I can see how a set could be neither open nor closed, but I cannot invision something concrete to see how a set could be both open and closed, save defining some set to not contain its boundary points.
I guess I'm a bit new to this game, because things such as the above still seem way to...
An open set:
A set is open if every point of the set lies in an open interval entirely contained in the interval.
A closed set:
A set is said to be closed if it contains all its limit points.
I'm ok with the definition of open sets, but I'm still working on really...
The union/intersection/whatever neurocomp2003 meant to say about [-1, 1) and (-1, 1] is something I can understand.
Correct me if I'm wrong, but the intersection of the two would be open and the union would be closed, right?
I also can understand why the set [-1, 1) is neither open or...
This is not a specific homework question so much as it is a general conceptual question.
My analysis book includes a theorem that states:
1. The union of any number of open sets is an open set.
2. The intersection of a finite number of open sets is an open set.
I follow the proof of...