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:
“When a poor disconsolated drooping creature is terrified from all enjoyment,—prays without ceasing ‘till his imagination is heated,—fasts and mortifies and mopes, till his body is in as bad a plight as his mind; is it a wonder, that the mechanical disturbances ... of an empty belly, interpreted by an empty head, should be mistook for [the] workings [of God].”
—Laurence Sterne (1713–1768)
“But now I see I was not plucked for naught,
And after in life’s vase
Of glass set while I might survive,
But by a kind hand brought
Alive
To a strange place.”
—Henry David Thoreau (1817–1862)