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iterated_function [2013/09/13 20:22] nikolaj |
iterated_function [2014/02/08 18:33] nikolaj |
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| ===== Iterated function ===== | ===== Iterated function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| | @#88DDEE: $ f:X\to X $ | | | @#88DDEE: $ f:X\to X $ | | ||
| | @#88DDEE: $ n\in \mathbb N, n\neq 0 $ | | | @#88DDEE: $ n\in \mathbb N, n\neq 0 $ | | ||
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| ==== Discussion ==== | ==== Discussion ==== | ||
| - | We call a function //idempotent// if $f^2=f$. We say it's an //involution// if $f^2=\text{id}$. | ||
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| - | | @#EEEE55: $f$ ... idempotent $\equiv f^2=f$ | | ||
| - | | @#EEEE55: $f$ ... involution $\equiv f^2=\text{id}$ | | ||
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| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
