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.

Read more about Empty Set:  Notation, Properties

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

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 ...
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 bag—an empty bag undoubtedly still exists ...
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 ...
Live Variable Analysis
... 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 ...
Polyhedral Combinatorics - Faces and Face-counting Vectors
... 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)