dc.description.abstract | In this paper, we will examine Riemann's rearrangement theorem for sequences of real numbers. Continuing on, we will briefly discuss previous
generalizations of the theorem to the n dimensional case. Because of the
difficulty of that proof, we present a more approachable proof for the case
of complex numbers. Our proof is not significantly more difficuult than
the proof for real numbers. Furthermore, key aspects of the proof can
be applied to the n dimensional case. From there, we are able to prove
the n dimensional case using elementary techniques. We conclude by considering the possibility of an infinite dimensional generalization through
sequence or function spaces. | en |