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Face (geometry)
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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-polytopeProbability 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 contributionsInterior (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 emptyUniversal 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 expressesAxiom 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 uninterestingComputational 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 problemTotally 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 connectedAtari 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, andFinite-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 anGenerating 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 productConjugate 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 closureShotgun 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 snapUninterpreted 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 equationalArrangement 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. TheProperty 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 subsetCofinality (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 partiallyBoundary (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 neighborhoodConstant 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 equalPrincipal 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, yMathematical 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 ∩ ∩︀ withSurreal 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 surrealAffine 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 theLinear 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 inCenterpoint (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 relatedTopology (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 τSmith 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 everyPolyhedral 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 PNP-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 theCWI-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 | BULLETLévy–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 isScott 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 LeagueKlein 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 ofSunny 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 alreadyTuring 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 setsBounding 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 boundingScott 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) fromConvex 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 joinRon 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 ofRelational 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 appearingHeap (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 [xDescriptive 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-aryTree (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 satisfiedSchwartz 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 pairwiseSet (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, initiallyAdditive 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 beType (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 {\mathcalProbability 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 propertyDimension (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 classLarry 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 particularLogical 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 tableHahn–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 \SigmaOrientation (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 equivalenceSilent 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 theAntichain (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 noBowyer–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 trianglesDistributive 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 distributiveEntity 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 keySemiautomaton (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 transitionTopological 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 pointDependence 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 {\displaystyleAbstract 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 thisDouble 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 ⊨ {\displaystyleStrong 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 antichainKalai'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 polygonsLogical 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 {\displaystyleScott 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 SiglerSigma-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 conceptBalanced 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 twoPower 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 squarePi-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-algebraBasic 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. EdbergEmpty 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 orderISO 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 ℕZorn'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 thenLine 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 closedRelevance 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 0Erdős–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 ∈ APlanar 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\colonTychonoff'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 straightforwardOrdinal 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 elementComparison 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 measuresDan 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 ChewbaccaLeast-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 {\displaystyleGeneralized 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 GNFAData-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 theDifference 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 toSimplex 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 cliqueMorse 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) FilterTuring 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 {\displaystylePolyhedral 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 isGrothendieck 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_{\omegaMonotonic 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 analysisBottom 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 isUtility 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'llLimit 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 considerRegular 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 onlyTop 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: BasicObjectAlmost 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, relativeCandidate 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 functionalThree-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 aMaximal 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 fromKleinian 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 limitSmooth 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 andUrelement (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 mustWilliam 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 downGraph 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 graphWeight 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 ( aSemiring (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 productCommutative 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 ifTotal 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 (moreEquivalence 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 alsoAtom (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. ThusTree 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 functionClause (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 inAlfred 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 cataloguePrime 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 {\displaystyleEnumerator (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 {\displaystyleExtended 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 − ∞ {\displaystyleBorel 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 nodePartially 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 posetalPseudorandom 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 betweenSphere (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 nonemptyAnne 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/HumanitySaul 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 worldsWeak 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 equivalenceVulnerability (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 specificHyperarithmetical 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 TuringGranger 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 ) {\displaystyleConvex 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 problemDijkstra'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 nodeThe 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 earlyKnapsack problem (6,539 words) [view diff] exact match in snippet view article find links to article

{\displaystyle m[0]=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, RobertSchröder–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; itKuratowski 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 functionsKnowledge 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 {\displaystyleFair 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), andTimestamp-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 objectsGroupoid (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 \astCorporate 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 ofAida (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 centerSet-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} forMethod 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 areOverlapping 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 topologicallyNormal 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 theIrreducible 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 setSaturated 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 familyReed'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 subsetsSheaf (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 setsQuadric (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 theLL 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 variantsLocally 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. IndeedStokes' 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 factSharkovskii'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 ofTwelvefold 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 thatStar 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 regularRead-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 {\displaystyleDennis 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 McCaugheyShapley 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 functionPre-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 someMetric 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} isGeorge 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 scienceKripke 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 worldsPregeometry (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 {\displaystyleTreap (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 algorithmsRegular 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 realisedKleene'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 inductivelyDFA 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 suchConstraint 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 unsatisfiabilityNoetherian 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 elementConvex 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 conicalMathematical 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 assertionSimplex (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 stillHalting 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 toGröbner 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 coefficientsGlossary 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 upperAssociation 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 growsComplete 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 numerousQuasitransitive 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. IntransitivityRegular 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 introducedWorcester 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 EnglandYoung 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 evenZero 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. LikewiseEspecially 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 wasArgumentation 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 associatesOutline 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 oneSemigroup 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 TFrölicher 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 curvesComposition 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 logicalBenford'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'sExtensive-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 distributionMorley 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 emptyModal 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 containedTiny 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 barTwo-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 AprilEvent-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 generatorWeighted 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 } {\displaystyleBose–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 ) {\displaystyleSimple 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. HeReal 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 unionsHahn–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 ofDarryl 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, DarrylOrder 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} _{+}} itDenotational 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 anotherBlackadder 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. ThisEilenberg–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 coordinatesAbsoluteness (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) aEuclidean 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 theoremFinitist 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 noMeasurable 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 sequenceSymbolic 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 {\mathcalNakamura 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 simpleFirst-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 gainHomogeneous 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 projectiveHemicontinuity (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), thenDynamical 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\subseteqPositional 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},\ldotsMedial 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 weightZhegalkin 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 monomialsMetric 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 byInquisitive 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 theCooperative 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 calledAlain 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 philosophyArithmetical 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 setAssociahedron (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 lateStalk (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 ⊆ {\displaystyleRationalizability (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. ConsiderFrege 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-provablePost'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 changingProjective 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, aAronszajn 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 ofSunny 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}}} countableWithout (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 differentBijection, 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} \toMex (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 willZero-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 twoPolyhedral 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 polyhedraThreat (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 theU-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) theoryList 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 realisedParser 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 elementSieve (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 answerCombinatory 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