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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-polytopeInterior (topology) (1,053 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) (4,478 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 emptyAxiom 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)Universal quantification (2,644 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 expressesProbability axioms (1,173 words) [view diff] no match in snippet view article find links to article

The Kolmogorov axioms are a fundamental part of Andrey Kolmogorov's probability theory. In it, the probability P of some event E, denoted P ( E ) {\displaystyleInteresting number paradox (606 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 uninterestingTotally 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 connectedConjugate 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 closureAtari ST character set (1,064 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, andUninterpreted function (440 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 equationalFinite-state machine (4,484 words) [view diff] exact match in snippet view article find links to article

} 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}} isGenerating set of a group (1,453 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 productAxiom of global choice (454 words) [view diff] exact match in snippet view article find links to article

non-empty set. The axiom of global choice states that there is a global choice function τ, meaning a function such that for every non-empty set z, τ(z)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 partiallyBoundary (topology) (1,122 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 neighborhoodProperty 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 subsetConstant 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, yLinear span (1,347 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 relatedArrangement of hyperplanes (1,800 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 subspaces are called the flats of A. The intersection semilatticeMathematical 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 ∩ ∩︀ withSmith set (663 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 everyTree (data structure) (6,951 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: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 theHyperstructure (291 words) [view diff] exact match in snippet view article find links to article

structures. A hyperoperation ( ⋆ ) {\displaystyle (\star )} on a non-empty set H {\displaystyle H} is a mapping from H × H {\displaystyle H\times H}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'}Relational model (5,290 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 appearingScott 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) fromSurreal number (11,188 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 surrealTopology (4,185 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 τNP-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 theConvex polytope (2,328 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 joinBounding 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 boundingLévy–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 (1,707 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 LeagueHeap (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 [xSilent letter (3,622 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 theSet (abstract data type) (2,907 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, initiallyBalanced set (386 words) [view diff] exact match in snippet view article find links to article

space. The balanced sets are C {\displaystyle \mathbb {C} } itself, the empty set and the open and closed discs centered at zero. Contrariwise, in the twoDescriptive 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-aryDefinable set (1,231 words) [view diff] exact match in snippet view article find links to article

definable in M {\displaystyle {\mathcal {M}}} with parameters from the empty set (that is, with no parameters in the defining formula). A function is definableTuring 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 setsBowyer–Watson algorithm (629 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 trianglesSuccessor function (352 words) [view diff] exact match in snippet view article find links to article

proposed. For example, John von Neumann constructs the number 0 as the empty set {}, and the successor number S(n) as the set n ∪ { n }. The axiom of infinityEntity 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 keySchwartz 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 pairwiseAntichain (701 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 noLogical conjunction (1,186 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 tableAbstract and concrete (924 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 thisLogical 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 {\displaystylePrimitive permutation group (668 words) [view diff] exact match in snippet view article find links to article

In mathematics, a permutation group G acting on a non-empty set X is called primitive if G acts transitively on X and G preserves no nontrivial partitionHahn–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 \SigmaCWI-2 (543 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 | BULLETSunny Day Real Estate (3,458 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 alreadyProbability measure (779 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 propertySemiautomaton (1,618 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 transitionLarry 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 particularDependence 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 {\displaystyleKalai's 3^d conjecture (583 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 polygonsDimension (3,936 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 classWell-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 ofStrong antichain (286 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 antichainZorn's lemma (2,514 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 thenPolyhedral combinatorics (2,184 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 PPlanar ternary ring (1,588 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\colonSunny Day Real Estate discography (284 words) [view diff] case mismatch in snippet view article find links to article

