Example 4.7.1.32. Let $(T, \leq )$ be a linearly ordered set. Then the cofinality $\mathrm{cf}(T)$ is equal to $\omega $ if and only if $T$ contains an unbounded increasing sequence $\{ t_0 < t_1 < t_2 < \cdots \} $.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$