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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
So, we would have a
1
=1, a
2
=2,a
3
=1/2,a
4
=1/3,a
5
=3,a
6
=4, a
7
=3/2,. All the elements i n
the list are distinct because repetitions have been eliminated. All the positive rational numbers will be
listed because the fraction m/n will appear for sure in the list before the (m + n)
th
place. So,
+
is counta-
ble and its size is
0
.
Clearly the listing shown above is not the only possible one. A nd for those who do not like proofs
that rely on graphs and tables, there are other proofs that rely o n formulas (see the exercises). A proof
similar to the one above c an b e used to show t hat the set of all negative integers,
, is also counta ble.
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Publisher Resources

ISBN: 9780123822178