Rearranging Series Constructively

Josef Berger (Ludwig-Maximilians-Universität 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 Bishop-style 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