Assignment
following Week #11 (Due 11/30 in class)
(Section 004 - Due 10/19 in class)
(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.)
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 |
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:
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:
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?
Do you agree with Kline's criticism of mathematics (see p. 257)? Why or why not?
At the bottom of p. 249, what is George Berkeley saying about the nature of mathematical truth? Do you agree?
How do we show that two sets have the same number of elements without physically counting them?
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.
What does "denumerable" mean? List five sets that are denumerable. Give an example of an infinite set that is not denumerable.
What did Cantor prove about the relationship between natural numbers and real numbers?
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?
Is there an infinity greater than the infinity of the set of real numbers?
Are there infinitely many different sizes of infinity?
Is there a largest infinity - one that encompasses all others?
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?)
What is the continuum hypothesis?
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