Thread: dense

Hi--

is the set {1/n | n \in N} dense in [0,1].

Originally Posted by Chandru1

Hi--

is the set {1/n | n \in N} dense in [0,1].

A set is dense in if the set unioned with its limit points gives you . Now, there is nothing between 1/2 and 1 in your set; your set intersect trivially with . 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.