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Longer titles found: Axiom of empty set (view)

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alternate case: empty set

Face (geometry) (991 words) [view diff] exact match in snippet view article

of faces of a polytope includes the polytope itself and the empty set, where the empty set is for consistency given a "dimension" of −1. For any n-polytope
Probability axioms (1,525 words) [view diff] no match in snippet view article find links to article
The Kolmogorov axioms are the foundations of probability theory introduced by Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions
Interior (topology) (1,237 words) [view diff] exact match in snippet view article
see interior operator below. In any space, the interior of the empty set is the empty set. In any space X, if A ⊂ X {\displaystyle A\subset X} , then int(A)
Lattice (order) (4,476 words) [view diff] exact match in snippet view article
empty set. This implies that the join of an empty set is the least element ⋁ ∅ = 0 {\displaystyle \bigvee \varnothing =0} , and the meet of the empty
Universal quantification (2,657 words) [view diff] no match in snippet view article find links to article
In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses
Axiom of adjunction (256 words) [view diff] exact match in snippet view article find links to article
weak set theory whose axioms are extensionality, the existence of the empty set, and the axiom of adjunction (Tarski 1953, p.34). Bernays, Paul (1937)
Interesting number paradox (620 words) [view diff] exact match in snippet view article find links to article
is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting
Computational problem (881 words) [view diff] no match in snippet view article find links to article
viewed as an infinite collection of instances together with a, possibly empty, set of solutions for every instance. For example, in the factoring problem
Totally disconnected space (557 words) [view diff] exact match in snippet view article find links to article
topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connected
Atari ST character set (1,090 words) [view diff] exact match in snippet view article find links to article
codepoint 249, black square (■) at codepoint 254 (as in code page 437), empty set (∅) at code point 255, GEM-specific characters at codepoints 5, 6, and
Finite-state machine (4,441 words) [view diff] exact match in snippet view article find links to article
\Sigma } is the input alphabet (a finite non-empty set of symbols); S {\displaystyle S} is a finite non-empty set of states; s 0 {\displaystyle s_{0}} is an
Generating set of a group (1,457 words) [view diff] exact match in snippet view article find links to article
elements in S are called generators or group generators. If S is the empty set, then ⟨S⟩ is the trivial group {e}, since we consider the empty product
Conjugate closure (349 words) [view diff] exact match in snippet view article find links to article
the smallest (by inclusion) normal subgroup of G which contains the non-empty set S. For this reason, the conjugate closure coincides with the normal closure
Shotgun formation (1,514 words) [view diff] exact match in snippet view article find links to article
defense knows a pass is more than likely coming, particularly from an empty set lacking any running backs, and there is a higher risk of a botched snap
Uninterpreted function (340 words) [view diff] exact match in snippet view article find links to article
theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational
Arrangement of hyperplanes (1,804 words) [view diff] exact match in snippet view article find links to article
intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces of A are also called the flats of A. The
Property of Baire (448 words) [view diff] exact match in snippet view article find links to article
open sets is again almost open. Since every open set is almost open (the empty set is meager), it follows that every Borel set is almost open. If a subset
Cofinality (1,068 words) [view diff] exact match in snippet view article find links to article
cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member. The cofinality of a partially
Boundary (topology) (1,126 words) [view diff] exact match in snippet view article
set: ∂S = ∂(SC). The interior of the boundary of a closed set is the empty set. Hence: p is a boundary point of a set if and only if every neighborhood
Constant sheaf (816 words) [view diff] exact match in snippet view article find links to article
axiom on the empty set. This is because the empty set is covered by the empty family of sets: Vacuously, any two sections of F over the empty set are equal
Principal homogeneous space (1,687 words) [view diff] exact match in snippet view article find links to article
trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively (meaning that, for any x, y
Mathematical Operators (182 words) [view diff] case mismatch in snippet view article find links to article
Variation sequences Base character Base +VS01 Description U+2205 EMPTY SET ∅ ∅︀ zero with long diagonal stroke overlay form U+2229 INTERSECTION ∩ ∩︀ with
Surreal number (11,207 words) [view diff] exact match in snippet view article find links to article
S i {\displaystyle \cup _{i<0}S_{i}} is the empty set; the only subset of the empty set is the empty set, and therefore S0 consists of a single surreal
Affine hull (614 words) [view diff] exact match in snippet view article find links to article
\sum _{i=1}^{k}\alpha _{i}=1\right\}.} The affine hull of the empty set is the empty set. The affine hull of a singleton (a set made of one single element)
Live variable analysis (784 words) [view diff] exact match in snippet view article find links to article
equations starts with initializing all in-states and out-states to the empty set. The work list is initialized by inserting the exit point (b3) in the
Linear span (1,381 words) [view diff] exact match in snippet view article find links to article
and (0, 1, 0). It does, however, span R2. The empty set is a spanning set of {(0, 0, 0)} since the empty set is a subset of all possible vector spaces in
Centerpoint (geometry) (491 words) [view diff] exact match in snippet view article
the median, a centerpoint need not be one of the data points. Every non-empty set of points (with no duplicates) has at least one centerpoint. Closely related
Topology (4,160 words) [view diff] exact match in snippet view article find links to article
family of subsets of X. Then τ is called a topology on X if: Both the empty set and X are elements of τ. Any union of elements of τ is an element of τ
Smith set (988 words) [view diff] exact match in snippet view article find links to article
or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats every
Polyhedral combinatorics (2,189 words) [view diff] exact match in snippet view article find links to article
pairs of vertices. Note that this definition also includes as faces the empty set and the whole polytope P. If P itself has dimension d, the faces of P
NP-equivalent (383 words) [view diff] exact match in snippet view article find links to article
nonempty subset of the integers that adds up to zero (or returning the empty set if there is no such subset). This optimization problem is similar to the
CWI-2 (546 words) [view diff] case mismatch in snippet view article find links to article
GREEK SMALL LETTER BETA E6 | U+03BC | GREEK SMALL LETTER MU ED | U+2205 | EMPTY SET F8 | U+2218 | RING OPERATOR F9 | U+00B7 | MIDDLE DOT FA | U+2022 | BULLET
Lévy–Steinitz theorem (184 words) [view diff] exact match in snippet view article find links to article
of vectors in a finite-dimensional real Euclidean space is either the empty set or a translate of a subspace (i.e., a set of the form v + M, where v is
Scott Sigler (1,731 words) [view diff] case mismatch in snippet view article find links to article
novels, six novellas, and dozens of short stories. He is the co-founder of Empty Set Entertainment, which publishes his young adult Galactic Football League
Klein quadric (377 words) [view diff] exact match in snippet view article find links to article
in a point, and planes in different classes meet in a line or in the empty set. Let these classes be C {\displaystyle C} and C ′ {\displaystyle C'}
Well-ordering principle (579 words) [view diff] exact match in snippet view article find links to article
In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a least element. In other words, the set of
Sunny Day Real Estate (3,484 words) [view diff] case mismatch in snippet view article find links to article
name "Empty Set". Post-release, the band changed their name from Empty Set to Chewbacca Kaboom, upon realization that a band with the name Empty Set already
