers is a rational number. C. Explain why the sum of a rational number and an irrational number must be irrational.