TAILIEUCHUNG - SAT II Math Episode 1 Part 5

Tham khảo tài liệu 'sat ii math episode 1 part 5', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Math Review Illustrative Problems and Solutions 75 13. Number Systems and Concepts The Set of Integers 1. The set of natural numbers is made up of the ordinary counting numbers 1 2 3 . 2. The set of integers is made up of all positive and negative whole numbers and zero. An even integer is any multiple of two that is it is any integer that can be written in the form 2n where n is any integer. Thus zero is considered an even integer 2 X 0 . An odd integer is any integer that is not even. 3. The sum of two odd integers or two even integers is an even integer. The sum of an odd integer and an even integer is an odd integer. 4. The product of two odd integers is an odd integer. Any power of an odd integer is also an odd integer. The product of any integer and an even integer is an even integer. 5. The set of integers is closed under addition subtraction or multiplication that is if any of these operations is performed upon two integers the result will also be an integer. The set of integers is not closed under division since the quotient of two integers is not always an integer. The Set of Rational Numbers 1. 2. 3. 4. 5. . . p_ A rational number is any number that can be written in the form where p and q are integers and q 0. The set of integers is a subset of the set of rational numbers since any integerp can be written in the form of a ratio ofp to 1. The set of decimal fractions that can be written as finite decimals is also a subset of the set of rational numbers since a finite decimal can always be written as the ratio of an integer and a power of10. We can also show that infinite decimals that have repeating groups of digits can be expressed as rational numbers. An irrational number is any real number that is not rational. We can show that numbers like - JĨ ị ĩỉ and n are irrational numbers. Irrational numbers are infinite decimals whose digits do not repeat endlessly in groups. The set of rational numbers is closed under addition subtraction multiplication and .

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