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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
parameter. As an example, we can write a = b + 3, and then choose any value we like for b.Ifb = 0,
we obtain the polynomial Pð x Þ= 3x
2
1. Clearly, this is only one of infinitely many possibilities.
40. As b
a
will be a negative number, b must be negative. Indeed powers of positive numbers are alway s
positive. Moreover, a cannot be an even number, because an even exponent generates a positive
result. The numbers a and b can be either fractions or integer numbers.
Let us try b = 27 and a = 1/3. Then a
b
= ð1/3Þ
27
= 3
27
, which is a positive integer number, and
b
a
= ð27Þ
1/3
= 3, which is a negative integer.
41. We can consider two cases: either a
n
> 0o ...
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Publisher Resources

ISBN: 9780123822178