No set (0,1) as accumulation points
Hello again. My current problem is that I don't understand how this can be:
Show that there is no set with the interval (0,1) as it's accumulation points.
To me it seemes as though the set itself has accumulation points within it so why wouldn't it itself have accumulation points. It's hard to imagine that there is no sequence contained in (0,1) that does not contain an accumulation point in it.
Unfortunately most of the sequences I can think of have an accumulation point of 0 or 1 so I can't think of one specifically.
A useful hint would be appreciated or perhaps a disproof of my assumptions. Thanks.