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surjective_function [2014/03/21 11:11] 127.0.0.1 external edit |
surjective_function [2014/10/29 19:53] nikolaj |
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==== Set ==== | ==== Set ==== | ||
| @#55CCEE: context | @#55CCEE: $X,Y$ | | | @#55CCEE: context | @#55CCEE: $X,Y$ | | ||
- | + | | @#FFBB00: definiendum | @#FFBB00: $f\in$ it | | |
- | | @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{Surjective}(X,Y) $ | | + | | @#AAFFAA: inclusion | @#AAFFAA: $f:X\to Y $ | |
- | + | | @#55EE55: postulate | @#55EE55: $\text{im}(f)=Y $ | | |
- | | @#55CCEE: context | @#55CCEE: $ f:X\to Y $ | | + | |
- | + | ||
- | | @#55EE55: postulate | @#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 === | + | |
- | | @#EEEE55: predicate | @#EEEE55: $Y$ ... countable $\equiv \mathrm{Surjective}(\mathbb{N},Y)\neq\emptyset$ | | + | |
==== Parents ==== | ==== Parents ==== | ||
=== Subset of === | === Subset of === |