So basically, I have no idea how to answer this problem. I tried a few different approaches, including trying to show that the complement of A was closed. I am stuck at the very beginning as I do not know where to start with this problem. Could someone please, at the very least, outline what I am supposed to do to prove this? Thank you.
Here's the problem:
Show that is not a closed set, but that is a closed set.
Okay, I see what you are saying.
Right now, I have supposed c is a cluster point of A.
I used the definition of a cluster point to say that every e-neighborhood of c contains a point x in A such that x is not equal to c
==> x is contained in the e-neighborhood of c= (c-e, c+e) for some e>0
==> |x-c| < e
1. is this right?
2. How would I go about showing 0 is a cluster point and that A doesn't contain it? I'm slightly confused as what to do with the e.
EDIT: wow, sorry guys. just realized I made a grave mistake. Please re-read my question