Rearranging Series Constructively
Josef Berger (LudwigMaximiliansUniversität München, Germany)
Douglas S. Bridges (University of Canterbury, New Zealand)
Abstract: Riemann's theorems on the rearrangement of absolutely convergent and conditionally convergent series of real numbers are analysed within Bishopstyle constructive mathematics. The constructive proof that every rearrangement of an absolutely convergent series has the same sum is relatively straightforward; but the proof that a conditionally convergent series can be rearranged to converge to whatsoever we please is a good deal more delicate in the constructive framework. The work in the paper answers affirmatively a question posed many years ago by Beeson.
Keywords: Rieman's theorems, constructive analysis
Categories: G.0
