March 8, 2017

Introduction to the theory of categories and functors by I. Bucur, A. Deleanu

By I. Bucur, A. Deleanu

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015 (g) - 6 = - 61 2 1- 62 = - 4 3 NOW TRY OBJECTIVE 5 Find reciprocals and divide real numbers. The definition of division depends on the idea of a multiplicative inverse, or reciprocal. Two numbers are reciprocals if they have a product of 1. Reciprocal The reciprocal of a nonzero number a is 1a . The table gives several numbers and their reciprocals. 05 20 0 None A B =1 7 11 11 7 Reciprocals have a product of 1. 051202 = 1 There is no reciprocal for 0 because there is no number that can be multiplied by 0 to give a product of 1.

There is no reciprocal for the number 0, so division by 0 is undefined. For example, 1 15 0 is undefined and - 0 is undefined. CAUTION Division by 0 is undefined. However, dividing 0 by a nonzero number gives the quotient 0. For example, 6 is undefined, 0 but 0 = 0 6 (since 0 # 6 = 0). Be careful when 0 is involved in a division problem. Since division is defined as multiplication by the reciprocal, the rules for signs of quotients are the same as those for signs of products. Dividing Real Numbers Same sign positive.

1. 5. A factor is A. the answer in an addition problem B. the answer in a multiplication problem C. one of two or more numbers that are added to get another number D. any number that divides evenly into a given number. 6. An exponential expression is A. a number that is a repeated factor in a product B. a number or a variable written with an exponent C. a number that shows how many times a factor is repeated in a product D. an expression that involves addition. 7. A term is A. a numerical factor B.

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