A problem in Real Analysis/Topology

[mtayab1994]

Why are you saying $m$ is inf(B)? The problem statement only says to show that $m$ bounds B from below and is greater than or equal to $x$. It's not necessarily the greatest lower bound.

Wow I'm really sorry that's another typo the problem statement says to show that B has a and inferior bound not just a lower bound. Hence why I proceeded like that. Is my reasoning correct?