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:
“Had I been less resolved to work, I would perhaps had made an effort to begin immediately. But since my resolution was formal and before twenty four hours, in the empty slots of the next day where everything fit so nicely because I was not yet there, it was better not to choose a night at which I was not well-disposed for a debut to which the following days proved, alas, no more propitious.... Unfortunately, the following day was not the exterior and vast day which I had feverishly awaited.”
—Marcel Proust (1871–1922)
“Anyone who seeks for the true causes of miracles, and strives to understand natural phenomena as an intelligent being, and not to gaze at them like a fool, is set down and denounced as an impious heretic by those, whom the masses adore as the interpreters of nature and the gods. Such persons know that, with the removal of ignorance, the wonder which forms their only available means for proving and preserving their authority would vanish also.”
—Baruch (Benedict)