From: "Oleg V. Poliannikov" Subject: Re: Riemann integration Date: Sun, 19 Sep 1999 00:01:41 -0400 Newsgroups: sci.math Keywords: Standard definition of Riemann integral > > Not even the limit of a sequence, since uncountably many objects are > > taken into account. > > You need to go back to your textbook to understand the definition of a > Riemann integral. Thank you very much for the advise. I won't use if you don't mind since I know the definition by heart. I'll give it to you so that you would also learn something. Let [a,b] be a segment. Definition. We will call T a partition of [a,b] if T={x_n},n=0...N, a=x_0<...R Definition. A Riemann sum of function f is mapping from P to R defined by the following formula: S_f(T)=\sum_{i=1}^{N}{f(\ksi_i)(x_i-x_{i-1})} Definition. A function f is called Riemann integrable is there exists a limit J = lim_{d(T)->0}{S_f(T)} J is then called the Riemann integral of f over [a,b]. Hope it wasn't very difficult for you. Oleg*