What are the maximal chains and antichains of $S=\{0,1,4,6,7,8,9\}$ under the order of divisibility?

Question

I just really don't understand what 'maximal' is.

Answer 1

A maximal chain is one that cannot be extended.

$1 \mid 4$ is not maximal because it can be extended to $1 \mid 4 \mid 8$.