Euler's work on divergent series was guided by computational procedures, rather than any definition of the "value" of such a series. E.g., he was happy to have half a dozen procedures that indicated ...
Here is a basic, though very important, example: Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of ...
Recently, while undertaking a study of commutative algebra, I learned three concepts: (i) a local ring, (ii) a regular local ring and (iii) a regular ring. At the end, I found myself asking this ...