In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set.
Read more about Family Of Sets: Examples, Properties, Hall's Marriage Theorem, Related Concepts
Famous quotes containing the words family of, family and/or sets:
“Our civility, England determines the style of, inasmuch as England is the strongest of the family of existing nations, and as we are the expansion of that people. It is that of a trading nation; it is a shopkeeping civility. The English lord is a retired shopkeeper, and has the prejudices and timidities of that profession.”
—Ralph Waldo Emerson (1803–1882)
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—Stephanie Coontz (20th century)
“Willing sets you free: that is the true doctrine of will and freedom—thus Zarathustra instructs you.”
—Friedrich Nietzsche (1844–1900)