Changes

Using the axiom of choice, we pick a single point from each orbit and call this set <math>W \ </math>. Note that <math>\mathbb{F}(W) = \mathbb{S}^2 - B \ </math>.

Using the axiom of choice, we pick a single point from each orbit and call this set <math>W \ </math>. Note that <math>\mathbb{F}(W) = \mathbb{S}^2 - B \ </math>.

Make sure you understand the notation: <math>\mathbb{F} \ </math> is a set of rotations, <math>W \ </math> is a set of points, and <math>\mathbb{F}(W) \ </math> is the set of points resulting from applying every rotation in <math>\mathbb{F} \ </math> to every point in <math>W \ </math>. Similarly we will be defining <math>U,D,L,R \ <math> as sets of rotations and <math>U(x), etc. \ </math> as the point <math>x \ </math> rotated by all the points in <math>U \ </math>.

Make sure you understand the notation: <math>\mathbb{F} \ </math> is a set of rotations, <math>W \ </math> is a set of points, and <math>\mathbb{F}(W) \ </math> is the set of points resulting from applying every rotation in <math>\mathbb{F} \ </math> to every point in <math>W \ </math>. Similarly we will be defining <math>U,D,L,R \ </math> as sets of rotations and <math>U(x), etc. \ </math> as the point <math>x \ </math> rotated by all the points in <math>U \ </math>.

==Interpretation==

==Interpretation==