Honors Interdisciplinary Seminar (175)

 Infinity


Assignment following Week #11 (Due 11/30 in class) 
(Section 004 - Due 10/19 in class)

  1. There are three assigned readings:

    (Remember that if you print any of these excerpts, the reproduction is not to be used for any purpose other than private study, scholarship, or research. If you use a photocopy or reproduction for purposes in excess of fair use, then you may be liable for copyright infringement.)

  2. Complete the Study Questions below.
  3. Complete Response Paper #2.  Parameters for the Response Papers can be found HERE, and possible topics for your essay can be found HERE.  Quotes from our round of "speeddating" from class on Monday, November 23, can be found HERE. 
  4. Preparation for your Final Project:   Remember that your group needs to meet with Steve in his office at least once between Monday, November 23 and Thursday, December 3. At this meeting you should be prepared to give a rough description of the types of things your group will be arguing in the debate.  It will also be an opportunity for your group to ask questions regarding things such as organization, sources, and format of your debate, so think about those questions before you come.  I am, of course, available at lots of other times to discuss your project.  Feel free to ask!

Available times:

Tuesday, November 24

8:00 am, 10:30 am, 11:00 am, 1:30 pm, 2:00 pm

Tuesday, December  1

9:00 am, 9:30 am, 10:00 am, 10:30 am, 1:30 pm, 2:00 pm

Wednesday, December 2

8:00 am, 2:00 pm, 2:30 pm, 3:00 pm, 3:30 pm

Thursday, December 3

8:00 am, 8:30 am, 9:00 am, 9:30 am, 10:00 am, 2:00 pm, 2:30 pm, 3:00 pm, 3:30 pm

  1. Read any emails I send you, and respond if requested.
  2. There may be a brief quiz at the start of the next class.

Study Questions 

Please carefully write out your answers to these questions.  Make a copy of your answers and be prepared to hand that copy in at the start of class.  Look at the Study Questions Main Page for general guidelines on study questions in Steve's section.

Followup from Class on November 23:

  1. What was the flaw in the proof that 1=2?  As a reminder, here is the proof:

    Theorem:  1=2
    "Proof:"

    (Note:  the flaw is not in the first step.)

From the readings on infinity:  

  1. Comment on the relationship between mathematics and art in the late 19th century.  How does Dunham compare the work of the great impressionists with the state of the logical foundations of mathematics at that time?  Is it a good analogy? Why or why not?

  2. Do you agree with Kline's criticism of mathematics (see p. 257)?  Why or why not?

  3. At the bottom of p. 249, what is George Berkeley saying about the nature of mathematical truth?  Do you agree?

  4. How do we show that two sets have the same number of elements without physically counting them?

  5. What does "cardinality" mean?  Give an example of two finite sets with the same cardinality.  Give an example of two infinite sets with the same cardinality.

  6. What does "denumerable" mean?  List five sets that are denumerable.  Give an example of an infinite set that is not denumerable.

  7. What did Cantor prove about the relationship between natural numbers and real numbers?

  8. What is a "power set"?  Given the set A={x,y}, find P(A).  What did Cantor prove about the power set of a set?

  9. Is there an infinity greater than the infinity of the set of real numbers?

  10. Are there infinitely many different sizes of infinity?

  11. Is there a largest infinity - one that encompasses all others?

  12. Is there an infinity that is greater than the infinity of the set of natural numbers yet less than the larger infinity of the set of real numbers?  (Is the cardinality of the reals the next bigger infinity after the cardinality of the natural numbers?)

  13. What is the continuum hypothesis?


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