Practice Theorem On Countable Sets (3.5) - Countable and Uncountable Sets

Practise this section

9 questions

Flashcard drill
5 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a countable set.
Show hintHide hint
Think about the types of numbers you can count.
Question 2.
What is a bijection?
Show hintHide hint
Consider how each element from one set relates to the other.
3Question 3.
What is a countable set?
- A set that is finite and can’t be listed
- A set with more than one element only
- A set that can be put into one-to-one correspondence with positive integers
Show hintHide hint
Focus on how we understand counting beyond finite numbers.
4Question 4.
True or False: The set of real numbers is countable.
- True
- False
Show hintHide hint
Recall the characteristics of uncountable sets.
Question 5.
Prove that the set of natural numbers is countable by establishing a bijection with the integers.
Show hintHide hint
Consider how you can start pairing from 0.
Question 6.
Show why the set of rational numbers is countable.
Show hintHide hint
Think about how to organize and sequence pairs.

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