If $(Q,\leq)$ is any preordered set (that is, $\leq$ is a reflexive and transitive, but not necessarily anti-symmetric relation), then we say that $S\subseteq Q$ is

*unbounded*if for all $q\in Q$ there is $s\in S$ such that $s \not \leq q$, and*dominating*if for all $q\in Q$ there is $d \in S$ such that $q\leq d$.

We let the *unbounded number* ${\frak b}(Q)$ and the *dominating number* ${\frak d}(Q)$ be the smallest cardinality of an unbounded, respectively dominating subset of $Q$.

Let $\text{NPU}(\omega)$ be the set of non-principal ultafilters on $\omega$. The *Rudin-Keisler preorder* on $\text{NPU}(\omega)$ is defined by
$${\cal U} \leq_{RK} {\cal V} :\Leftrightarrow (\exists f:\omega\to\omega)(\forall U\in{\cal U}) f^{-1}(U)\in {\cal V} .$$ It is easy to verify that $\leq_{RK}$ is a preorder.

**Question.** What are ${\frak b}(\text{NPU}(\omega))$ and ${\frak d}(\text{NPU}(\omega))$?