JUCS - Journal of Universal Computer Science 15(17): 3160-3168, doi: 10.3217/jucs-015-17-3160
Rearranging Series Constructively
expand article infoJosef Berger‡, Douglas S. Bridges§
‡ Ludwig-Maximilians-Universität München, Munich, Germany§ University of Canterbury, Christchurch, New Zealand

Corresponding author: Josef Berger ( jberger@math.lmu.de )

© Josef Berger, Douglas Bridges.
This article is freely available under the J.UCS Open Content License.
Citation: Berger J, Bridges DS (2009) Rearranging Series Constructively. JUCS - Journal of Universal Computer Science 15(17): 3160-3168. https://doi.org/10.3217/jucs-015-17-3160
Open Access
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