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Unformatted text preview: 1.6. DIVISIBILITY IN THE INTEGERS 25 the set of permutations of a collection of identical objects has an algebraic structure. We can do computations in these algebraic systems in order to answer natural (or unnatural) questions, for example, to find out the order of a perfect shuffle of a deck of cards. In this section, we return to more familiar mathematical territory. We study the set of integers, probably most familiar algebraic system. The in tegers have two operations, addition and multiplication, but as you learned in elementary school, multiplication in the integers can be interpreted in terms of repeated addition: For integers a and n , with n > 0 , we have na D a C C a ( n times), and . n/a D n. a/ . Finally, 0a D . We denote the set of integers f 0; 1; 2;::: g by Z and the set of natural numbers f 1;2;3;::: g by N . We write n > 0 , and say that n is positive , if n 2 N . We write n and say that n is nonnegative , if n 2 N [ f g . The absolute value j a j of an integer...
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 Fall '08
 EVERAGE
 Algebra, Permutations, Integers

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