An algorithmic problem is specified by describing the complete set of instances it must work on and of its output after running on one of these instances. This distinction, between a problem and an instance of a problem, is fundamental. The algorithmic problem known as sorting is defined as follows: [Skiena:2008:ADM:1410219]

• Problem: Sorting
• Input: A sequence of n keys, a_1, a_2, ..., a_n.
• Output: The reordering of the input sequence such that a'_1 <= a'_2 <= ... <= a'_{n-1} <= a'_n

An instance of sorting might be an array of strings, such as { Haskell, Emacs } or a sequence of numbers such as { 154, 245, 1337 }.