Rearranging Series Constructively

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.