Prove that for every natural number n, the set { m/n :m is a natural numer} is unbounded above in R.
Prove: , is unbounded above in .
Proof: Fix . Assume is bounded; i.e. such that . This implies that . Because is a constant, though, the previous statement implies that is bounded above by , which is of course a ridiculous statement. Thus we have a contradiction and is unbounded above.