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 iterated_function [2013/12/21 19:57]127.0.0.1 external edit iterated_function [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2014/02/08 18:33 nikolaj 2013/12/21 19:57 external edit2013/09/13 20:22 nikolaj 2013/09/09 15:52 nikolaj 2013/09/06 22:04 external edit2013/08/16 14:52 nikolaj 2013/08/15 09:14 nikolaj 2013/08/14 22:11 nikolaj 2013/08/14 22:11 nikolaj 2013/08/06 11:56 nikolaj 2013/08/06 11:54 nikolaj 2013/08/06 11:45 nikolaj old revision restored (2013/05/23 16:28)2013/08/06 11:45 nikolaj 2013/05/23 16:28 nikolaj 2013/05/23 16:21 nikolaj 2013/05/23 16:21 nikolaj 2013/05/23 16:19 nikolaj 2013/05/23 16:19 nikolaj 2013/05/23 16:18 nikolaj 2013/05/23 16:17 nikolaj 2013/05/23 16:16 nikolaj 2013/05/23 16:16 nikolaj created Next revision Previous revision 2014/02/08 18:33 nikolaj 2013/12/21 19:57 external edit2013/09/13 20:22 nikolaj 2013/09/09 15:52 nikolaj 2013/09/06 22:04 external edit2013/08/16 14:52 nikolaj 2013/08/15 09:14 nikolaj 2013/08/14 22:11 nikolaj 2013/08/14 22:11 nikolaj 2013/08/06 11:56 nikolaj 2013/08/06 11:54 nikolaj 2013/08/06 11:45 nikolaj old revision restored (2013/05/23 16:28)2013/08/06 11:45 nikolaj 2013/05/23 16:28 nikolaj 2013/05/23 16:21 nikolaj 2013/05/23 16:21 nikolaj 2013/05/23 16:19 nikolaj 2013/05/23 16:19 nikolaj 2013/05/23 16:18 nikolaj 2013/05/23 16:17 nikolaj 2013/05/23 16:16 nikolaj 2013/05/23 16:16 nikolaj created Line 1: Line 1: ===== Iterated function ===== ===== Iterated function ===== ==== Set ==== ==== Set ==== - | @#88DDEE: $f:X\to X$ | + | @#55CCEE: context ​    | @#55CCEE: $f:X\to X$ | - | @#88DDEE: $n\in \mathbb N, n\neq 0$ | + | @#55CCEE: context ​    | @#55CCEE: $n\in \mathbb N, n\neq 0$ | - | @#FFBB00: $f^n$ | + | @#FFBB00: definiendum ​| @#FFBB00: $f^n$ | Iteratively defined as follows: Iteratively defined as follows: - | @#FFBB00: $f^1:=f$ | + | @#FFBB00: definiendum ​| @#FFBB00: $f^1:=f$ | - | @#FFBB00: $f^{n}:​=f\circ f^{n-1}$ | + | @#FFBB00: definiendum ​| @#FFBB00: $f^{n}:​=f\circ f^{n-1}$ | ==== Discussion ==== ==== Discussion ==== - We call a function //​idempotent//​ if $f^2=f$. We say it's an //​involution//​ if $f^2=\text{id}$. - - | @#EEEE55: $f$ ... idempotent $\equiv f^2=f$ | - | @#EEEE55: $f$ ... involution $\equiv f^2=\text{id}$ | - ==== Parents ==== ==== Parents ==== === Subset of === === Subset of === [[Unary operation]] [[Unary operation]] - === Requirements ​=== + === Context ​=== [[Relation concatenation]],​ [[Relation concatenation]],​ [[Natural number]] [[Natural number]]