Practice Countability Of Set P (5.2.2) - Countability of the set of all strings over a finite alphabet

Practice: Countability of set P

Lesson 5.2.2Countability of the set of all strings over a finite alphabet

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8 questions

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6 sample questions

Question 1.
What is a finite alphabet?
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Think about letters in the English alphabet or symbols in a programming language.
Question 2.
How many strings can you form of length 1 from an alphabet of 4 characters?
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Count each character as one string.
3Question 3.
What does it mean for a set to be countable?
- It can only contain finite elements.
- It can be placed in one-to-one correspondence with the natural numbers.
- It contains no duplicates.
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Think about how we can organize elements.
4Question 4.
True or False: All infinite sets are uncountable.
- True
- False
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Consider the definition of countability.
Question 5.
Create a finite alphabet with four characters and list all possible strings of length 2. How many total strings can you form?
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Use every character in combinations regardless of order.
Question 6.
If you have a set of infinite valid programs, how can you prove that this set is countable?
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Think about organizing programs just like you'd list books by title.

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