Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 42 — #50
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Chapter 2
The Well Ordering Principle
Problem 2.15.
Use the Well Ordering Principle (WOP) to prove that
for all n > 0.
2 C 4 C C 2n D n.n C 1/ (2.10)
Problem 2.16.
Prove by the Well Ordering Principle that for all nonnegative integers, n:
n.n C 1/ 2
0 3 C 1 3 C 2 3 C C n 3 D
: (2.11)
2
Problem 2.17.
Use the Well Ordering Principle to prove that
for all integers n 1.
1 2 C 2 3 C 3 4 C C n.n C 1/ D
n.n C 1/.n C 2/
3
(*)
Problem 2.18.
Say a number of cents is makeable if it is the value of some set of 6 cent and 15
cent stamps. Use the Well Ordering Principle to show that every integer that is a
multiple of 3 and greater than or equal to twelve is makeable.
Problems for Section 2.4
Homework Problems
Problem 2.19.
Complete the proof of Lemma 2.4.5 by showing that the number n S C f S is the
minimum element in S.
Practice Problems
Problem 2.20.
Indicate which of the following sets of numbers have a minimum element and