Problem 117 (difficulty: 7/10)

Given an ordered field \(\displaystyle R\) and a subfield \(\displaystyle \Q\) show that if

\(\displaystyle (\forall a,b \in R) \; \bigg((1<a<b<2) \Rightarrow \Big((\exists q\in \Q) \; (a<q<b)\Big)\bigg), \)

then \(\displaystyle R\) satisfies the Archimedean axiom.

Give me another random problem!

Subject, section:
Requested difficulty:
Request for a concrete problem:I want problem no.

Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government