Lesson 56a.

Due Monday, April 5

Sect. 10:
  1. Suppose you wanted to find the shortest person on the UA women's basketball team. Suppose you find a member of the team who is 6 ft 2 in tall. Explain briefly why you would not have to check those over 6 ft 2 in tall to find the shortest player.

  2. Suppose you wanted to find the smallest person (in terms of weight) on the UA men's football team. Suppose you find a member of the team who weighs 300 lb. Explain briefly why you would not have to check those over 300 pounds to find the smallest player.

  3. The result of a previous lesson (Lesson 48) is that every nonempty finite subset of the set of natural numbers has a least element.  Use this result, and smell the clover, to prove the Well-Ordering Property of the set of natural numbers.  I.e., complete the solution of Exercise 10.30.  Of course, in order to do this, you need to know what the Well-Ordering Property is.
    Note:  Exercise 10.30 asks you to “use induction” to prove the Well-Ordering Property.  You have already done the induction part in Lesson 48; now all you have to do is complete the proof for the general Well-Ordering Property.  Induction is not needed here.

NOTE: Be sure to read  Homework Format  and Homework Writing Policy BEFORE writing up your solutions to be turned in.


NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.


Last modified May 3, 2008 7:33 AM

Go to Lesson 57 (due Apr 30).

Go to Lesson 59 (due May 5).

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