A computable function is a mathematical function that can be calculated by a computer or an algorithm. This means that there exists a step-by-step procedure, or algorithm, that can take an input and produce an output in a finite amount of time. Examples of computable functions include basic arithmetic operations, such as addition and multiplication, as well as more complex functions like sorting a list of numbers. The concept of computable functions is closely related to Turing machines, which are theoretical models of computation. Alan Turing introduced these machines to explore the limits of what can be computed. Functions that cannot be computed by any algorithm are known as non-computable functions, highlighting the boundaries of computational capabilities.