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:::In [[mathematics]], '''function iteration''' is the process of [[function composition|composing]] a function ''f'': ''X'' → ''X'' (that is, a [[function (mathematics)|function]] from some [[set (mathematics)|set]] ''X'' to itself) with itself a certain number ''n'' of times. In this process, starting from some initial element of ''X'', the output of ''f'' is fed again into ''f'' as input, and this process is repeated. The result of function composition is again a function ''f''<sup>''n''</sup>: ''X'' → ''X'', it is called an '''iterated function'''.
::or something similar? The sentence ''"The process of repeatedly applying the same function is called [[iteration]]."'' could be moved down e.g. to the "Definition" section, and adapted to e.g. ''"Function iteration is a particular example of [[iteration]] in general."'' if it is considered worth to be kept at all. In contrast, the possibility of fractional iterates ''should'' be mentioned already in the lead, I think. - [[User:Jochen Burghardt|Jochen Burghardt]] ([[User talk:Jochen Burghardt|talk]]) 17:31, 18 February 2015 (UTC)
== Slight Ambiguity ==
When the article says, "Note: these two special cases of ax2 + bx + c are the only cases that have a closed-form solution. Choosing b = 2 = –a and b = 4 = –a, respectively, further reduces them to the nonchaotic and chaotic logistic cases discussed prior to the table." Does it mean that we only know of two closed form solutions, or has it been proven that there are no others?
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