Block, SkipCaptcha, Automoderated users, edit, rollback
5,023
edits
Changes
→Bernhard Riemann: new section
:Merriam-Webster's definition of infinity is unusually inadequate: "an indefinitely great number or amount." The essence of infinity is not that it is indefinite.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 00:36, 18 May 2018 (EDT)
:Merriam-Webster's definition of infinity is unusually inadequate: "an indefinitely great number or amount." The essence of infinity is not that it is indefinite.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 00:36, 18 May 2018 (EDT)
== Bernhard Riemann ==
''Inherent in the concept of infinity is the concept of infinitesimal: infinity small. Bernhard Riemann identified the sum of infinitesimal strips of area under a function to establish a rigorous definition of the integral, now known as the Riemann Integral. ''
I think that this misrepresents Bernhard Riemann's ideas:
The infinitesimals were tools of the creative geniuses of the 18th century, as Euler, Leibniz, and Newton. Riemann took a step away: he does not talk about things which ''are'' infinitely small, but which ''become'' infinitely small - using the idea of limits. Therefore, the integral is not the sum of infinitesimal strips, but the limit of finite sums of small stripes, becoming smaller and smaller.
That may sound like hair-splitting, but his approach could be rigorously formalized quite easily, while this was much more difficult for infinitesimals.--[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 10:36, 30 July 2018 (EDT)