Shattered set

Slam is a concept from the field of group theory and set theory in mathematics.

Definition

Be a quantity system and. is - shattered, that is, if and only if one can create any subset of an element of cutting through with.

Example

Be. Is now = three points in that do not lie on a straight line, it is of shattered because you can separate each of the subsets of three points by means of a closed half-plane.

If the points are, however, all on a straight line, so can not be separated from the other two the middle point, and thus is not shattered. Furthermore, no four points can be shattered in the plane by closed half- planes.

• Set theory