Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration.
It is permissible, and often necessary, to use values from other parts of the program outside the bracketed block of statements, to perform the desired function.
Iterators constitute alternative language constructs to loops, which ensure consistent iterations over specific data structures. They can eventually save time and effort in later coding attempts. In particular, an iterator allows one to repeat the same kind of operation at each node of such a data structure, often in some pre-defined order.
Iteratees are purely functional language constructs, which accept or reject data during the iterations.
Recursions and iterations have different algorithmic definitions, even though they can generate identical effects/results. The primary difference is that recursion can be employed as a solution without prior knowledge as to how many times the action will have to repeat, while a successful iteration requires that foreknowledge.
The classic example of recursion is in list-sorting algorithms such as merge sort. The merge sort recursive algorithm will first repeatedly divide the list into consecutive pairs; each pair is then ordered, then each consecutive pair of pairs, and so forth until the elements of the list are in the desired order.
The code below is an example of a recursive algorithm in the Scheme programming language that will output the same result as the pseudocode under the previous heading.
Unlike computing and math, educational iterations are not predetermined; instead, the task is repeated until success according to some external criteria (often a test) is achieved.