Whilst trying to follow a proof from my lecture notes, I stumbled upon the following: $$\gamma \text{ limit, }A\subseteq \gamma, \sup A=\gamma\implies \text{type}(A)\text{ limit}$$ It sounds true, being unbounded in a limit should have a limit for its order type, but I can really put my finger on why exactly that's the case.
Thanks in advance for any ideas and insights!