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

‘Dialectic of Arithmetical Operations’ --

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

Dear Reader,

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

The Triadic, Platonian-format ‘dialectogram’, posted herein 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 direct Operations of “Natural Numbers” arithmetic. 

Those categories, in that order, we name additions, multiplications, & ‘‘‘distributions’’’.

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

E.g., 5 x 4 = 4 + 4 + 4 + 4 + 4  =  20  = 5 + 5 + 5 + 5 = 4 x 5.

This ‘dialectogram’ also points out that each instance of a [compound] ‘‘‘distribution’’’ Operation is a ‘complex unity’, combination, unification, or hybridization of addition and multiplication Operations. 

E.g.,

a x (b + c) =  (a x b) + (a x c)

-- and --

(b + c) x a  = (b x a) + (c x a).

 

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