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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
CHAPTER
5
Review Exercises
Discuss the truth of the following statements. Prove the ones that are true; find a counterexample for each
one of the false statements, and follow directions. The exercises with the symbol (*) require knowledge of
calculus and/or linear algebra.
1. If P(x
1
, y
1
)andQ( x
2
, y
2
) are two d istinct points in the plane, then the d istance between the two of
them, defined as
dðP, QÞ= ðx
2
x
1
Þ
2
+ ðy
2
y
1
Þ
2
,
q
is a positive number.
2. Let a be a real number. Then the opposite of a is unique.
3. If n is any positive integer number, then ln n < n. Prove this statement in all of the following ways:
a. By induction.
b. By gr aphing the two fun ...
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Publisher Resources

ISBN: 9780123822178