In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.
Null set was once a common synonym for "empty set", but is now a technical term in measure theory.
Read more about Empty Set: Notation, Properties
Famous quotes containing the words empty and/or set:
“The river’s tent is broken; the last fingers of leaf
Clutch and sink into the wet bank. The wind
Crosses the brown land, unheard. The nymphs are departed.
Sweet Thames, run softly, till I end my song.
The river bears no empty bottles, sandwich papers,
Silk handkerchiefs, cardboard boxes, cigarette ends
Or other testimony of summer nights.”
—T.S. (Thomas Stearns)
“Mothers are not the nameless, faceless stereotypes who appear once a year on a greeting card with their virtues set to prose, but women who have been dealt a hand for life and play each card one at a time the best way they know how. No mother is all good or all bad, all laughing or all serious, all loving or all angry. Ambivalence rushes through their veins.”
—Erma Bombeck (20th century)