Question about Dense sets in R.

[cragar]

Homework Statement

Decide wheter the following sets are dense in ℝ, nowwhere dense in ℝ
, or somewhere in between.
a) A= $\mathbb{Q} \bigcap [0,5]$
b) $B= \{ \frac{1}{n} : n \in \mathbb{N}$
d) the cantor set.

The Attempt at a Solution

a) so we have the rationals intersected with [0,5], so we have all the rationals from
[0,5], which is dense on that interval.
b) this set does not seem like it is dense, except maybe close to zero, but even then
I could find an interval close to zero that did not contain any elements in my set.
d) The cantor set is nowhere dense because it has no intervals, if I have an interval of positive length stating at one of the endpoints of the cantor set it would stick out and it wouldn't contain any points in my set.

 

[Office_Shredder]

Your answer for d is confusing, a set does not need to contain an interval to be dense, for example the rationals

 

[cragar]

is the second thing I said in part d okay. " if I have an interval of positive length stating at one of the endpoints of the cantor set it would stick out and it wouldn't contain any points in my set."