Practice Definition Of Countable Sets (3.3) - Countable and Uncountable Sets

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6 sample questions

Question 1.
Define a countable set.
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Think about the characteristics of finite sets.
Question 2.
Is the set of prime numbers countable?
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Can you list them in order?
3Question 3.
What defines a countable set?
- It must have a finite number of elements.
- It can be either finite or have the same cardinality as positive integers.
- It cannot have an infinite number of elements.
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Remember the definition of countability.
4Question 4.
Which set is not countable?
- The set of natural numbers.
- The set of real numbers.
- The set of odd numbers.
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Think about how many numbers are between any two integers.
Question 5.
Determine if the set of all even integers is countable and justify your answer.
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Consider the way they pair with positive integers.
Question 6.
Show whether the set of all subsets of natural numbers is countable.
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Think about how many subsets can exist versus elements.

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