Turing jump (809 words) [view diff] exact match in snippet view article find links to article
the Turing jump of the empty set. It is read zero-jump or sometimes zero-prime. Similarly, 0(n) is the nth jump of the empty set. For finite n, these sets
Bounding sphere (1,394 words) [view diff] exact match in snippet view article find links to article
In mathematics, given a non-empty set of objects of finite extension in d {\displaystyle d} -dimensional space, for example a set of points, a bounding
Scott domain (1,026 words) [view diff] exact match in snippet view article find links to article
the empty set certainly has some upper bound, we can conclude the existence of a least element ⊥ {\displaystyle \bot } (the supremum of the empty set) from
Convex polytope (2,506 words) [view diff] exact match in snippet view article find links to article
definition of a face given above allows both the polytope itself and the empty set to be considered as faces, ensuring that every pair of faces has a join
Ron Asheton (1,261 words) [view diff] case mismatch in snippet view article find links to article
band New Order), Destroy All Monsters, Dark Carnival, New Race and The Empty Set. More recently he played with Wylde Ratttz, a band composed of some of
Relational model (5,356 words) [view diff] exact match in snippet view article find links to article
"value unknown". For example, the sum of the empty set is NULL, meaning zero, the average of the empty set is NULL, meaning undefined, and NULL appearing
Heap (mathematics) (1,372 words) [view diff] exact match in snippet view article
abstract algebra, a semiheap is an algebraic structure consisting of a non-empty set H with a ternary operation denoted [ x , y , z ] ∈ H {\displaystyle [x
Descriptive interpretation (387 words) [view diff] exact match in snippet view article find links to article
model) of these sciences, only insofar as these sciences are true. Any non-empty set may be chosen as the domain of a descriptive interpretation, and all n-ary
Tree (data structure) (9,122 words) [view diff] exact match in snippet view article
induced inclusion order. Consider a structure (U, ℱ) such that U is a non-empty set, and ℱ is a set of subsets of U such that the following are satisfied
Schwartz set (607 words) [view diff] exact match in snippet view article find links to article
union of all Schwartz set components. A Schwartz set component is any non-empty set S of candidates such that Every candidate inside the set S is pairwise
Set (abstract data type) (2,930 words) [view diff] exact match in snippet view article
Dynamic set structures typically add: create(): creates a new, initially empty set structure. create_with_capacity(n): creates a new set structure, initially
Additive combinatorics (780 words) [view diff] exact match in snippet view article find links to article
the form that either A {\displaystyle A} or B {\displaystyle B} is the empty set; however, in literature, such problems are sometimes considered to be
Type (model theory) (2,234 words) [view diff] exact match in snippet view article
partial or complete, over any chosen set of parameters (possibly the empty set). An n-type p(x) is said to be realized in M {\displaystyle {\mathcal
Probability measure (818 words) [view diff] exact match in snippet view article find links to article
must return results in the unit interval [0, 1], returning 0 for the empty set and 1 for the entire space. μ must satisfy the countable additivity property
Dimension (4,102 words) [view diff] exact match in snippet view article find links to article
Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension -1. Similarly, for the class
Larry Miller (guitarist) (848 words) [view diff] case mismatch in snippet view article
Arbor bands as Destroy All Monsters, Sproton Layer, M3, Nonfiction, The Empty Set, and Larynx Zillion's Novelty Shop. Destroy All Monsters, in particular
Logical conjunction (1,192 words) [view diff] exact match in snippet view article find links to article
or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result true. The truth table
Hahn–Kolmogorov theorem (734 words) [view diff] exact match in snippet view article find links to article
\Sigma _{0}} . Since every non-empty set in Σ 0 {\displaystyle \Sigma _{0}} is infinite, we have, for every non-empty set A ∈ Σ 0 {\displaystyle A\in \Sigma
Orientation (vector space) (1,874 words) [view diff] exact match in snippet view article
Consequently, the only basis of a zero-dimensional vector space is the empty set ∅ {\displaystyle \emptyset } . Therefore, there is a single equivalence
Silent letter (4,386 words) [view diff] case mismatch in snippet view article find links to article
linguistics, a silent letter is often symbolised with a null sign U+2205 ∅ EMPTY SET. Null is an unpronounced or unwritten segment. The symbol resembles the
Antichain (1,032 words) [view diff] exact match in snippet view article find links to article
A000372 in the OEIS). Even the empty set has two antichains in its power set: one containing a single set (the empty set itself) and one containing no
Bowyer–Watson algorithm (658 words) [view diff] exact match in snippet view article find links to article
add all the points one at a time to the triangulation badTriangles := empty set for each triangle in triangulation do // first find all the triangles
Distributive lattice (2,011 words) [view diff] exact match in snippet view article find links to article
operations are joins and meets of finite sets of elements, including the empty set. If empty joins and empty meets are disallowed, the resulting free distributive
Entity integrity (232 words) [view diff] exact match in snippet view article find links to article
its content, that is, by a unique and minimal value. The PK is a not empty set of attributes (or columns). The same format applies to the foreign key
Semiautomaton (1,610 words) [view diff] exact match in snippet view article find links to article
T)} where Σ {\displaystyle \Sigma } is a non-empty set, called the input alphabet, Q is a non-empty set, called the set of states, and T is the transition
Topological property (1,876 words) [view diff] exact match in snippet view article find links to article
sets. Equivalently, a space is connected if the only clopen sets are the empty set and itself. Locally connected. A space is locally connected if every point
Dependence relation (463 words) [view diff] exact match in snippet view article find links to article
spans X . {\displaystyle X.} Remark. If X {\displaystyle X} is a non-empty set with a dependence relation ◃ {\displaystyle \triangleleft } , then X {\displaystyle
Abstract and concrete (932 words) [view diff] exact match in snippet view article find links to article
causal power has the ability to affect something causally. Thus, the empty set is abstract because it cannot act on other objects. One problem for this
Double turnstile (348 words) [view diff] exact match in snippet view article find links to article
expression φ {\displaystyle \varphi } is a semantic consequence of the empty set. In TeX, the turnstile symbols ⊨ {\displaystyle \vDash } and ⊨ {\displaystyle
Strong antichain (280 words) [view diff] exact match in snippet view article find links to article
ordered by inclusion, and closed under subsets, but does not contain the empty set, this is simply a family of pairwise disjoint sets. A strong upwards antichain
Kalai's 3^d conjecture (587 words) [view diff] exact match in snippet view article find links to article
faces (including the polytope itself as a face but not including the empty set). In two dimensions, the simplest centrally symmetric convex polygons
Logical disjunction (1,182 words) [view diff] exact match in snippet view article find links to article
or function of arbitrary arity, the empty disjunction (OR-ing over an empty set of operands) is generally defined as false. The truth table of A ∨ B {\displaystyle
Scott Sigler bibliography (202 words) [view diff] case mismatch in snippet view article find links to article
Narrated by Podcast dates Notes 2001 - 2017 EARTHCORE iPublish - Re-write: Empty Set Entertainment (May 30, 2017) 978-0759550421 - 978-1939366979 Scott Sigler
Sigma-ideal (335 words) [view diff] exact match in snippet view article find links to article
_{n\in \mathbb {N} }A_{n}\in N.} Briefly, a sigma-ideal must contain the empty set and contain subsets and countable unions of its elements. The concept
Balanced set (840 words) [view diff] exact match in snippet view article find links to article
as a 1-dimensional vector space. The balanced sets are ℂ itself, the empty set and the open and closed discs centered at zero. Contrariwise, in the two
