Let $\{a_n\}$ be a sequence of reals such that $a_n=1$ or $a_n=-1$.
Let $A=\{n\in \mathbb{N}|a_n=1\}$ and $B=\{n\in \mathbb{N}|a_n=-1\}$.
Suppose $A$ is equipotent with $B$. That is, $|A|=|B|=\aleph_0$.
Here, how do i prove that partial sum of $\sum a_n$ form a bounded sequence?
Or is it false?