dense

• July 12th 2010, 11:46 PM
Chandru1
dense
Hi--

is the set {1/n | n \in N} dense in [0,1].
• July 13th 2010, 01:12 AM
Swlabr
Quote:

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?
• July 13th 2010, 02:23 AM