Practice Non-constructive Proofs (8.4) - Uncomputable Functions - Discrete Mathematics

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6 sample questions

Question 1.
Define a computable function.
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Think about whether you can write a program for it.
Question 2.
What does it mean if a function is uncomputable?
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Consider the implications of a program not existing for that function.
3Question 3.
What defines a computable function?
- A function with no program
- A function computable by a program
- A function that always produces an output
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Consider if you can find a program for it.
4Question 4.
True or False: All functions are computable.
- True
- False
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Think of examples like the Halting Problem.
Question 5.
Using Cantor's argument, prove that the set of all functions from {1,2,3,...} to {0,1} is uncountable.
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Reflect on how listing elements could lead to missing at least one function.
Question 6.
Discuss the implications of the Halting Problem within programming and computation limits.
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Consider programming tasks where it's impossible to predict behavior.

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