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

- function – operation – procedure
- series – polynomial
- 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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