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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
In general, the value of ε that will enable us to complete the proof depends on the behavior of the
function around c, and smaller values of ε aremorelikelytowork.InExample 4.5.15 we used ε =1/2,
but, if one looks carefully thr ough the ste ps of the p roof, any value of ε smaller than or equal t o 1
(which is one of the values of the function) wo uld be a cceptab le. Thus, in gener al the choice of ε is not
unique.
The proof te chni qu es i llustr ate d in the exam ple s ar e not always easy to im ple ment . As one adva nces
in the study of real analysis, one builds more and more tools to deal efficiently with the nonexistence of
limits. Some of
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Publisher Resources

ISBN: 9780123822178