Hoerner as vocalist, the band released a two song demo under the name 'Empty Set' and then released a six song demo under the name 'Chewbacca Kaboom' beforeOrientation (vector space) (1,876 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 equivalenceType (model theory) (2,236 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 {\mathcalScott 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 conceptMonotonic function (1,959 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 analysisISO 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 ℕDouble turnstile (310 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 ⊨ {\displaystyleISO 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 ℕCosheaf (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 {\displaystyleMorse theory (2,887 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)}Pi-system (2,316 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-algebraPolyhedral 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 isComparison 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 measuresRon Asheton (1,263 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 The Wylde Ratttz, a band composed of someBasic Latin (Unicode block) (564 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. EdbergSimplex 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 cliqueEmpty 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 orderRelevance logic (3,378 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 0Affine hull (408 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)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 ∈ ADan 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 ChewbaccaGeneralized 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 GNFADistributive lattice (2,006 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 distributiveGraph theory (5,699 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 graphUrelement (979 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 mustTuring machine (9,035 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 {\displaystyleTopological property (1,859 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 pointNeighbourhood system (486 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. Neighbourhood BaseMaximal independent set (5,311 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 fromRegular expression (7,384 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 onlyAlmost everywhere (1,100 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, relativeTychonoff's theorem (2,007 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 straightforwardImpredicativity (1,743 words) [view diff] exact match in snippet view article find links to article

definitions and his failure to retain the "theorem that an arbitrary non-empty set M of real numbers having an upper bound has a least upper bound (cf. alsoGrothendieck 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_{\omegaBottom type (957 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. Top type NaN Fail-stop PierceHyperreal number (4,324 words) [view diff] exact match in snippet view article find links to article

Finally, we do not want the empty set to belong to U because then everything would belong to U, as every set has the empty set as a subset. Any family ofDifference bound matrix (4,733 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 toOrdinal 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 elementLine 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 closedThree-dimensional space (2,967 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 aClause (logic) (456 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 ∅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 catalogueEquivalence relation (3,848 words) [view diff] exact match in snippet view article find links to article

not have a common factor greater than 1). The empty relation R on a non-empty set X (i.e. aRb is never true) is vacuously symmetric and transitive, butLarry 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 (5,799 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 considerEnumerator (computer science) (253 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 {\displaystyleCandidate 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 functionalUtility functions on indivisible goods (1,801 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 ) >Top type (939 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: BasicObjectTree 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 functionSaul Kripke (6,180 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 worldsTotal order (2,245 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 (moreBorel subgroup (926 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 nodeAtom (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. ThusAida (musical) (3,503 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 centerSchröder–Hipparchus number (1,257 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; itSphere (5,865 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 nonemptyLeast-upper-bound property (1,354 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 ≥Dijkstra's algorithm (5,551 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 return failure node ← frontier.pop() if node isConvex optimization (1,996 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 problemPrime number (13,908 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 {\displaystylePseudorandom number generator (3,269 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 betweenKleinian 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 limitContinuous function (7,169 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 functionsVulnerability (computing) (3,435 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 specificSheaf (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 setsKnowledge 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 {\displaystylePartially ordered set (3,686 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 posetalWeight 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 ( aAnne Waldman (2,925 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/HumanitySet-theoretic definition of natural numbers (508 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} forGranger causality (2,732 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 ) {\displaystyleWilliam Goldsmith (1,451 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 downOverlapping interval topology (291 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 topologicallyCorporate election (8,125 words) [view diff] exact match in snippet view article find links to article

time that the elect people is an empty set. Another reason to reject that corporate election is an election of an empty set is seen in the election of a corporateCommutative 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 ifSemiring (4,091 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 productKuratowski closure axioms (3,727 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 } ;Quadric (4,924 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 theAlfred 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:Knapsack problem (6,552 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 ] , . .Additive number theory (862 words) [view diff] exact match in snippet view article find links to article

small and the structural conclusion then being that either A or B is the empty set; such problems are often considered direct problems as well). ExamplesStar 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 regularIrreducible component (648 words) [view diff] exact match in snippet view article find links to article

the plane. 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. It is thusAdditive number theory (862 words) [view diff] exact match in snippet view article find links to article

small and the structural conclusion then being that either A or B is the empty set; such problems are often considered direct problems as well). ExamplesStar 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 regularFair division (2,609 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), andWeak ordering (3,084 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 equivalenceSLD 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 inConical combination (448 words) [view diff] exact match in snippet view article find links to article

