MathDB

Countable Zorn Lemma

Source: Iranian National Olympiad (3rd Round) 2006

September 11, 2006

combinatorics proposedcombinatorics

Problem Statement

Let

C

be a (probably infinite) family of subsets of

\mathbb{N}

such that for every chain

C_{1}\subset C_{2}\subset \ldots

of members of

C

, there is a member of

C

containing all of them. Show that there is a member of

C

such that no other member of

C

contains it!