Read e-book online The reflection of life : functional entailment and imminence PDF
By Aloisius Ho-Yin Louie
Mapping Origins.- From issues to Sets.- rules of Set-Valued Mappings.- Censusing Independence.- Set-Valued Mappings Redux.- The good judgment of Entailment.- The Imminence Mapping.- Imminence of Life.- Imminence in Models.- Connections.- Symbiosis.- Pathophysiology.- Relational Virology.- Therapeutics
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Extra resources for The reflection of life : functional entailment and imminence in relational biology
Defining a choice mapping f ) is a simple procedure; not so when I is infinite. There is no prescription of how infinitely many choices are to be made, and that is why the existence of the choice mapping has to be postulated in an axiom. It is almost a convention in mathematics that one explicitly acknowledges when a consequence depends on the Axiom of Choice. , n ` ^x ` An indexed family i iI (for some natural number n ) or I in X with an index set 1 is called a sequence (finite or infinite, respectively) in X .
The ‘set-to-set’ mapping 3F : 3X o 3Y has the following properties (cf. 10 Theorem Let F : X –l Y be a set-valued mapping and A, B X . Then: i. A F A ii. A B F A F B . iii. F A * B . F A * F B . iv. F A B F A F B . v. F B A F B F A . Since a (single-valued) mapping is a specialized set-valued mapping through the correspondence (4), whatever properties that set-valued mappings have cannot be contradictory to (but may be weaker than) their analogs for mappings. 19. i now only goes one way.
F 1 B A Let f : X o Y and A, B Y . Then: f 1 A f . A f 1 B . f 1 A * f 1 B . f 1 A f 1 B . f 1 B f 1 A . 20, one sees that now in properties iv and v, set inclusion has been replaced by equality. 15) that the inverse mapping f 1 is necessarily a bijective mapping of ran f onto X dom f . These ‘improvements’ result as a consequence. 20 says that 3f : 3Y o 3X is in fact a Boolean algebra homomorphism. Note also that f 1 and f 1 Y X ; thus the least and greatest elements are preserved 1 by the inverse mapping f .
The reflection of life : functional entailment and imminence in relational biology by Aloisius Ho-Yin Louie