The over 150 years old Riemann's rearrangement-of-series Theorem (R)
states that one can rearrange the terms of a given conditionally
convergent series of real numbers to obtain a "rearranged" series that
converges to an arbitrarily given real.
LS (early 20th century) is a beautiful generalization of R.
It tells us that in Rn, SS(h), the set-of-sums of the convergent rearrangements of a given series Σh(n), where h = (h(1), h(2),.,h(n),.) is a given sequence in Rn, if nonempty, is an affine subspace (a displacement of a linear subspace) of Rn. R, LS and the situation beyond finite dimensions will be discussed. An interesting instance of h in the infinite dimensional setting that extends Riemann's theorem R and Levy-Steinitz Theorem LS will be presented.