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sav08:sets_and_relations [2009/03/10 20:29] vkuncak |
sav08:sets_and_relations [2009/03/10 20:29] vkuncak |
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Generalization of function update is override of partial functions, $f \oplus g$ | Generalization of function update is override of partial functions, $f \oplus g$ | ||
+ | |||
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==== Range, Image, and Composition ==== | ==== Range, Image, and Composition ==== | ||
+ | The following properties follow from the definitions: | ||
\[ | \[ | ||
- | S \bullet r = ran(\Delta_S \circ r) | + | (S \bullet r_1) \bullet r_2 = S \bullet (r_1 \circ r_2) |
\] | \] | ||
\[ | \[ | ||
- | (S \bullet r_1) \bullet r_2 = S \bullet (r_1 \circ r_2) | + | S \bullet r = ran(\Delta_S \circ r) |
\] | \] | ||