Cardinality of stationary subsets I am using the following definition of a stationary set:
Assuming that $cof(\kappa)>\omega$, we call a subset $A$ of $\kappa$ stationary if it meets every closed unbounded subset of $\kappa$.
[Here, for $κ ∈$ Card and $C ⊆ κ$, $C$ is unbounded in $κ$ if
$∀α < κ$ $∃β ∈ C$ $α < β$.
$C$ is closed in $κ$ if
$∀λ < κ (λ$ is a limit ordinal ∧ $C ∩λ$ is unbounded in $λ→λ ∈ C)$.
Thus $C$ contains its limit points $<κ$.]
Now I need to show that every stationary subset of $\kappa$ has cardinality at least $cof(\kappa)$ and that there is a stationary subset of $\kappa$ of cardinality $cof(\kappa)$
Does anyone have any hint of how to do that?

For the first one, prove that a stationary set is always unbounded, so its cardinality is at least as $\operatorname{cf}(\kappa)$.
For the second one, prove that if $\alpha=\operatorname{cf}(\kappa)$, then there is a continuous function from $\alpha$ to $\kappa$ with an unbounded range. This range is now closed and unbounded, and therefore stationary.
