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First Course in Abstract Algebra A, 8th Edition Solution Manual
0. Sets and Relations √ √ 1. { 3,− 3} 2. The set is empty. 3. {1,−1,2,−2,3,−3,4,−4,5,−5,6,−6,10,−10,12,−12,15,−15,20,−20,30,−30, 60,−60} 4. {−10,−9,−8,−7,−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,8,9,10,11} 5. It is not a well-defined set. (Some may argue that no element of Z+ is large, because every element exceeds only a finite number of other elements but is exceeded by an infinite number of other elements. Such people might claim the answer s...
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0. Sets and Relations √ √ 1. { 3,− 3} 2. The set is empty. 3. {1,−1,2,−2,3,−3,4,−4,5,−5,6,−6,10,−10,12,−12,15,−15,20,−20,30,−30, 60,−60} 4. {−10,−9,−8,−7,−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,8,9,10,11} 5. It is not a well-defined set. (Some may argue that no element of Z+ is large, because every element exceeds only a finite number of other elements but is exceeded by an infinite number of other elements. Such people might claim the answer s...
First Course in Abstract Algebra A
The name two-to-two function suggests that such a function f should carry every pair of distinct points into two distinct points. Such a function is one-to-one in the conventional sense. (If the domain has only one element, the function cannot fail to be two-to-two, because the only way it can fail to be two-to-two is to carry two points into one point, and the set does not have two points.) Conversely, every function that is one-to-one in the conventional sense carries each pair of distinct...
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The name two-to-two function suggests that such a function f should carry every pair of distinct points into two distinct points. Such a function is one-to-one in the conventional sense. (If the domain has only one element, the function cannot fail to be two-to-two, because the only way it can fail to be two-to-two is to carry two points into one point, and the set does not have two points.) Conversely, every function that is one-to-one in the conventional sense carries each pair of distinct...