Chapter 2 The Well Ordering Principle40
(f)LetWWWDN[Fbe the set consisting of the nonnegative integers along with
all the fractions of the formn=.nC1/. Describe a length 5 decreasing sequence of
elements ofWstarting with 1,... length 50 decreasing sequence,... length 500.
Problem 2.16.
Use the Well Ordering Principle to prove that every finite, nonempty set of real
numbers has a minimum element.
Class Problems
Problem 2.17.
Prove that a set,R, of real numbers is well ordered iff there is no infinite decreasing
sequence of numbersR. In other words, there is no set of numbersri 2 Rsuch
that
r 0 > r 1 > r 2 > :::: (2.12)