Thanks to this we also may have the primitive predicate " bit ", where bit ( x, k ) is true if only the th bit of is 1 . ( We can replace addition and multiplication by ternary relations such that plus ( x, y, z ) is true iff x + y = z and times ( x, y, z ) is true iff x * y = z ).
12.
Moreover, Lacan's proposal that " the ternary relation of the Oedipus complex " liberates the " prisoner of the dual relationship " of the son mother relationship proved useful to later psychoanalysts; thus, for Bollas, the " achievement " of the Oedipus complex is that the " child comes to understand something about the oddity of possessing one's own mind [ . . . ] discovers the multiplicity of points of view ".
13.
An example of a " ternary relation " ( i . e ., between three individuals ) is : " X was introduced to Y by Z ", where \ left ( X, Y, Z \ right ) is a 3-tuple of persons; for example, " Beatrice Wood was introduced to Henri-Pierre Roch?by Marcel Duchamp " is true, while " Karl Marx was introduced to Friedrich Engels by Queen Victoria " is false.
14.
The " schemata " [ ? ? ] is a Transformation rules e . g . the rules of logical deduction : Define binary and ternary relations that such as " immediate consequence of " ( Godel 1931, Kleene 1952 ), or " conversion " ( Church 1934 ) with respect to two or three objects a and b and c e . g . the binary operation ( a, b ) and the ternary operation ( ( a, b ), c ) where ( a, b ) are an ordered pair of objects and c is the outcome:
15.
I figure that binary relations give 2 ^ n options for each element, so multiplying together for all n elements we get ( 2 ^ n ) ^ n = 2 ^ { n ^ 2 }, and similarly ternary relations give 2 ^ ( n ^ 2 ) options for each element because you're looking at relations on \ mathbb { X } \ times \ mathbb { X } ( that's the product if it's unclear ! )-continuing in this way you'd get the total number of relations, from binary to n-ary, equal to \ sum _ { r = 1 } ^ n 2 ^ { n ^ { r + 1 } }, right?
16.
For example the category "'Grp "'of groups and their homomorphisms is realized by "'Chu "'( "'Set "', "'8 "') since the group multiplication can be organized as a ternary relation . "'Chu "'( "'Set "', 2 ) realizes a wide range of " logical " structures such as semilattices, distributive lattices, complete and completely distributive lattices, Boolean algebras, complete atomic Boolean algebras, etc . Further information on this and other aspects of Chu spaces, including their application to the modeling of concurrent behavior, may be found at " Chu Spaces ".
