Changes

=====2.3.2.2.  Characteristic Relation=====

=====2.3.2.2.  Characteristic Relation=====

Characteristic relation denotes the two-way link that relates boolean functions with subsets of their boolean universes, whether pictured as Venn diagram regions or n-cube subsets does not matter.  Indicative conversion describes the traffic or exchange on this link between the two termini.  Given a set A, the function fA which has the value 1 on A and 0 off A is commonly called the characteristic function or indicator function of A.  Since every boolean function f determines a unique set S = Sf of which it is the indicator function f = fS, this forms a convertible relationship between boolean functions and sets of boolean vectors.  This fact is also described as an isomorphism between the function space (U → B) and the power set P(U) = 2U of the universe U.  The associated set Sf is often called the support of the function f.  Alternatively, it may serve as a helpful mnemonic and a useful handle on this edge of the analogy to call Sf the characteristic region, indicated set, or simply the indication of the function f, and to say that the function characterizes or indicates the set where its value is positive (that is, greater than 0, and therefore equal to 1 in B).

Characteristic relation denotes the two-way link that relates boolean functions with subsets of their boolean universes, whether pictured as Venn diagram regions or ''n''-cube subsets does not matter.  Indicative conversion describes the traffic or exchange on this link between the two termini.  Given a set ''A'', the function ''f''_''A'' which has the value 1 on ''A'' and 0 off ''A'' is commonly called the ''characteristic function'' or the ''indicator function'' of ''A''.  Since every boolean function ''f ''determines a unique set ''S'' = ''S''_''f'' of which it is the indicator function ''f'' = ''f''_''S'' , this forms a convertible relationship between boolean functions and sets of boolean vectors.  This fact is also described as an isomorphism between the function space (''U'' → '''B''') and the power set ''P''(''U'') = 2^''U'' of the universe ''U''.  The associated set ''S''_''f'' is often called the ''support'' of the function ''f''.  Alternatively, it may serve as a helpful mnemonic and a useful handle on this edge of the analogy to call ''S''_''f'' the ''characteristic region'', ''indicated set'', or simply the ''indication'' of the function ''f'', and to say that the function ''characterizes'' or ''indicates'' the set where its value is positive (that is, greater than 0, and therefore equal to 1 in '''B''').

=====2.3.2.3.  Indicative Conversion=====

=====2.3.2.3.  Indicative Conversion=====