Explain the existence of undecidable problems in computer science.
AAP-4.B.1 A decidable problem is a decision problem for which an algorithm can be written to produce a correct output for all inputs (e.g., “Is the number even?”).
AAP-4.B.2 An undecidable problem is one for which no algorithm can be constructed that is always capable of providing a correct yes-or-no answer.
AAP-4.B.3 An undecidable problem may have some instances that have an algorithmic solution, but there is no algorithmic solution that could solve all instances of the problem.