L25_Mon_Mar_22 - MAE3811Sp. 2010 Mahoney1 Division for the...

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MAE3811–Sp. 2010 Mahoney–1 Division for the Integers It is defined exactly the same as it was for whole numbers WHOLE #: Formally, for any whole numbers a and b , with b not equal to 0 , a ÷ b = c if and only if c is the unique whole number such that b∙c = a . INTEGERS: Formally, for any integers a and b , with b not equal to 0 , a ÷ b = c if and only if c is the unique whole number such that b∙c = a . So what’s the difference in the definitions? Examples: 12 ÷ - 4 - 12 ÷ 4 - 12 ÷ - 4 - 12 ÷ - 5 MAE3811–Sp. 2010 Mahoney–2 Ordering of the Integers It is defined exactly the same as it was for whole numbers Whole: Definition of Less Than: For any whole numbers a and b, a is strictly less than b, written a < b, if, and only if, there exists a natural number k such that a + k = b Integer: Definition of Less Than: For any integers a and b, a is strictly less than b, written a < b, if, and only if, there exists a positive integer k such that a + k = b So what’s the difference in the definitions? Theorem: a < b (or b > a) if
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L25_Mon_Mar_22 - MAE3811Sp. 2010 Mahoney1 Division for the...

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