= Bounding-to-almost-disjointness inequality
{title2=$\mathfrak b\le\mathfrak a$}
For an infinite <almost disjoint family on omega> of size less than the <bounding number>, select countably many members and remove their intersections with earlier selected members to obtain infinite disjoint <sets> $C_n$. Bound, eventually and simultaneously, the finite intersections of each member with $C_n$. Choose one point of each $C_n$ above its bound. The resulting infinite <set> is almost disjoint from every original member, proving the family is not maximal. A selected member has one exceptional infinite intersection, which is ignored in its bounding <function>.
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