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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
(Continued )
If we now set r = a qb, we can show that this number satisfies the conditions listed in the conclusion.
By the previous inequalities (*),0< r < b. By its definition, a = qb + r. Since the two cases presented cover
all the possibilities, we proved that the statement is true.
The statement in Example 2.6 is part of the theorem known as the division algorithm. The beginning
of the proof uses an idea that, while clever, might not look intuitive. But, on the other hand, it does not
use advanced mathematical concepts. It is an example of how the c ombination of basic ideas can yield
more advanced results.
Later on we will prove that the
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Publisher Resources

ISBN: 9780123822178