Practice Set Of Odd Positive Integers (3.7) - Countable and Uncountable Sets

Practise this section

9 questions

Flashcard drill
3 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.
List three odd positive integers.
Show hintHide hint
Start counting from 1 and only include numbers not divisible by 2.
Question 2.
Is the set of all odd positive integers finite or infinite?
Show hintHide hint
Consider how the odd positive integers continue indefinitely.
3Question 3.
What defines a countable set?
- Must be finite
- Can be matched with positive integers
- Has no elements
Show hintHide hint
Think about how we define sizes of sets.
4Question 4.
True or False: The set of odd positive integers has more elements than the set of positive integers.
- True
- False
Show hintHide hint
Consider the mapping function we introduced.
Question 5.
Prove that if two sets have the same cardinality, and one of them is finite, then the other must be finite as well.
Show hintHide hint
Consider how bijections relate to the size of both sets.
Question 6.
Demonstrate a bijection between the set of rational numbers and the set of positive integers, citing your methodology.
Show hintHide hint
Think about how you can systematically traverse all fractions.

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