Power of three (857 words) [view diff] exact match in snippet view article find links to article
and all other Hanner polytopes have a number of faces (not counting the empty set as a face) that is a power of three. For example, a 2-cube, or square
Pi-system (2,317 words) [view diff] exact match in snippet view article find links to article
the collection of all interval subsets of the real line, along with the empty set, which is a π-system that generates the very important Borel σ-algebra
Basic Latin (Unicode block) (565 words) [view diff] case mismatch in snippet view article
(2015-10-30). "L2/15-268: Proposal to Represent the Slashed Zero Variant of Empty Set" (PDF). "UTS #51 Emoji Variation Sequences". The Unicode Consortium. Edberg
Empty domain (506 words) [view diff] exact match in snippet view article find links to article
In first-order logic the empty domain is the empty set having no members. In traditional and classical logic domains are restrictedly non-empty in order
ISO 31-11 (117 words) [view diff] exact match in snippet view article find links to article
not to B. A ∖ B = { x ∣ x ∈ A ∧ x ∉ B } A − B should not be used. ∅ the empty set ℕ the set of natural numbers; the set of positive integers and zero ℕ
Zorn's lemma (2,529 words) [view diff] exact match in snippet view article find links to article
P (that is, T is a subset of P that is totally ordered). If T is the empty set, then the trivial ideal {0} is an upper bound for T in P. Assume then
Line segment (1,363 words) [view diff] exact match in snippet view article find links to article
{(c_{x}-a_{x})^{2}+(c_{y}-a_{y})^{2}}}\}} . A line segment is a connected, non-empty set. If V is a topological vector space, then a closed line segment is a closed
Relevance logic (3,384 words) [view diff] exact match in snippet view article find links to article
for a propositional language is a quadruple (W,R,*,0), where W is a non-empty set, R is a ternary relation on W, and * is a function from W to W, and 0
Erdős–Szemerédi theorem (524 words) [view diff] exact match in snippet view article find links to article
\max(|A+A|,|A\cdot A|)\geq c|A|^{1+\varepsilon }} whenever A is a finite non-empty set of real numbers of cardinality |A|, where A + A = { a + b : a , b ∈ A
Planar ternary ring (1,632 words) [view diff] exact match in snippet view article find links to article
algebraic structure ( R , T ) {\displaystyle (R,T)} consisting of a non-empty set R {\displaystyle R} and a ternary mapping T : R 3 → R {\displaystyle T\colon
Tychonoff's theorem (2,011 words) [view diff] exact match in snippet view article find links to article
Cartesian product of a family of nonempty sets is nonempty; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward
Ordinal optimization (2,561 words) [view diff] exact match in snippet view article find links to article
every finite set of elements (including the empty set) has a join and a meet. Here, the join of an empty set of elements is defined to be the least element
Comparison of topologies (672 words) [view diff] exact match in snippet view article find links to article
topology on X is the trivial topology; this topology only admits the empty set and the whole space as open sets. In function spaces and spaces of measures
Dan Hoerner (487 words) [view diff] case mismatch in snippet view article find links to article
After being joined by drummer William Goldsmith, they started the band Empty Set. After the band recorded a two song demo, they changed their name to Chewbacca
Least-upper-bound property (1,355 words) [view diff] exact match in snippet view article find links to article
least upper bound property is called a linear continuum. Let S be a non-empty set of real numbers. A real number x is called an upper bound for S if x ≥
Cosheaf (218 words) [view diff] exact match in snippet view article find links to article
topological space X (more precisely its nerve) to C such that (1) The F of the empty set is the initial object. (2) For any increasing sequence U i {\displaystyle
Generalized nondeterministic finite automaton (492 words) [view diff] exact match in snippet view article find links to article
is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic finite state machines. A GNFA
Data-flow analysis (3,295 words) [view diff] exact match in snippet view article find links to article
equations starts with initializing all in-states and out-states to the empty set. The work list is initialized by inserting the exit point (b3) in the
Difference bound matrix (4,728 words) [view diff] exact match in snippet view article find links to article
all encodes the empty set. We first give the canonical DBM for the empty set. We then explain why each of the DBM encodes the empty set. This allow to
Simplex graph (693 words) [view diff] exact match in snippet view article find links to article
two cliques differ in the presence or absence of a single vertex. The empty set is included as one of the cliques of G that are used to form the clique
Morse theory (2,876 words) [view diff] exact match in snippet view article find links to article
When a is less than f(p) = 0, then M a {\displaystyle M^{a}} is the empty set. After a passes the level of p, when 0 < a < f ( q ) {\displaystyle 0<a<f(q)}
Neighbourhood system (524 words) [view diff] exact match in snippet view article find links to article
topology is defined by a pseudometric. Every neighbourhood system for a non empty set A is a filter called the neighbourhood filter for A. Base (topology) Filter
Turing machine (9,064 words) [view diff] exact match in snippet view article find links to article
Q {\displaystyle Q} is a finite, non-empty set of states; Γ {\displaystyle \Gamma } is a finite, non-empty set of tape alphabet symbols; b ∈ Γ {\displaystyle
Polyhedral terrain (193 words) [view diff] exact match in snippet view article find links to article
particular line in a connected set (i.e., a point or a line segment) or the empty set. Without loss of generality, we may assume that the line in question is
Grothendieck universe (1,264 words) [view diff] exact match in snippet view article find links to article
universe. There are two simple examples of Grothendieck universes: The empty set, and The set of all hereditarily finite sets V ω {\displaystyle V_{\omega
Monotonic function (2,260 words) [view diff] no match in snippet view article find links to article
each element y {\displaystyle y} in Y {\displaystyle Y} the (possibly empty) set f − 1 ( y ) {\displaystyle f^{-1}(y)} is connected. In functional analysis
Bottom type (1,016 words) [view diff] exact match in snippet view article find links to article
Scala and represents the intersection of all other types as well as an empty set. In TypeScript, the bottom type is never. In Python, the bottom type is
Utility functions on indivisible goods (1,805 words) [view diff] exact match in snippet view article find links to article
{\displaystyle u(\emptyset )=0} , where ∅ {\displaystyle \emptyset } is the empty set. A cardinal utility function implies a preference relation: u ( A ) >
Larry Auerbach (750 words) [view diff] exact match in snippet view article find links to article
on television). The series concluded with Auerbach walking from empty set to empty set, turning off the lights, accompanied by Tony Bennett's song, "We'll
Limit superior and limit inferior (5,803 words) [view diff] exact match in snippet view article find links to article
particular, every subset Y of X is bounded above by X and below by the empty set ∅ because ∅ ⊆ Y ⊆ X. Hence, it is possible (and sometimes useful) to consider
Regular expression (7,959 words) [view diff] exact match in snippet view article find links to article
alphabet Σ, the following constants are defined as regular expressions: (empty set) ∅ denoting the set ∅. (empty string) ε denoting the set containing only
Top type (959 words) [view diff] exact match in snippet view article find links to article
owl:Thing, where all classes are subclasses of owl:Thing. (the bottom type or empty set corresponds to owl:Nothing). Singly rooted hierarchy "Class: BasicObject
Almost everywhere (1,244 words) [view diff] exact match in snippet view article find links to article
and U ⊆ V then V ∈ F The intersection of any two sets in F is in F The empty set is not in F A property P of points in X holds almost everywhere, relative
Candidate key (1,199 words) [view diff] exact match in snippet view article find links to article
every subset of the heading has the uniqueness property, including the empty set. The set of all candidate keys can be computed e.g. from the set of functional
Three-dimensional space (2,972 words) [view diff] exact match in snippet view article find links to article
