kelpfoot Imagine the line segment [0,1). I want you to divide this segment into four equal parts, [0,.25), [.25,.5), [.5,.75), and [.75,1). Remove the third segment, [.5,75), and leftover you have [0,.25), [.25,.5), [.75,1).

For each of the three segments you have left over, I want you to do the same thing as before: divide it into four equal segments, and remove the third segment.

Let's give a name to each of those sets we came up with. Let X0 be [0,1), let X1 be [0,.25) U [.25,.5) U [.75,1), let X2 be [0,.125) U [.1875,.25) U ..., et cetera, with Xn being the set you have left over after the nth iteration of the procedure I described. Let X be defined as the limit, as n approaches infinity, of Xn. This set, X, has "box-counting" dimension 0.5, because if you imagine any random line segment of very short length, (and that line segment is between 0 and 1,) there is a fifty percent chance the segment contains a point from X and a fifty percent chance it does not.

Also, you're a pedophile.