Practice Set Of Valid Programs In A Programming Language (5.2.1) - Countability of the set of all strings over a finite alphabet

Practice: Set of Valid Programs in a Programming Language

Lesson 5.2.1Countability of the set of all strings over a finite alphabet

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10 questions

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6 sample questions

Question 1.
What does it mean for a set to be countable?
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Think about how you could list natural numbers.
Question 2.
Define a valid program in programming languages.
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Consider the beginning and end instructions of a program.
3Question 3.
A set is countable if:
- It has a finite number of elements
- It can be listed using natural numbers
- It has no elements
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Recall our definition of countability.
4Question 4.
True or False: All strings over a finite alphabet form a countable set.
- True
- False
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Think about how we listed the strings.
Question 5.
Design a valid program using a made-up programming language that includes at least three distinct commands.
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Focus on ensuring your program has a start and a syntax that makes sense.
Question 6.
Prove that there are infinitely many programs even within a constrained limited programming language.
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Consider how you can add new steps between the start and end.

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