The well-known Riemann rearrangement theorem asserts that a series is absolutely convergent if and only if all its rearrangements are convergent; furthermore, any conditionally convergent series can be rearranged so as to converge to any desired extended real value. But how many rearrangements suffice to test for absolute convergence in this way? The rearrangement number, a new cardinal characteristic of the continuum, is the smallest size of a family of permutations, such that whenever the convergence and value of a convergent series is invariant by all these permutations, then the series is absolutely convergent. The exact value of the rearrangement number turns out to be independent of the axioms of set theory. In this talk, I shall place the rearrangement number into a discussion of cardinal characteristics of the continuum, including an elementary introduction to the continuum hypothesis and, time permitting, an account of Freiling’s axiom of symmetry.