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heres an example of a subset of real numbers thats made up of a union of three different pieces let me diagram out this set two just so that we have something to look at so the picture here is that everything on this number line thats shaded in red is part of my set E and so I want to use this set as my guinea pig to talk about these four different types of points that were concerned with lets start with what I believe to be the most important one of them all those are the interior points so starting from the first definition in this list a point is an interior point if there exists a C a positive number C such that the open interval X minus C to X plus C is all a subset is all contained within the set E so I like to think of this interior points are points to that breathing room or another way to think about it is that these are points that can stretch out their arms and remain inside the set so as an example would we say that for so let me pick the number four its an element t