$\le$ is less-than-or-equal relation.
Is $\langle\Bbb Q\cap((0,1)\cup(4,5)),\le\rangle>$ isomorphic with $\langle\Bbb Q \cap ((0,1)\cup(4,5)\cup\{2,3\},\le\rangle$ ?
They are both totally ordered, countable and none of them has greatest elements or minimum/maximum.
I thought that they are isomorphic but then I heard that they are not. I don't know why.
HINT: Show that having an immediate successor is something preserved by isomorphisms.