Wed. 9/19/2018: Discussed Section 13.2 (pp. 522-524 only) ---- gave example of the numerical sequence of positive numbers 1/n that is Cauchy, but does not converge to a positive number; gave example of the vector space of finite Fourier series and used the finite-series approximation of a square wave to give a sequence of waveforms that is Cauchy, but does not converge to a finite Fourier series. These examples motivate the need to consider normed vector spaces that are complete.
Problems:Chapter 13: 15(use the triangle inequality of norms), 21, 23, 41(generalize Example 13.15 on p. 534).
Find Rubric