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:
“There’s only one way for an individual to remain upright, not to fall to pieces, not to sink into the mire of self-oblivion ... or self-contempt. That’s calmly to turn away from everything, to say, “Enough!” and, folding one’s useless arms across one’s empty breast, to retain the ultimate, the sole attainable virtue, the virtue of recognizing one’s own insignificance.”
—Ivan Sergeevich Turgenev (1818–1883)
“She’s just a child,
but I’m the one who’s fainthearted.
She’s the woman,
but I’m the coward.
She bears that high, swollen set of breasts,
but I’m the one who’s burdened.
The heavy hips are hers,
but I’m unable to move.
It’s a wonder
how clumsy I’ve become
because of flaws
that shelter themselves
in another.”
—Amaru (c. seventh century A.D.)