# Empty Set

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.

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

Live Variable Analysis
... 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 ...
Polyhedral Combinatorics - Faces and Face-counting Vectors
... Note that this definition also includes as faces the empty set and the whole polytope P ... its top element P itself and as its bottom element the empty set ... 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 ...
Axioms Of Set Theory - Some Ontology
... 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 pure sets only ...
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 ...
Complex Numbers Exponential - Zero To The Power of Zero - For Discrete Exponents
... 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 ...

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

The monotonous dead clog me up and there is only
black done in black that oozes from the strongbox.
I must disembowel it and then set the heart, the legs,
of two who were one upon a large woodpile
and ignite, as I was once ignited, and let it whirl
into flame....
Anne Sexton (1928–1974)

I consider that a man’s brain originally is like a little empty attic, and you have to stock it with such furniture as you choose.
Sir Arthur Conan Doyle (1859–1930)