Practice Countably Infinite Sets (6.1.2) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
What is a countably infinite set?
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Think of how integers relate to naturals.
Question 2.
Can you list an example of a countably infinite set?
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What can be matched with 1, 2, 3, etc.?
3Question 3.
What defines a countably infinite set?
- It can't be listed
- It has one-to-one correspondence with naturals
- It includes irrationals
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Consider counting the elements.
4Question 4.
True or False: The set of binary strings of infinite length is countable.
- True
- False
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Remember Cantor's argument.
Question 5.
Using Cantor's argument, prove that the decimal representation of any irrational number is infinite and does not repeat.
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Focus on how equating with rationals fails.
Question 6.
Suppose you are asked to list the set of all real numbers. Describe why this is impossible.
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Connect to the earlier discussions about the diagonal.

5 more questions in this section. Enroll free to practise them all.