Skip to Main Content
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
(Continued )
A: Let n be an integer number with n = ±a
4
a
3
a
2
a
1
a
0
,0 a
i
9 for all i =0,1,2,3,4,anda
4
0, such
that a
4
+ a
3
+ a
2
+ a
1
+ a
0
=3t,wheret is an integer number. (The fact tha t n is an integer number is
an implicit hypothesis, since the concept of divisibility is defined only for integer numbers. The ± sign
indicates that the number n can be either positive or negative.)
B: The number n is divisible by 3; that is, n =3s with s an integer number.
Proof: As the hypothesis provides information about the digits of the number, we will separate the digits using
powers of 10. For sake of simplicity, let us assume that n is positive. Thus,
n = a
4
a
3
a
2
a
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Discrete Structures, Logic, and Computability, 4th Edition

Discrete Structures, Logic, and Computability, 4th Edition

James L. Hein

Publisher Resources

ISBN: 9780123822178