Proving Unboundedness of B if A is Unbounded

[Seacow1988]

If A, B are nonempty subsets of R and A is a subset of B, how can you prove that: if A is unbounded, B is unbounded?

 

[gb7nash]

Suppose to the contrary that B is bounded. So there exists a real number M such that |b| < M for all b in B. Do you see where the problem lies?

 

[Landau]

If you understand the definition of 'boundedness' and 'subset' then this is trivial.