Question

is the set {1/n : n natural } open? i suspect yes since every element is not an interior point

Answer 1

You need to give the set a topology before you can talk about open and closed.

Answer 2

Is this a subset of \(\mathbb{R}\) with the usual topology?

Answer 3

It's real analysis so no?

Answer 4

dumb question
do we also consider half open sets?
or are we only discussing open or closed?

Answer 5

only open and closed

Answer 6

In an open set every point IS an interior point. There are no boundary points

Answer 7

yes, so the given set is not open then?

Answer 8

Correct

Answer 9

but what about 1
I know 0 isn't included in the set but 1 is

Answer 10

1 is not interior though , so ..

Answer 11

oh ok

Answer 12

ok thank you everybody