Practice Countable And Uncountable Sets (3) - Countable and Uncountable Sets

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8 questions

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6 sample questions

Question 1.
What is the cardinality of the set X = {Alice, Bob}?
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Count the number of names in the set.
Question 2.
Is the set Y = {1, 2, 3, 4} countable?
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Check if it's possible to list elements.
3Question 3.
What is a countable set?
- A set with finite elements
- A set with the same cardinality as positive integers
- Both A and B
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Think about the definitions discussed regarding countable sets.
4Question 4.
True or False: The set of all real numbers is countable.
- True
- False
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Consider Cantor’s diagonal argument!
Question 5.
Show that the set of all even integers is countable by constructing a bijection with positive integers.
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Use the formula relating each even integer to positive integers.
Question 6.
Explain why the interval [0, 1] contains uncountably many numbers.
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Reflect back on concepts involving real numbers and enumeration.

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