Some Algebra of Dimensions

Construction of Intersections

The intersection of two sets, A and B, is the set consisting of all elements belonging to both sets.

For example,

A = {1,2,3}, B = {2,3,4,5}. Then A B = {2,3}

A is the square, B is the line segment, the smaller line segment is the intersection A B

There are other possibilities: the line segment could just touch the square in a single point, or miss the square completely.

A is the gasket, B is the line segment, the points in common are the intersection A B, here a very sparse set.

Return to the algebra of dimensions.