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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
Examining all other possible choices will show that there are only two possible structures for groups of
size four (if we ignore the names and placement of the elements), either G
1
or G
2
. In one case each element
is its own inverse, in the other case the identity and one other element are their own inverse elements, and
the other two elements are inverse elements of each other. Both gr oups are abelian. It is ea sy to gu ess tha t
proceeding in this way becomes more complicated as the number of elements increases, and it is essentially
impossible when a group has infinite size.
There are two families of sets commonly used as prototypes for other
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Publisher Resources

ISBN: 9780123822178