Practice Countably Finite Sets And Countably Infinite Sets (3.4)

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6 sample questions

Question 1.
Define a countably finite set.
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Think about a set you can count entirely—like a box of candies.
Question 2.
Is the set of all even numbers countable?
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Consider how you can list them.
3Question 3.
Which of the following is a countably finite set?
- Set of all positive integers
- Set of continents
- Set of all real numbers
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Think of how many continents exist.
4Question 4.
True or False: The set of all prime numbers is uncountable.
- True
- False
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Recall that primes can be listed as 2, 3, 5, 7, ...
Question 5.
Prove that the set of all even integers is countably infinite.
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Show that every positive integer has a unique even counterpart.
Question 6.
Explain Cantor’s diagonal argument and how it demonstrates that the reals are uncountable.
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Focus on the construction of a new number that differs from any given entry in the list.

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