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

### Other articles related to "empty, empty set, set, sets":

... for some settings that do involve continuity.) For example Regarding b0 as an

**empty**product assigns it the value 1, even when b = 0 ... The combinatorial interpretation of 00 is the number of

**empty**tuples of elements from the

**empty set**... There is exactly one

**empty**tuple ...

**Empty Set**- Questioned Existence - Philosophical Issues

... While the

**empty set**is a standard and widely accepted mathematical concept, it remains an ontological curiosity, whose meaning and usefulness are debated by philosophers and logicians ... The

**empty set**is not the same thing as nothing rather, it is a

**set**with nothing inside it and a

**set**is always something ... This issue can be overcome by viewing a

**set**as a bagâ€”an

**empty**bag undoubtedly still exists ...

... A

**set**is pure if all of its members are

**sets**, all members of its members are

**sets**, and so on ... For example, the

**set**containing only the

**empty set**is a nonempty pure

**set**... In modern

**set**theory, it is common to restrict attention to the von Neumann universe of pure

**sets**, and many systems of axiomatic

**set**theory are designed to axiomatize the ...

... The analysis is done in a backwards order, and the dataflow confluence operator is

**set**union ... The

**set**of live variables at line L3 is {b, c} because both are used in the addition, and thereby the call to f and assignment to a ... But the

**set**of live variables at line L1 is only {b} since variable c is updated in L2 ...

... Note that this definition also includes as faces the

**empty set**and the whole polytope P ... that has as its top element P itself and as its bottom element the

**empty set**... the face lattice on the left side of the vector, f-1 = 1 counts the

**empty set**as a face, while on the right side, fd = 1 counts P itself ...

### Famous quotes containing the words set and/or empty:

“You have a row of dominoes *set* up; you knock over the first one, and what will happen to the last one is that it will go over very quickly.”

—Dwight D. Eisenhower (1890–1969)

“January, month of *empty* pockets!... Let us endure this evil month, anxious as a theatrical producer’s forehead.”

—Colette [Sidonie Gabrielle Colette] (1873–1954)