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.


  • 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.


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