Solution for Section 4.4 Question 1

1a) The well-ordering principle for the integers does apply since, every nonnegative even integer is greater than -1. The least element of the set of all nonnegative even integers is 0.

b) The set of all negative integers of the form 46 - 7k = {-3, -10, -17, ...}. The values in this set were found by letting k = 7, k = 8, ....
The well-ordering principle for the integers does not apply since there is no integer x such that every element in this set is greater than x.

Back to Section 4.4