origin. If S is a compact set (in particular, when it is a finite non-empty set of points), then the condition "plus the origin" is unnecessary. If weShapley value (2,963 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 functionThe Stooges (4,600 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 earlyStokes' theorem (3,924 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 factConvex cone (2,383 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 conicalRay 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 Mathematical induction (6,574 words) [view diff] exact match in snippet view article find links to article

implies the well-ordering principle. Proof. Suppose there exists a non-empty set, S, of naturals that has no least element. Let P(n) be the assertion thatReed'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 subsetsRead-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 {\displaystyleNormal 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 theImieliński-Lipski algebra (931 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 variantsNoetherian ring (2,034 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 elementRegular polyhedron (2,941 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 realisedKripke semantics (4,283 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 worldsMethod 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 areKleene's recursion theorem (2,687 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 inductivelyMetric space (5,580 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} isHyperarithmetical 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 TuringTimestamp-based concurrency control (1,320 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 objectsLL parser (3,789 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(wi) for every rule Ai → wi, where Fi is defined as follows: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}Monoid (4,283 words) [view diff] exact match in snippet view article find links to article

form a commutative monoid under union operation (identity element is the empty set). Generalizing the previous example, every bounded semilattice is an idempotentAssociation rule learning (5,068 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 growsMonoid (4,283 words) [view diff] exact match in snippet view article find links to article

form a commutative monoid under union operation (identity element is the empty set). Generalizing the previous example, every bounded semilattice is an idempotentPregeometry (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 {\displaystyleQuasitransitive relation (755 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. IntransitivityBase (topology) (2,191 words) [view diff] exact match in snippet view article

using a convention that the union of empty collection of sets is the empty set. We are using a convention that the empty intersection of subsets of XGeorge Boole (5,632 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 scienceGlossary 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 upperHalting problem (5,841 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 toTreap (2,342 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 algorithmsSimplex (6,028 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 stillPithos (2,921 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 numerousYoung 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 evenConstraint programming (2,883 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 unsatisfiabilityWorcester Polytechnic Institute (5,351 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 EnglandFrölicher 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 curvesModal logic (7,373 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 relationComplete partial order (1,114 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”)Especially for You (The Smithereens album) (2,233 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 wasPre-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 someExtensive-form game (3,476 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 distributionGenerated σ-algebra (by sets) (581 words) [view diff] exact match in snippet view article

not empty, because they all contain the set X {\displaystyle X} and the empty set. The intersection of any number of σ-algebra is also a σ-algebra, seeGröbner basis (6,196 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(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 containedDFA 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 suchPermutohedron (1,131 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 ofTwo-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}Halfwidth and Fullwidth Forms (Unicode block) (384 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).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 introducedOutline of object recognition (2,699 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 oneEvent-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 } {\displaystyleDogville (3,588 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 AprilSemigroup action (1,966 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 TTwelvefold way (5,341 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 thatMorley rank (656 words) [view diff] exact match in snippet view article find links to article

categoricity theorem and in the larger area of stability theory. The empty set has Morley rank −1, and conversely anything of Morley rank −1 is emptyBlackadder Goes Forth (4,757 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. ThisReal analysis (7,672 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 unionsPositional notation (6,796 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},\ldotsArgumentation framework (3,198 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 associatesTimed 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} _{+}} itBose–Einstein statistics (5,424 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 ) {\displaystyleDenotational semantics (3,414 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 anotherTiny BASIC (2,206 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 barFirst-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 gainISO/IEC 2022 (7,500 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. Announcer sequences are as follows: Extended Unix Code (EUC) is an 8-bitEmpty sum (546 words) [view diff] exact match in snippet view article find links to article

extension, the zero-dimensional vector space V={0} has a basis, namely the empty set. Iterated binary operation Empty function Harper, Robert (2016). PracticalSimple 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. HeFinitist 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 noZero to the power of zero (2,864 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. LikewiseRationalizability (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 (606 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-provableEuclidean algorithm (14,304 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 theoremStalk (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 (Order topology (2,161 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),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 weightDarryl 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, DarrylComposition of relations (2,030 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 logicalList of first-order theories (5,276 words) [view diff] exact match in snippet view article find links to article

