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*= −2*x*+*k*where*k*represents the y-intercept of each line. The set of these lines forms a family of lines with the same slope.

- Some of the functions from the family of quadratic functions :