Bounding number
= Bounding number
{title2=$\mathfrak b$}
The least size of a family in $\omega^\omega$ having no common bound for <eventual domination>. Every countable family $(f_i)$ has the bound $g(n)=1+\max_{i\le n}f_i(n)$, so $\aleph_1\le\mathfrak b\le2^{\aleph_0}$.