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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
We dont t hink very often about the fact that the pairs ð, + Þ and ð
, × Þ (where
is the set of
nonzero real numbers) are commutative groups, but we find it to be very usef ul indeed. For example, the
group structure guarantees the existence of the identity elements and the inverses. It gives us the cancella-
tion laws (which we call simplifying), and the ability to solve equations.
For example, it would b e i mposs ibl e to solve the equation 2x = 3 if 2 did not have an inverse. If 2 had
more than one inverse, the first degree equation would have more than one solution. The Fundamental
Theorem of Algebra would not hold true anymore. From
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Publisher Resources

ISBN: 9780123822178