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Download Section 3.3 Reading Assignment Due 9 AM, Tuesday 5/7. Please
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Transcript
Section 3.3 Reading Assignment
Due 9 AM, Tuesday 5/7. Please read Sections 3.3 and 3.4 and respond to the following in a
Word document.
1. Let x be the number 0.29999999... and let y be the number 0.30000000... Does x = y?
Explain.
2. Let x be the number 0.29999999... and let w be the number 0.400000000... Does x = y?
Explain.
3. If a first real number has decimal expansion of the form 0.2????... and a second real
number has decimal expansion of the form 0.4???????..., can these two numbers be equal?
Explain.
4. True, or false? It is possible to find a one-to-one correspondence between the set of all
natural numbers and the set of all real numbers. Explain.
5. What did Georg Cantor do that "shook the foundations of infinity"?
6. Given a set S, we say that another set T is a "subset" of S provided...
7. How many subsets does the set S = {5} have? List them.
8. How many subsets does the set S = {3, w, #} have? List them.
9. State Cantor's Theorem regarding the cardinality of any power set.
10. Is there a "largest set", a set of everything? Explain.
