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)
“I concluded that I was skilled, however poorly, at only one thing: marriage. And so I set about the business of selling myself and two children to some unsuspecting man who might think me a desirable second-hand mate, a man of good means and disposition willing to support another man’s children in some semblance of the style to which they were accustomed. My heart was not in the chase, but I was tired and there was no alternative. I could not afford freedom.”
—Barbara Howar (b. 1934)