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surjective_function [2014/02/08 02:48] nikolaj |
surjective_function [2014/10/29 19:53] nikolaj |
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| ===== Surjective function ===== | ===== Surjective function ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $f\in$ it | | |
| - | | @#FFBB00: $ f\in \mathrm{Surjective}(X,Y) $ | | + | | @#AAFFAA: inclusion | @#AAFFAA: $f:X\to Y $ | |
| - | + | | @#55EE55: postulate | @#55EE55: $\text{im}(f)=Y $ | | |
| - | | @#88DDEE: $ f:X\to Y $ | | + | |
| - | + | ||
| - | | @#55EE55: $ \text{im}(f)=Y $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| A function can only be or not be surjective w.r.t. to a stated codomain. A function is always surjective w.r.t. it's own image. See [[Function]] for further discussion. | A function can only be or not be surjective w.r.t. to a stated codomain. A function is always surjective w.r.t. it's own image. See [[Function]] for further discussion. | ||
| === Predicates === | === Predicates === | ||
| - | | @#EEEE55: $Y$ ... countable $\equiv \mathrm{Surjective}(\mathbb{N},Y)\neq\emptyset$ | | + | | @#EEEE55: predicate | @#EEEE55: $Y$ ... countable $\equiv \mathrm{Surjective}(\mathbb{N},Y)\neq\emptyset$ | |
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Function]] | [[Function]] | ||
| - | === Requirements === | + | === Context === |
| [[Image]] | [[Image]] | ||
