Question

what is the boundary of {1/n:n in N}

Answer 1

is it (0,1)??

Answer 2

Hmm, what is the definition of the boundary in this case?

Answer 3

well I thought boundary is just a point which has a neighborhood that contains points in the set and not in the set.

Answer 4

I would think the boundary would be maybe \[
\{0\}\cup \{1\}
\]

Answer 5

why would it be that and not include 1/2, 1/3, 1/4... etc.?

Answer 6

Oh, I see what you mean...

Answer 7

The boundary can't be in the interior, correct?

Answer 8

correct. this set does not have any interior points because every neighborhood of x must contain every point in the set.

Answer 9

Then the boundary is just the set itself.

Answer 10

so I would just say bd = {1/n}

Answer 11

\[
\partial \left\{\frac 1n:n \in N\right\} = \left\{\frac 1n:n \in N\right\}
\]