paraboloid Hyperbolic paraboloid The degenerate quadric surfaces are the empty set, a single point, a single line, a single plane, a pair of planes or a
Maximal independent set (5,324 words) [view diff] exact match in snippet view article find links to article
to find a single MIS using the following algorithm: Initialize I to an empty set. While V is not empty: Choose a node v∈V; Add v to the set I; Remove from
Kleinian group (2,135 words) [view diff] exact match in snippet view article find links to article
contracts down to the empty set; these groups are called singly degenerate. If both components of the regular set contract down to the empty set, then the limit
Smooth scheme (1,046 words) [view diff] exact match in snippet view article find links to article
all (n−m) × (n − m) minors of the matrix of derivatives are zero is the empty set. Equivalently, the ideal in the polynomial ring generated by all gi and
Urelement (969 words) [view diff] exact match in snippet view article find links to article
urelements do not, the unary relation is only needed to distinguish the empty set from urelements. Note that in this case, the axiom of extensionality must
William Goldsmith (1,453 words) [view diff] case mismatch in snippet view article find links to article
tenacity and strong focus. The band went through many names, such as Empty Set, Chewbacca Kaboom and One Day I Stopped Breathing, before settling down
Graph theory (5,922 words) [view diff] exact match in snippet view article find links to article
Moreover, V is often assumed to be non-empty, but E is allowed to be the empty set. The order of a graph is |V|, its number of vertices. The size of a graph
Weight function (1,155 words) [view diff] exact match in snippet view article find links to article
B w ( a ) . {\displaystyle \sum _{a\in B}w(a).} If A is a finite non-empty set, one can replace the unweighted mean or average 1 | A | ∑ a ∈ A f ( a
Semiring (4,135 words) [view diff] exact match in snippet view article find links to article
the empty class as the zero object, the class consisting only of the empty set as the unit, disjoint union of classes as addition, and Cartesian product
Commutative algebra (2,358 words) [view diff] exact match in snippet view article find links to article
Noetherian ring, named after Emmy Noether, is a ring in which every non-empty set of ideals has a maximal element. Equivalently, a ring is Noetherian if
Total order (2,506 words) [view diff] exact match in snippet view article find links to article
ordered for the restriction of the order on X. The unique order on the empty set, ∅, is a total order. Any set of cardinal numbers or ordinal numbers (more
Equivalence relation (3,801 words) [view diff] exact match in snippet view article find links to article
1). The empty relation R (defined so that aRb is never true) on a non-empty set X is vacuously symmetric and transitive, but not reflexive. (If X is also
Atom (order theory) (355 words) [view diff] exact match in snippet view article
context of order theory of the ability to select an element from a non-empty set. The terms coatom, coatomic, and coatomistic are defined dually. Thus
Tree stack automaton (876 words) [view diff] exact match in snippet view article find links to article
grammars (or linear context-free rewriting systems). For a finite and non-empty set Γ, a tree stack over Γ is a tuple (t, p) where t is a partial function
Clause (logic) (457 words) [view diff] exact match in snippet view article
{\displaystyle l_{1}\vee \cdots \vee l_{n}} A clause can be empty (defined from an empty set of literals). The empty clause is denoted by various symbols such as ∅
SLD resolution (1,558 words) [view diff] exact match in snippet view article find links to article
procedure to the remaining unselected subgoals. The empty clause is simply an empty set of subgoals, which signals that the initial conjunction of subgoals in
Alfred Tarski (5,287 words) [view diff] exact match in snippet view article find links to article
truth value True with the domain set and the truth-value False with the empty set, then the following operations are counted as logical under the proposal:
Original Sin (James novel) (444 words) [view diff] exact match in snippet view article
reviewed the book for the London Review of Books and wrote "This is an empty set, a set defined by its architecture... An increasingly silly catalogue
Prime number (14,011 words) [view diff] no match in snippet view article find links to article
{\displaystyle n} are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form 2 a 3 b + 1 {\displaystyle
Enumerator (computer science) (254 words) [view diff] exact match in snippet view article
Q {\displaystyle Q} is a finite, non-empty set of states. Σ {\displaystyle \Sigma } is a finite, non-empty set of the output / print alphabet Γ {\displaystyle
Extended real number line (1,974 words) [view diff] exact match in snippet view article find links to article
{\overline {\mathbb {R} }}} has a supremum and an infimum (the infimum of the empty set is + ∞ , {\displaystyle +\infty ,} and its supremum is − ∞ {\displaystyle
Borel subgroup (928 words) [view diff] exact match in snippet view article find links to article
the corresponding Dynkin diagram; the Borel subgroup corresponds to the empty set and G itself corresponding to the set of all nodes. (In general each node
Partially ordered set (3,702 words) [view diff] exact match in snippet view article find links to article
More explicitly, let hom(x, y) = {(x, y)} if x ≤ y (and otherwise the empty set) and (y, z)∘(x, y) = (x, z). Such categories are sometimes called posetal
Pseudorandom number generator (3,281 words) [view diff] exact match in snippet view article find links to article
depending on context. A ⊆ R {\displaystyle A\subseteq \mathbb {R} } – a non-empty set (not necessarily a Borel set). Often A {\displaystyle A} is a set between
Sphere (5,884 words) [view diff] exact match in snippet view article find links to article
the case of a unit sphere. Unlike a ball, even a large sphere may be an empty set. For example, in Zn with Euclidean metric, a sphere of radius r is nonempty
Anne Waldman (2,842 words) [view diff] case mismatch in snippet view article find links to article
to be Born, Coffee House Press, 2016 Dream Book of Fez, The Lune, 2016 Empty Set, Overpass Books, 2016 The Iovis Trilogy, Coffee House Press, 2011 Manatee/Humanity
Saul Kripke (6,260 words) [view diff] exact match in snippet view article find links to article
pair ⟨ W , R ⟩ {\displaystyle \langle W,R\rangle } , where W is a non-empty set, and R is a binary relation on W. Elements of W are called nodes or worlds
Weak ordering (3,086 words) [view diff] exact match in snippet view article find links to article
of the permutohedron (including the permutohedron itself, but not the empty set, as a face). The codimension of a face gives the number of equivalence
Vulnerability (computing) (3,491 words) [view diff] exact match in snippet view article
an agent or collection of agents); we write: V(i,e) where: e may be an empty set. 5. Susceptibility to various threats. 6. A set of properties of a specific
Hyperarithmetical theory (2,016 words) [view diff] exact match in snippet view article find links to article
follows. If δ = 0 then 0 ( δ ) = 0 {\displaystyle 0^{(\delta )}=0} is the empty set. If δ = λ + 1 then 0 ( δ ) {\displaystyle 0^{(\delta )}} is the Turing
Granger causality (2,825 words) [view diff] exact match in snippet view article find links to article
{P} } refers to probability, A {\displaystyle A} is an arbitrary non-empty set, and I ( t ) {\displaystyle {\mathcal {I}}(t)} and I − X ( t ) {\displaystyle
Convex optimization (2,184 words) [view diff] exact match in snippet view article find links to article
problem is said to be unbounded. Otherwise, if C {\displaystyle C} is the empty set, then the problem is said to be infeasible. A convex optimization problem
Dijkstra's algorithm (5,700 words) [view diff] exact match in snippet view article find links to article
start cost ← 0 frontier ← priority queue containing node only explored ← empty set do if frontier is empty then return failure node ← frontier.pop() if node
The Stooges (4,629 words) [view diff] case mismatch in snippet view article find links to article
musician in various ensembles, including New Race, Dark Carnival and the Empty Set. Williamson worked with Pop as a producer and engineer during his early
Knapsack problem (6,539 words) [view diff] exact match in snippet view article find links to article
{\displaystyle m=0\,\!} (the sum of zero items, i.e., the summation of the empty set). 2. m [ w ] = max ( v 1 + m [ w − w 1 ] , v 2 + m [ w − w 2 ] , . .
