Algorithm

An algorithm is an effective method defined as a series of steps for calculating a function. Algorithms are maps between natural numbers, such that:

$$f:\mathbb{N}\to \mathbb{N}$$

Meaning that, in words, algorithms yield a natural number for every natural input.  Algorithms must also obey the following properties:

• Finite: An algorithm must stop after a finite number of steps.
• Definite: Each step of an algorithm has to be explicitly defined, and each action must be unambiguously and rigorously specified.
• Input: An algorithm may take any number, including zero, of inputs taken for a certain set of objects.
• Effectiveness: All operations of an algorithm must have precise definitions which do not interfere with its definiteness.