same as the theory of the empty set (in versions of first-order logic that allow a model to be empty): the theory of the empty set has exactly one model,Constructible number (2,667 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) aEilenberg–MacLane space (1,427 words) [view diff] exact match in snippet view article find links to article

a: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 ) =Continuous mapping theorem (1,006 words) [view diff] exact match in snippet view article find links to article

second term converges to zero as δ → 0, since the set Bδ shrinks to an empty set. And the last term is identically equal to zero by assumption of the theoremCylindric algebra (1,020 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 ⊆ {\displaystylePost'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 changingDynamical 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\subseteqAlain Badiou (7,183 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 (4,428 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 setMetric 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 byDynamical 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\subseteqCooperative game theory (6,026 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 calledWithout (The X-Files) (2,104 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 differentNakamura 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 simpleHemicontinuity (1,060 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), thenCombinatory logic (5,308 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 intuitionisticallyZhegalkin polynomial (4,062 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 monomialsNull (SQL) (7,594 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 answerPolyhedral 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 polyhedraCellular homology (1,515 words) [view diff] exact match in snippet view article find links to article

X_{n-2})\to \cdots ,} where X − 1 {\displaystyle X_{-1}} is taken to be the empty set. The group H n ( X n , X n − 1 ) {\displaystyle {H_{n}}(X_{n},X_{n-1})}Zero-suppressed decision diagram (3,686 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 twoProjective plane (6,554 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, aList of regular polytopes and compounds (5,983 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 realisedFlood fill (2,275 words) [view diff] exact match in snippet view article find links to article

is true and findloop is false and either front-pixel or left-pixel is empty set findloop to true end if turn right PAINT: move forward end if START: setHomogeneous 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 projectiveRamsey's theorem (4,719 words) [view diff] exact match in snippet view article find links to article

{\displaystyle C_{k}^{2}} as the set of all such restrictions, a non-empty set. Continuing so, define C k m {\displaystyle C_{k}^{m}} for all integersSympathy for the Record Industry (502 words) [view diff] case mismatch in snippet view article find links to article

Sticks/Gila Monster split 7" SFTRI 162 Gibson Bros. White Nigger 7" SFTRI 163 Empty Set Down On The Street 7" SFTRI 164 Mono Men Took That Thing 7" SFTRI 165True arithmetic (1,074 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}}} countableAssociahedron (1,423 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 lateLPBoost (1,952 words) [view diff] exact match in snippet view article find links to article

very well. LPBoost constructs f {\displaystyle f} by starting with an empty set of weak classifiers. Iteratively, a single weak classifier to add to theMeasurable cardinal (2,024 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,Set estimation (775 words) [view diff] exact match in snippet view article find links to article

When outliers occur, the set estimation method generally returns an empty set. This is due to the fact that the intersection between of sets of parameterU-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) theoryZeckendorf's theorem (1,382 words) [view diff] exact match in snippet view article find links to article

(uniqueness) requires the following lemma: Lemma: The sum of any non-empty set of distinct, non-consecutive Fibonacci numbers whose largest member isCondorcet method (7,515 words) [view diff] exact match in snippet view article find links to article

least one candidate. Such sets include the Smith set: The smallest non-empty set of candidates in a particular election such that every candidate in theQuotient automaton (740 words) [view diff] exact match in snippet view article find links to article

Sf⟩, where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s0 is the initial state, an element ofSylvester's sequence (2,481 words) [view diff] exact match in snippet view article find links to article

. {\displaystyle s_{n}=1+\prod _{i=0}^{n-1}s_{i}.} The product of an empty set is 1, so s0 = 2. Alternatively, one may define the sequence by the recurrenceSieve (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′)P-basis (221 words) [view diff] exact match in snippet view article find links to article

indeterminate, and K the field generated by all elements x1/pn then the empty set is a p-basis, though the extension is separable and has transcendenceThreat (computer) (4,379 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 thePéter Frankl (566 words) [view diff] exact match in snippet view article find links to article

union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets inMex (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