Prove that for every natural number n, the set { m/n :m is a natural numer} is unbounded above in R.

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- September 17th 2009, 09:26 AMJdg6057Proving sets unbounded
Prove that for every natural number n, the set { m/n :m is a natural numer} is unbounded above in R.

- September 17th 2009, 11:30 AMredsoxfan325
__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.