Examples 7.1.2(b):

What is the norm of a partition of n equally spaced points in the interval [a, b] ?
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If we want to divide [a, b] into n subintervals so that each of them has the same width, then we must choose the width of those subintervals to be b - a / n. Moreover, the partition would consist of the following n+1 points:
x0 = a = a + 0 . b - a / n
x1 = a + 1 . b - a / n
...
xn-1 = a + (n-1) . b - a / n
xn = a + n . b - a / n = b

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007