Empty sum (340 words) [view diff] exact match in snippet view article find links to article
allows the zero-dimensional vector space V={0} to have a basis, namely the empty set. Empty product Iterated binary operation Empty function Harper, Robert
Schröder–Hipparchus number (1,378 words) [view diff] exact match in snippet view article find links to article
including the associahedron itself as a face, but not including the empty set. For instance, the two-dimensional associahedron K4 is a pentagon; it
Kuratowski closure axioms (3,745 words) [view diff] exact match in snippet view article find links to article
(X)\to \wp (X)} with the following properties: [K1] It preserves the empty set: c ( ∅ ) = ∅ {\displaystyle \mathbf {c} (\varnothing )=\varnothing } ;
Ray class field (775 words) [view diff] exact match in snippet view article find links to article
generated by the mth roots of unity. The ray class field for (m) and the empty set of places is its maximal totally real subfield -- the field Q ( cos ⁡
Continuous function (7,210 words) [view diff] exact match in snippet view article find links to article
with the indiscrete topology (in which the only open subsets are the empty set and X) and the space T set is at least T0, then the only continuous functions
Knowledge space (1,125 words) [view diff] exact match in snippet view article find links to article
approach - A tuple ( Q , K ) {\displaystyle (Q,K)} consisting of a non-empty set Q {\displaystyle Q} and a set K {\displaystyle K} of subsets from Q {\displaystyle
Fair division (2,610 words) [view diff] exact match in snippet view article find links to article
functions are assumed to be normalized, so that every person values the empty set as 0 ( V i ( ∅ ) = 0 {\displaystyle V_{i}(\emptyset )=0} for all i), and
Timestamp-based concurrency control (1,301 words) [view diff] exact match in snippet view article find links to article
initially empty set of transactions upon which it depends, D E P ( T i ) = [ ] {\displaystyle DEP(T_{i})=[]} , and an initially empty set of old objects
Groupoid (4,840 words) [view diff] exact match in snippet view article find links to article
algebraic structure ( G , ∗ ) {\displaystyle (G,\ast )} consisting of a non-empty set G {\displaystyle G} and a binary partial function ' ∗ {\displaystyle \ast
Corporate election (8,195 words) [view diff] exact match in snippet view article find links to article
that the elect people is an empty set. Another reason given to reject that corporate election is an election of an empty set is seen in the election of
Aida (musical) (3,564 words) [view diff] exact match in snippet view article
production. The original Atlanta staging conceived of the play with a nearly empty set, displaying only a six-ton gold pyramid-shaped set piece in the center
Set-theoretic definition of natural numbers (546 words) [view diff] exact match in snippet view article find links to article
the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 = n ∪ {n} for each n. In this way n = {0, 1, ..., n − 1} for
Method of conditional probabilities (3,103 words) [view diff] exact match in snippet view article find links to article
process for constructing an independent set S: 1. Initialize S to be the empty set. 2. For each vertex u in V in random order: 3. If no neighbors of u are
Overlapping interval topology (288 words) [view diff] exact match in snippet view article find links to article
a<0<b} , together with [ − 1 , 1 ] {\displaystyle [-1,1]} itself and the empty set. Any two distinct points in [ − 1 , 1 ] {\displaystyle [-1,1]} are topologically
Normal function (412 words) [view diff] exact match in snippet view article find links to article
f(f(γ)) < f(γ), contradicting minimality of γ. Furthermore, for any non-empty set S of ordinals, we have f(sup S) = sup f(S). Proof: "≥" follows from the
Irreducible component (736 words) [view diff] exact match in snippet view article find links to article
xy = 0}. For the Zariski topology, its closed subsets are itself, the empty set, the singletons, and the two lines defined by x = 0 and y = 0. The set
Saturated family (350 words) [view diff] exact match in snippet view article find links to article
given non-empty family 𝒢 of subsets of X containing at least one non-empty set, the saturated hull of 𝒢 is well-defined. Note that a saturated family
Reed's law (571 words) [view diff] exact match in snippet view article find links to article
whether to include that element, or not. However, this includes the (one) empty set, and N singletons, which are not properly subgroups. So 2N − N − 1 subsets
Sheaf (mathematics) (7,432 words) [view diff] exact match in snippet view article
family is a terminal object, and consequently the value of a sheaf on the empty set must be a terminal object. If sheaf values are in the category of sets
Quadric (4,971 words) [view diff] exact match in snippet view article find links to article
^{2}+X_{1}^{2}-X_{2}^{2}-X_{3}^{2}\end{cases}}} The first case is the empty set. The second case generates the ellipsoid, the elliptic paraboloid or the
LL parser (4,025 words) [view diff] exact match in snippet view article find links to article
and Fi(Ai) for every rule as follows: initialize every Fi(Ai) with the empty set add Fi(wi) to Fi(Ai) for every rule Ai → wi, where Fi is defined as follows:
Imieliński–Lipski algebra (941 words) [view diff] exact match in snippet view article find links to article
'Spring') OR (GRADE = 'A' AND SEMESTER <> 'Spring') SQL query Q will return empty set (no results) under 3-valued semantics currently adopted by all variants
Locally finite collection (728 words) [view diff] exact match in snippet view article find links to article
of these sets is locally finite (since the only closures are R and the empty set). No infinite collection of a compact space can be locally finite. Indeed
Stokes' theorem (3,952 words) [view diff] exact match in snippet view article find links to article
have zero integral over cycles, i.e. if the boundaries sum up to the empty set: ∑c Mc = ∅. De Rham's theorem shows that this homomorphism is in fact
Sharkovskii's theorem (1,115 words) [view diff] exact match in snippet view article find links to article
1-2|x-1/2|)} for h ∈ [ 0 , 1 ] {\displaystyle h\in [0,1]} , except for the empty set of periods which is achieved by T : R → R {\displaystyle T:\mathbb {R}
Permutohedron (1,125 words) [view diff] exact match in snippet view article find links to article
permutohedron (including the permutohedron itself, but not including the empty set) are in 1-1 correspondence with the strict weak orderings on a set of
Twelvefold way (5,339 words) [view diff] exact match in snippet view article find links to article
surjective unless X is (also) empty. For every non-empty set N there are no functions from N to the empty set (there is at least one value of the function that
Star height (1,322 words) [view diff] exact match in snippet view article find links to article
\scriptstyle \emptyset } is the special regular expression denoting the empty set and ε the special one denoting the empty word; E and F are arbitrary regular
