Practice Set Of Rational Numbers (4.2.2) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
Define a countable set in your own words.
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Remember the definition of natural numbers.
Question 2.
What is the significance of the Cartesian product in enumerating rational numbers?
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Think about how ordered pairs work.
3Question 3.
What distinguishes countable sets from uncountable sets?
- Countable sets are finite
- Countable sets can be listed with natural numbers
- Countable sets have a finite number of elements
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Think about how we defined countability.
4Question 4.
Are the rational numbers countably infinite?
- True
- False
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Recall the enumeration discussion about rational numbers.
Question 5.
Prove that the union of two countable sets A and B is also countable.
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Think about listing elements alternately from both sets.
Question 6.
Demonstrate why the set of real numbers is uncountable.
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Consider how to list real numbers and where the diagonal argument comes into play.

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