Algebraic Concepts Characterized

Polynomials and Series

How can the differences between the following notions be distinguished, how are the involved levels of abstraction to be properly organized?

  1. function – operation – procedure
  2. series – polynomial
  3. Differential – Integral

A polynomial is responsive (literally) to many “sets of rules” (many (Gk. poly) precepts (Gk. nomos, in German “Satzung” oder “Gesetz”, also name or family, German “Geschlecht” ). A polynomial consists of the product of a constant (coefficient, can be integer, complex, algebraic…) and an finite number of indeterminates. (-> it is inadequate to call them variables, the term variable should be reserved only for functions. A polynomial defines a function, but is itself more abstract than any particular function).

A series is defined by one nomos, one “precept” or “set of rules” which gives the guidance to construct a series (and thus define it even though it may be infinite / non-denumberable). A series comprehends the added values of a variable (in a sequence).

——-> post to be continued! 

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