Right now in my introductory real analysis course, we are studying integration theory, and in particular the Archimedes-Riemann theorem. The Archimedes-Riemann theorem requires the existence of an Archimedean sequence of partitions, $\{P_n\}$, for integrability.
But what is a sequence of partitions, $\{P_n\}$? In particular, what is $P_i$? This is never clarified in the book. My intuition, however, based on all of the limits involving ${P_n}$, is that $i$ corresponds in some way with the number of partitions, and as $n \rightarrow \infty$, $P_n$ gets finer and finer.
Is this correct?