We show that exact counting and approximate counting are polynomially equivalent. That is $P^\{\#P\}\; =\; P^\{Approx\#P\}$, where #$P$ is a function that computes the number of solutions to a given Boolean formula $f$ (denoted by $||f||$), and Approx#P computes a short list that contains $||f||$. It follows that if there is a good polynomial time approximator for #$P$ (i.e., one where the list has at most $O(|f|1-ϵ)$ elements), then $P\; =\; NP\; =\; P^\{\#P\}$ and probabilistic polynomial time equals polynomial time. Thus we have strong evidence that #$P$ cannot be easily approximated.