# Family

## Family

Synonym for sets in the case in which the elements of the set are themselves sets.

Elements of a family that have common characteristics can be described using rules in which the parameters are called parameters of the family.

### Examples

• The set of parts of a set E, written as $$mathcal{P} left(Eright)$$ is an example of a family whose elements are themselves sets.
• The direction of line D, written as dir D, is a family whose elements are lines parallel to line D.
• The pencil of lines with a centre p is a family of lines that intersect at the point p.
• The equation of the lines with a slope of m = −2 is y = −2x + k where k represents the y-intercept of each line. The set of these lines forms a family of lines with the same slope.