‘Dialectic of Arithmetical Operations’ -- ‘Dialectogram’: ‘The Systematic Dialectic of the Domain of Standard Elementary Arithmetical INVERSE Operations, First Triad.

‘Dialectic of the Standard Arithmetical Operations’ Series --

‘Dialectogram’: ‘The Systematic Dialectic of the Domain of Standard Elementary Arithmetical INVERSE Operations’, First Triad.

Dear Reader,

The simple, everyday case treated in this blog entry can serve as yet another example of the ubiquity of a ‘dialecticality’ that so often goes unnoticed today.

The Triadic, Platonian-format ‘dialectogram’ below describes, in systematic order -- in consecutive, simplest to more complex order -- the first three categories of a systematic, dialectical method of presentation of the Domain of the elementary INVERSE Operations of “Whole Numbers” arithmetic. 

Those categories, in that order, we name subtractions, divisions, & ‘‘‘divided differences’’’.

The phonetic-textual, phonogramic content of this ‘phono-ideo-pictogramic dialectogram’, points out that each instance of the division Operation is an «aufheben» transformation/elevation/conservation of a number of subtraction Operations, i.e., is a ‘meta-instance-ization’ of those multiple subtraction Operation instances, each such single instance of a division Operation being made up out of a multiplicity of subtraction Operations. 

E.g.,   12/3  =  4 because 12 - 3 - 3 - 3 - 3  =  0;

        12/4   =  3 because 12 - 4 - 4 - 4  =  0, etc., etc.

This ‘dialectogram’ also points out that each instance of a [compound] ‘‘‘divided differences’’’ Operation is a ‘complex unity’, combination, unification, or hybridization of subtraction and division Operations, as in the classic Newtonian “divided differences”, “calculus of finite differences”-invoking definition ('=') of the “non-elementary” differentiation operation of the Newtonian/Leibnizian “differential calculus” -- 

df(x)/dx   =   lim( (f(x + Dx) - f(x))/((x + Dx) - (x)) )

                      Dx ---> 0

FYI:  Much of the work of Karl Seldon, and of his collaborators, including work by “yours truly”, is available for free-of-charge download via --

www.dialectics.info

Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],

Officer, F.E.D. Office of Public Liaison