I have a problem that I am seriously stuck on. I'm not sure what to do I've seen similar proofs online with the least positive rational number but this is apparently different and I'm not sure why.
Prove the statement “There is no smallest rational number greater than 2” by contradiction.
Suppose there was a smallest rational number greater than $2$. Call it $k =p/q$.
Then consider $ k' = \frac{2+k}{2}$. This is a number bigger than $2$ and less than $k$. Also $k'$ is rational. Therefore there is no smallest rational number greater than $2$.