Read-only right moving Turing machines (325 words) [view diff] exact match in snippet view article find links to article
{\displaystyle b=0} , "blank" Σ = ∅ {\displaystyle \Sigma =\varnothing } , empty set δ = {\displaystyle \delta =} see state-table below q 0 = A {\displaystyle
Dennis Diken (1,147 words) [view diff] case mismatch in snippet view article find links to article
"The Sun's Gonna Shine in the Morning" With Jimmy Silva Remnants of the Empty Set, 1986 (PopLlama) Fly Like a Dog, 1987 (PopLlama) With Scott McCaughey
Shapley value (3,038 words) [view diff] exact match in snippet view article find links to article
{\displaystyle v(\emptyset )=0} , where ∅ {\displaystyle \emptyset } denotes the empty set. The function v {\displaystyle v} is called a characteristic function
Pre-measure (440 words) [view diff] exact match in snippet view article find links to article
{\displaystyle A\in R} (in particular, Σ includes R). The infimum of the empty set is taken to be + ∞ {\displaystyle +\infty } . (Note that there is some
Metric space (5,581 words) [view diff] exact match in snippet view article find links to article
is connected if the only subsets that are both open and closed are the empty set and M {\displaystyle M} itself. A metric space M {\displaystyle M} is
George Boole (5,783 words) [view diff] exact match in snippet view article find links to article
British mathematician George Boole, which attempts to incorporate the "empty set." List of Boolean algebra topics List of pioneers in computer science
Kripke semantics (4,287 words) [view diff] no match in snippet view article find links to article
W , R ⟩ {\displaystyle \langle W,R\rangle } , where W is a (possibly empty) set, and R is a binary relation on W. Elements of W are called nodes or worlds
Pregeometry (model theory) (1,438 words) [view diff] exact match in snippet view article
the closure of singletons are singletons and the closure of the empty set is the empty set. Given sets A , B ⊂ S {\displaystyle A,B\subset S} , A {\displaystyle
Treap (2,341 words) [view diff] exact match in snippet view article find links to article
input sets as result, while the difference function should return the empty set. Let d be the size of the symmetric difference. The modified merge algorithms
Regular polyhedron (2,939 words) [view diff] exact match in snippet view article find links to article
maximal element), its faces, edges, vertices and the null polytope or empty set. These abstract elements can be mapped into ordinary space or realised
Kleene's recursion theorem (2,839 words) [view diff] exact match in snippet view article find links to article
beginning with the empty set. First, a sequence Fk is constructed, for k = 0 , 1 , … {\displaystyle k=0,1,\ldots } . Let F0 be the empty set. Proceeding inductively
DFA minimization (2,384 words) [view diff] exact match in snippet view article find links to article
let reachable_states := {q0}; let new_states := {q0}; do { temp := the empty set; for each q in new_states do for each c in Σ do temp := temp ∪ {p such
Constraint programming (2,267 words) [view diff] exact match in snippet view article find links to article
may prove that the problem has no solution by reducing a domain to the empty set, but may also terminate without proving satisfiability or unsatisfiability
Noetherian ring (2,415 words) [view diff] exact match in snippet view article find links to article
R a 1 + ⋯ + R a n {\displaystyle I=Ra_{1}+\cdots +Ra_{n}} . Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element
Convex cone (2,828 words) [view diff] exact match in snippet view article find links to article
C and C + C = C, for any positive scalar α. For a vector space V, the empty set, the space V, and any linear subspace of V are convex cones. The conical
Mathematical induction (6,576 words) [view diff] exact match in snippet view article find links to article
induction and the first and fourth axioms. Proof. Suppose there exists a non-empty set, S, of natural numbers that has no least element. Let P(n) be the assertion
Simplex (6,326 words) [view diff] exact match in snippet view article find links to article
regular tetrahedron is 4 · ( ) or {3,3} and so on. In some conventions, the empty set is defined to be a (−1)-simplex. The definition of the simplex above still
Halting problem (5,835 words) [view diff] exact match in snippet view article find links to article
the set of partial functions that satisfy the property is neither the empty set nor the set of all partial functions. For example, "halts or fails to
Gröbner basis (6,201 words) [view diff] exact match in snippet view article find links to article
two versions. The first one asserts that a set of polynomials has an empty set of common zeros in an algebraic closure of the field of the coefficients
Glossary of order theory (3,995 words) [view diff] exact match in snippet view article find links to article
Another common term for this element is top. It is the infimum of the empty set and the supremum of P. The dual notion is called zero. Up-set. See upper
Association rule learning (4,262 words) [view diff] exact match in snippet view article find links to article
{\displaystyle I} and has size 2 n − 1 {\displaystyle 2^{n}-1} (excluding the empty set which is not a valid itemset). Although the size of the power-set grows
Complete partial order (1,115 words) [view diff] exact match in snippet view article find links to article
can be also a pointed dcpo), because the set of all consequences of the empty set (i.e. “the set of the logically provable / logically valid sentences”)
Pithos (2,958 words) [view diff] no match in snippet view article find links to article
which there is no evidence, is unlikely. They were perhaps brought in empty, set in place, and then filled from smaller pithoi with some of the numerous
Quasitransitive relation (766 words) [view diff] exact match in snippet view article find links to article
transitive. A quasitransitive relation needn't be acyclic: for every non-empty set A, the universal relation A×A is both cyclic and quasitransitive. Intransitivity
Regular chain (1,302 words) [view diff] exact match in snippet view article find links to article
described by these triangular sets. A triangular set may merely describe the empty set. To fix this degenerated case, the notion of regular chain was introduced
Worcester Polytechnic Institute (5,477 words) [view diff] case mismatch in snippet view article find links to article
school's three comedy troupes, KILROY Sketch Comedy, Guerilla Improv, and {Empty Set} as well as collegiate and alumni comedy groups from across New England
Young tableau (2,691 words) [view diff] no match in snippet view article find links to article
matrix while BA is the 0-by-0 matrix, but both A and B have the same (empty) set of entries; for skew tableaux however such distinction is necessary even
Zero to the power of zero (2,781 words) [view diff] exact match in snippet view article find links to article
