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characteristic_function [2013/09/06 22:04] 127.0.0.1 external edit |
characteristic_function [2014/04/08 14:48] nikolaj |
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| ===== Characteristic function ===== | ===== Characteristic function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#88DDEE: $A\subseteq X$ | | + | | @#55CCEE: context | @#55CCEE: $A\subseteq X$ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $\chi_A:X\to \{0,1\} $ | | |
| - | | @#55EE55: $ \chi_A $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \chi_A(x) := \begin{cases} 1 & \mathrm{if}\ x\in A\\\\ 0 & \mathrm{else} \end{cases}$ | |
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| - | | @#88DDEE: $\chi_A:X\to \{0,1\} $ | | + | |
| - | + | ||
| - | | @#55EE55: $ \chi_A(x) := \begin{cases} 1 & \mathrm{if}\ x\in A\\\\ 0 & \mathrm{else} \end{cases}$ | | + | |
| The complement $A^c$ is taken w.r.t. $X$. | The complement $A^c$ is taken w.r.t. $X$. | ||
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| - | === Discussion === | + | |
| The symbols "$0,1$" here are essentially placeholders. One could choose any set of two distinct elements as codomain. | The symbols "$0,1$" here are essentially placeholders. One could choose any set of two distinct elements as codomain. | ||
| === Reference === | === Reference === | ||
| Line 20: | Line 15: | ||
| === Refinement of === | === Refinement of === | ||
| [[Function]] | [[Function]] | ||
| - | === Requirements* === | + | === Context === |
| [[Subset complement]] | [[Subset complement]] | ||
