I asked on MSE this question which I am going to copy-paste here:

"Wikipedia:

"In mathematics, the Riemann series theorem (also called the Riemann rearrangement theorem), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges."

Question of mine is:

If $\sum a_k$ is some conditionally convergent series and $c \in (- \infty, + \infty)$ then is there at least a countably infinite number of permutations $\sigma_m(c);m=1,2,...$ such that $\sum a_{\sigma_m(c)}=c$ for every $c \in (- \infty, + \infty)$?"

There I received a very nice answer:

"Yes. Let the sum of the first $n$ terms of your series be $s_n$. Then the remainder of the series is conditionally convergent, so it can be rearranged to achieve a sum of $c-s_n$. Choose one, and then move on. For each $n$ this yields at least $n!$ permutations that give the desired sum, no more than $n$ of which can have been duplicated at a prior step."

I got an idea from the comment on that answer for a question to ask it here on MO, here it is:

For $\sum a_k$, which is some conditionally convergent series, the number of sums $\sum a_{\sigma}$, where $\sigma$ is some permutation, is uncountable. For every $c \in (-\infty, + \infty)$ there is the set $P_c$ of all permutations $\psi(c)$ for which $\sum a_{\psi(c)}=c$. Can every $P_c$ be uncountable?