# Thread:

1. ## dense

Hi--

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

2. Originally Posted by Chandru1
Hi--

is the set {1/n | n \in N} dense in [0,1].
A set is dense in $[0, 1]$ if the set unioned with its limit points gives you $[0, 1]$. Now, there is nothing between 1/2 and 1 in your set; your set intersect trivially with $(1/2, 1)$. So, well, does there exist a sequence in your set which has limit, say, 3/4?

3. 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.
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