# Definition talk:Definite Integral/Riemann

My $\$0.02$? Rollback to the previous edit, but replace "Let$S \left({ f; \Delta }\right)$denote the Riemann sum of$f$" with Let$S \left({ f; \Delta }\right)$denote a Riemann sum of$f$. Then make it a theorem/definition/explanation/whatever that all Riemann Sums with such-and-such something converge to the same integral, and you can put that stuff about samplepoint sequences there. --GFauxPas (talk) 13:41, 9 December 2016 (EST) Unfortunately there are always idiosyncrasies in the messy details establishing Riemann integration (subdivisions, "sample points"). Once you've seen them once, the rest is trivially equivalent. Here on$\mathsf{Pr} \infty \mathsf{fWiki}\$, such a heuristic is undesired and we should create a presentation which does this nicely and rigorously. We can do better than selecting an arbitrary approach and declaring it sacrosanct. — Lord_Farin (talk) 16:30, 9 December 2016 (EST)