@XanderHenderson It is off-topic in that it is not actually a reference request by definition. That being said I think MathOverflow might welcome the question.
Some of the answers aren't even answers, I'm surprised the question hasn't been at least protected during its ten-year span.
this answer came in review queue. Ideally this should have been a comment. I saw some more examples of such answers (which should have been comments) by high rep users in review queue.
Let $x, y\in\mathbb R$ and $x<y$. Show that there exist an irrational number $m$ such that $x<m<y$.
