Practice Set Of Real Numbers Between 0 And 1 (6.1.7) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
Define a countably infinite set.
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Think about a set you can list or count.
Question 2.
What is an uncountable set?
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Consider whether you can list all elements.
3Question 3.
What does uncountable mean?
- Able to be listed
- Cannot be listed
- Can be represented on a number line
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Consider if you can list out all elements.
4Question 4.
True or False: All infinite sets are countable.
- True
- False
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Think about the set of real numbers.
Question 5.
Construct a set to show that the set of real numbers cannot be counted. Use Cantor's method to illustrate.
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Think about how flipping each digit creates a new, unlisted number.
Question 6.
Using a bijection, explain how the infinite binary strings are related to real numbers between 0 and 1.
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Look at binary representations and their decimal equivalents in the specified interval.

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