I'm having difficulty knowing where to start with this question:
Show that:
($\mathbb{Q}(\sqrt{2})$,<)$\cong$($\mathbb{Q}$,<)
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1https://en.m.wikipedia.org/wiki/Back-and-forth_method , look at the application for dense linear orders. – Shervin Sorouri Mar 17 '19 at 11:28
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1Also you may want to look at this: https://math.stackexchange.com/questions/2940700/let-p-q-prec-be-countable-dense-and-linearly-ordered-sets-without-end/2940728 – Shervin Sorouri Mar 17 '19 at 11:32
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1And does the back and forth method show that these are isomorphic? – MicroscooterMan Mar 17 '19 at 13:23
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Yes. You have to show that $\mathbb{Q}(\sqrt{2})$ is a dense countable linearly ordered set tho. – Shervin Sorouri Mar 17 '19 at 17:37