Hi--
is the set {1/n | n \in N} dense in [0,1].
A set is dense in $\displaystyle [0, 1]$ if the set unioned with its limit points gives you $\displaystyle [0, 1]$. Now, there is nothing between 1/2 and 1 in your set; your set intersect trivially with $\displaystyle (1/2, 1)$. So, well, does there exist a sequence in your set which has limit, say, 3/4?
simply ask yourself the following:
is every number in [0,1] either a limit point of the given set or in it?
if yes, then you have a dense set in [0,1]
else, you don't
in this case, the example given (3/4) does not satisfy any of the two conditions. (why?)
Conclude.