Lesson 48a.

NOTE: Be sure to read  Homework Format  and Homework Writing Policy BEFORE writing up your solutions to be turned in.
PROBLEMS WILL NOT BE GRADED AND NO CREDIT WILL BE GIVEN if these guidelines are not followed.

Due Monday, April 28

If you have already done this problem correctly in Lesson 48 (it was Problem 4 in Lesson 48), you don't have to redo it; you have already received credit for it, as should be noted on your homework paper for Lesson 48 when it is returned.
Warmup:
Induction proofs should start by identifying a function  P  whose domain is (usually) the set of natural numbers and whose outputs are statements.
  1. Write down the statement  P(n)  given to you in Lesson 46 (not in the problems assigned from the book, but in the Lesson).
  2. Write down the statement  P(n)  given to you in Exercise 10.15(a).
Sect. 10:
Be sure to read the Induction Warnings and Induction Checklist before doing the induction part of these problems. Solutions which do not follow these guidelines will not be graded.
Use induction to prove that if a set  S  of real numbers has  n  elements* (for a natural number  n),  then  S  has a least element.
* Here we mean that  S  has exactly  n  elements.
CAUTION. We have discussed frequently throughout the semester, and also in connection with induction, good and “bad” approaches to proving such statements. Try to avoid the bad. See also Notes, added to Lesson 48 on April 20.

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 Apr 24, 2008 1:28 PM

Go to Lesson 49 (due April 21).

Go to Lesson 54 (due April 28).

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