set-theoretic interpretation of 00 is the number of functions from the empty set to the empty set; there is exactly one such function, the empty function. Likewise
Especially for You (The Smithereens album) (2,241 words) [view diff] case mismatch in snippet view article
who recorded his own version of the song on his album Remnants of the Empty Set in 1986 featuring Dennis Diken on drums. DiNizio explained that it was
Argumentation framework (3,207 words) [view diff] exact match in snippet view article find links to article
arguments and a binary relation on this set), V {\displaystyle V} is a non empty set of values, val {\displaystyle {\textit {val}}} is a mapping that associates
Outline of object recognition (2,698 words) [view diff] exact match in snippet view article find links to article
Each node in the tree represents a set of matches. Root node represents empty set Each other node is the union of the matches in the parent node and one
Semigroup action (1,970 words) [view diff] exact match in snippet view article find links to article
semiautomaton is a triple (Σ,X,T), where Σ is a non-empty set called the input alphabet, X is a non-empty set called the set of states and T is a function T
Frölicher space (284 words) [view diff] exact match in snippet view article find links to article
the mathematician Alfred Frölicher. A Frölicher space consists of a non-empty set X together with a subset C of Hom(R, X) called the set of smooth curves
Composition of relations (2,136 words) [view diff] exact match in snippet view article find links to article
with zero, where the identity map on X is the neutral element, and the empty set is the zero element. Finite binary relations are represented by logical
Benford's law (6,059 words) [view diff] exact match in snippet view article find links to article
is true but trivial: All binary and unary numbers (except for 0 or the empty set) start with the digit 1. (On the other hand, the generalization of Benford's
Extensive-form game (3,734 words) [view diff] exact match in snippet view article find links to article
the "nodes of the player". (A game of complete information thus has an empty set of Chance nodes.) Each node of the Chance player has a probability distribution
Morley rank (661 words) [view diff] exact match in snippet view article find links to article
theorem and in the larger area of model theoretic stability theory. The empty set has Morley rank −1, and conversely anything of Morley rank −1 is empty
Modal logic (7,680 words) [view diff] exact match in snippet view article find links to article
usually given as follows: First we define a frame, which consists of a non-empty set, G, whose members are generally called possible worlds, and a binary relation
(B, N) pair (735 words) [view diff] exact match in snippet view article
is generated by a set S of elements wi of order 2, for i in some non-empty set I. If wi is an element of S and w is any element of W, then wiBw is contained
Tiny BASIC (2,321 words) [view diff] exact match in snippet view article find links to article
operator; parentheses group objects; and an epsilon ("ε") signifies the empty set. As is common in computer language grammar notation, the vertical bar
Two-way finite automaton (1,582 words) [view diff] exact match in snippet view article find links to article
{\displaystyle Q} is the finite, non-empty set of states Σ {\displaystyle \Sigma } is the finite, non-empty set of input alphabet L {\displaystyle L}
Dogville (3,614 words) [view diff] case mismatch in snippet view article find links to article
Angeles Times. Retrieved 13 October 2016. Corliss, Richard (4 April 2004). "Empty Set, Plot to Match". TIME. Retrieved 13 October 2016. Ebert, Roger (9 April
Event-driven architecture (2,123 words) [view diff] exact match in snippet view article find links to article
representation in the form of an event structure and ending with a non-empty set of reactions to that event. The first logical layer is the event generator
Weighted matroid (1,212 words) [view diff] exact match in snippet view article find links to article
algorithm for finding a basis: Initially let A {\displaystyle A} be the empty set. For each x {\displaystyle x} in E {\displaystyle E} if A ∪ { x } {\displaystyle
Bose–Einstein statistics (5,850 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \displaystyle (\omega )\longleftrightarrow S(0,2)=\varnothing } (empty set). Thus we can write S ( 4 , 3 ) = ⋃ k = 0 4 S ( 4 − k , 2 ) {\displaystyle
Simple set (518 words) [view diff] exact match in snippet view article find links to article
result, one is that the simple set, say A, does not Turing-reduce to the empty set, and that the K, the halting problem, does not Turing-reduce to A. He
Real analysis (7,610 words) [view diff] exact match in snippet view article find links to article
sets that are closed and bounded, and therefore compact, include the empty set, any finite number of points, closed intervals, and their finite unions
Hahn–Banach theorem (6,192 words) [view diff] exact match in snippet view article find links to article
functional problem) — Let X be a real or complex normed space, I a non-empty set, ( c i ) i ∈ I {\displaystyle \left(c_{i}\right)_{i\in I}} a family of
Darryl Neudorf (915 words) [view diff] case mismatch in snippet view article find links to article
worked at The Pop Shop, skateboarded around Kelowna and formed the band Empty Set with his sister Adele Neudorf, Kevin Kane and Jon Brotherton. At 18, Darryl
Order topology (2,159 words) [view diff] exact match in snippet view article find links to article
disconnected (connected components are points), scattered (every non-empty set has an isolated point; in this case, just take the smallest element),
Timed propositional temporal logic (1,230 words) [view diff] exact match in snippet view article find links to article
be defined from other operators. A closed formula is a formula over an empty set of clocks. Let T ⊆ R + {\displaystyle T\subseteq \mathbb {R} _{+}} it
Denotational semantics (3,437 words) [view diff] exact match in snippet view article find links to article
partial function. At the beginning, we start with the empty function (an empty set). Next, we add the ordered pair (0,1) to the function to result in another
Blackadder Goes Forth (4,847 words) [view diff] exact match in snippet view article find links to article
running the video and audio in slow motion and fading another video of the empty set over the top to make it appear as if the characters had disappeared. This
Eilenberg–MacLane space (1,541 words) [view diff] exact match in snippet view article find links to article
a\colon G\to G'} is any homomorphism of Abelian groups, then there is a non-empty set K ( a , n ) = { [ f ] : f : K ( G , n ) → K ( G ′ , n ) , H n ( f ) =
Halfwidth and Fullwidth Forms (Unicode block) (441 words) [view diff] case mismatch in snippet view article
Barbara; Freytag, Asmus; Iancu, Laurențiu; Sargent, Murray (2015-10-30). "L2/15-268: Proposal to Represent the Slashed Zero Variant of Empty Set" (PDF).
