This is an exercise question from Chapter 2 of A Course in Galois Theory by D.J.H. Garling:
Suppose that $(A,\leq)$ is an infinite well-ordered set. Show that there is a unique element $a$ such that $\{x:x is infinite, while $\{x:x is finite for each $b.
Am I missing something here? $\mathbb{N}$ is well-ordered, but does not satisfy the described property...?