yeah it isn't, however we can always choose an r so that it is?
Look this is a waste of time.
We have no idea where your going with this thread.
Post a problem. A complete well formed problem. Stop making us guess as to what you are trying to ask.
If A is an open subset then proof
Assume that .
Then as A is open from the definition we have that for .
Contradiction- as we assumed that but .
I was asking if I can always choose an r such that ?
Well thank you for finally posting an intelligible problem.
It is well know that an open set in cannot contain a maximal element.
Recall that between any two real numbers there is a real number.