Whilst reading the answers to this question, one of the answers states:
"The problem of series that are not absolutely convergent is that you can't make arbitrary rearrangement of the terms."
However, my understanding was that due to the commutative law, we could write the following (c.f. Concrete Mathematics):
$$\sum_{k\in\mathbb{K}}{a_{k}}=\sum_{p(k)\in\mathbb{K}}{a_{p(k)}},$$
For any permutation function $p(k):\mathbb{Z}\to\mathbb{Z}, \space\forall k \in\mathbb{Z}$, in which all integers are mapped to an integer without duplicity, and for all sequences $a_{k}$.
Is this true even for conditionally converging series, if so, is my confusion based on the author of that answer's definition of "arbitrary rearrangement" (I'm assuming that a permutation is a form of "arbitrary rearrangement")?
Thanks in advance!