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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
EXISTENCE THEOREMS
Existence theorems are ofte n easy to recognize bec ause t hey claim that at least one object having some
required properties does indeed exist. Usually this kind of theorem is proved in one of two ways:
1. If it is possible, use an algorithm (a procedure) to construct explicitly at least one object with the
required properties.
2. Sometimes, especially in m ore advanced mathematical theories, t he ex plicit construction is not
possible. Therefore, we must be able to find a general argument t hat guarantees the existence of the
object in consideration, without being able to provide an actual examp le of it.
EXAMPLE 3.16
Given any
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Publisher Resources

ISBN: 9780123822178