8.3. Cardinality of Sets of Functions and Programs

Try these first

1. 1.

   What is a computable function?

   Hint

   Think about functions that can be executed by writing code.

2. 2.

   Define an uncomputable function.

   Hint

   Consider functions for which no program can yield outputs for all inputs.

3. 3.

   What is the definition of a computable function?

   • A function that can be approximated
   • A function for which there exists a program
   • A function that always runs fast

   Hint

   Think about how functions are executed in programming.

4. 4.

   True or False: Every computable function is also uncomputable.

   • True
   • False

   Hint

   Consider the definitions of both types of functions.

5. 5.

   Discuss the implications of uncomputable functions in practical applications such as software development.

   Hint

   Think about tasks you might wish to automate that involve complex decision-making.

6. 6.

   Create a scenario that illustrates a function you believe would be uncomputable. Justify your reasoning.

   Hint

   Consider the chess game's extensive possible moves.