Computable Function

A computable function is a function that can be defined as an algorithm, or a series of well-defined and finite steps. For any input, it will determine an outcome in a finite amount of time. One thing I was confused on is that division would have an invalid input of 0 but it is still computable because it is able to determine that 0 is an invalid input. Intuitively, all computable functions are always able to determine an outcome for all inputs, not necessarily an output.

Examples

Computable Functions:

• Addition, subtraction, polynomial functions

Non-computable Functions:

• The Halting Problem
• Busy Beaver Function