Practice Definition Of Π* (5.1.2) - Countability of the set of all strings over a finite alphabet
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Definition of Π*

Practice - Definition of Π*

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a finite alphabet.

💡 Hint: Think of the letters you can use in a language.

Question 2 Easy

What is a countable set?

💡 Hint: Can you list all numbers? That is an example!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines a countable set?

Can be listed without omission
Contains infinite elements only
Random ordering

💡 Hint: Recall the definition from the beginning of our lesson.

Question 2

True or False: All substrings of a string form a countable set.

True
False

💡 Hint: Think about how many parts make up a whole string.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Construct all possible valid programs of length 2 using a 3-character alphabet.

💡 Hint: Focus on ensuring both start and end instructions are present.

Challenge 2 Hard

Prove that the intersection of two countable sets is also countable.

💡 Hint: Can you list pairs from both sets systematically?

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Reference links

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