Constructible number (2,643 words) [view diff] exact match in snippet view article find links to article
using the geometric definition of a constructible point, let P be a non-empty set of points in ℝ2 and K the subfield of ℝ generated by all the coordinates
Absoluteness (1,191 words) [view diff] exact match in snippet view article find links to article
following (see Jech (2003 sec. I.12) and Kunen (1980 sec. IV.3)). x is the empty set. x is an ordinal. X is a finite ordinal. x = ω. x is (the graph of) a
Euclidean algorithm (14,379 words) [view diff] exact match in snippet view article find links to article
well-ordering property of the non-negative integers, which asserts that every non-empty set of non-negative integers has a smallest member. The fundamental theorem
Finitist set theory (7,003 words) [view diff] exact match in snippet view article find links to article
x\exists r(r\in x)} . Every set has either a set or an ur as a member. The empty set { } {\displaystyle \{\}} has no members, and therefore there exists no
Measurable cardinal (2,057 words) [view diff] exact match in snippet view article find links to article
there is an atomless probability measure on the power set of some non-empty set. Solovay (1971) showed that existence of measurable cardinals in ZFC,
ISO/IEC 2022 (8,984 words) [view diff] exact match in snippet view article find links to article
and G3 designations for level 1), with an F-byte of 0x7E denoting an empty set. Each ISO/IEC 4873 level has its own single ISO/IEC 2022 announcer sequence
Symbolic method (combinatorics) (4,965 words) [view diff] exact match in snippet view article
z ) {\displaystyle G(z)} to indicate the presence of one copy of the empty set. It is possible to assign meaning to both C ∈ Z [ A ] {\displaystyle {\mathcal
Nakamura number (3,448 words) [view diff] exact match in snippet view article find links to article
coalitions, one can sometimes obtain an empty set. But by intersecting less than this number, one can never obtain an empty set.) The Nakamura number of the simple
First-order inductive learner (1,304 words) [view diff] exact match in snippet view article find links to article
Literal is operational Return Literal Initialize OperationalLiterals to the empty set For each clause in the definition of Literal Compute information gain
Homogeneous coordinate ring (1,252 words) [view diff] exact match in snippet view article find links to article
containing the ideal J generated by all the Xi, which corresponds to the empty set because not all homogeneous coordinates can vanish at a point of projective
Hemicontinuity (1,059 words) [view diff] exact match in snippet view article find links to article
closed domain (that is, the set of points a ∈ A where Γ(a) is not the empty set is closed) and closed values (i.e. Γ(a) is closed for all a in A), then
Dynamical system (definition) (1,830 words) [view diff] exact match in snippet view article
a tuple (T, M, Φ) where T is a monoid, written additively, M is a non-empty set and Φ is a function Φ : U ⊆ ( T × M ) → M {\displaystyle \Phi :U\subseteq
Positional notation (6,952 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \nu _{1},\ldots ,\nu _{n}\in \mathbb {N} } , then with the non-empty set of denominators S := { p 1 , … , p n } {\displaystyle S:=\{p_{1},\ldots
Medial graph (855 words) [view diff] no match in snippet view article find links to article
using n colors in the directed medial graph of G so that each (possibly empty) set of monochromatic edges forms a directed Eulerian graph, where the weight
Zhegalkin polynomial (4,068 words) [view diff] exact match in snippet view article find links to article
a finite set of distinct variables (hence square-free), including the empty set whose product is denoted 1. There are 2n possible Zhegalkin monomials
Metric outer measure (470 words) [view diff] exact match in snippet view article find links to article
be a set function defined on a class Σ of subsets of X containing the empty set ∅, such that τ(∅) = 0. One can show that the set function μ defined by
Inquisitive semantics (1,094 words) [view diff] exact match in snippet view article find links to article
proposition which contains only a singleton information state {w} and the empty set ∅ {\displaystyle \emptyset } . This inquisitive proposition conveys the
Cooperative game theory (6,094 words) [view diff] exact match in snippet view article find links to article
assumed that a simple game is nonempty or that it does not contain an empty set. However, in other areas of mathematics, simple games are also called
Alain Badiou (7,597 words) [view diff] exact match in snippet view article find links to article
prohibition (cf. p. 190 in Being and Event). (This axiom states that every non-empty set A contains an element y that is disjoint from A.) Badiou's philosophy
Arithmetical hierarchy (4,430 words) [view diff] exact match in snippet view article find links to article
∅ ( n ) {\displaystyle \emptyset ^{(n)}} (the nth Turing jump of the empty set) is many-one complete in Σ n 0 {\displaystyle \Sigma _{n}^{0}} . The set
Associahedron (1,439 words) [view diff] exact match in snippet view article find links to article
(including the associahedron itself as a face, but not including the empty set) is a Schröder–Hipparchus number (row sums of the triangle). In the late
Stalk (sheaf) (1,357 words) [view diff] exact match in snippet view article
the one point space {x} are {x} and ∅, and there is no data over the empty set. Over {x}, however, we get: i − 1 F ( { x } ) = lim → U ⊇ { x } ⁡ F (
Cylindric algebra (1,105 words) [view diff] exact match in snippet view article find links to article
instead of ⋅ {\displaystyle \cdot } , set complement for complement, empty set as 0, X α {\displaystyle X^{\alpha }} as the unit, and ⊆ {\displaystyle
Rationalizability (865 words) [view diff] exact match in snippet view article find links to article
finitely many actions, this process always terminates and leaves a non-empty set of actions for each player. These are the rationalizable actions. Consider
Frege system (741 words) [view diff] exact match in snippet view article find links to article
rule from R. An F-proof of a formula A is an F-derivation of A from the empty set of axioms (X=∅). F is called a Frege system if F is sound: every F-provable
Post's theorem (3,448 words) [view diff] exact match in snippet view article find links to article
\emptyset ^{(n)}} , that is, finitely iterated Turing jumps of the empty set. (The empty set could be replaced with any other computable set without changing
Projective plane (6,507 words) [view diff] exact match in snippet view article find links to article
degenerate planes according to (Albert & Sandler 1968). They are: the empty set; a single point, no lines; a single line, no points; a single point, a
Aronszajn tree (959 words) [view diff] exact match in snippet view article find links to article
levels Uα by transfinite induction on α as follows starting with the empty set as U0: If α + 1 is a successor then Uα+1 consists of all extensions of
Sunny Day Real Estate discography (138 words) [view diff] case mismatch in snippet view article find links to article
Year Album details 1992 Empty Set Demo Tape Release date: 1992 Label: One Day I Stopped Breathing Format: CS Chewbacca Kaboom Demo Tape Release date:
True arithmetic (1,124 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \kappa } . As there are continuum many types over the empty set, true arithmetic also has 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} countable
Without (The X-Files) (2,108 words) [view diff] exact match in snippet view article
scenes. To accomplish the effect, the cameras first filmed a pass over the empty set and lighting elements. Then, the production crew filmed five different
Bijection, injection and surjection (1,849 words) [view diff] exact match in snippet view article find links to article
Injective and surjective (bijective) The identity function idX for every non-empty set X, and thus specifically R → R : x ↦ x . {\displaystyle \mathbf {R} \to
Mex (mathematics) (741 words) [view diff] exact match in snippet view article
of stones. If n is zero stones, the nimber is 0 because the mex of the empty set of legal moves is the nimber 0. If n is 1 stone, the player to move will
Zero-suppressed decision diagram (3,660 words) [view diff] exact match in snippet view article find links to article
can be no other nodes, and F represents the family containing just the empty set { Ø }. We call this a unit family, and denote it by . 3. If v has two
Polyhedral complex (317 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \sigma _{1}} and σ 2 {\displaystyle \sigma _{2}} . Note that the empty set is a face of every polyhedron, and so the intersection of two polyhedra
Threat (computer) (4,356 words) [view diff] exact match in snippet view article
T(e;i) where: e is an external entity; i is an internal entity or an empty set. 6. An undesirable occurrence that might be anticipated but is not the
U-rank (574 words) [view diff] exact match in snippet view article find links to article
set of parameters, with rank at least α, then there is a type over the empty set of rank at least α. Thus, we can define, for a complete (stable) theory
List of regular polytopes and compounds (6,031 words) [view diff] exact match in snippet view article find links to article
maximal element), its faces, edges, vertices and the null polytope or empty set. These abstract elements can be mapped into ordinary space or realised
Parser combinator (1,823 words) [view diff] exact match in snippet view article find links to article
parser returns a singleton set containing j + 1; otherwise, it returns the empty set. t e r m ( x , j ) = { { } , j ≥ # i n p u t { j + 1 } , j t h  element
Sieve (category theory) (768 words) [view diff] exact match in snippet view article
the empty sieve on c, that is, the sieve for which ∅(d) is always the empty set, then for any f:c′→c, f*∅c is ∅c′. Furthermore, f*Hom(−, c) = Hom(−, c′)
Null (SQL) (7,599 words) [view diff] exact match in snippet view article
fit the given criteria? Calculating the minimum or maximum value of an empty set is impossible, so those results must be NULL, indicating there is no answer
Combinatory logic (5,319 words) [view diff] exact match in snippet view article find links to article
the calculus. Then A does not belong to the deductive closure X of the empty set, thus X ⊮ A {\displaystyle X\not \Vdash A} , and A is not intuitionistically