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Topics referred to by the same term
Finite completeness may refer to: Complete category, a category in which all finite limits exist Completeness (order theory)#Finite completeness, a condition
Finite_completeness
Existence of certain infima or suprema of a given poset
notion of bounded completeness given below. Further simple completeness conditions arise from the consideration of all non-empty finite sets. An order in
Completeness_(order_theory)
Category in which all small limits exist
completeness is that of finite completeness. A category is finitely complete if all finite limits exists (i.e. limits of diagrams indexed by a finite
Complete_category
Fundamental theorem in mathematical logic
Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically
Gödel's_completeness_theorem
Partially ordered set in which all subsets have both a supremum and infimum
supremum and an infimum. Every non-empty finite lattice is complete, but infinite lattices may be incomplete. Complete lattices appear in many applications
Complete_lattice
Ability of a computing system to simulate Turing machines
able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule
Turing_completeness
Finite-state machine
deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state
Deterministic finite automaton
Deterministic_finite_automaton
Mathematical model of computation
theoretical computer science, a finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine
Finite-state_machine
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Attempt to formalize all of mathematics, based on a finite set of axioms
possible to prove forms of completeness for many other interesting systems. An example of a non-trivial theory for which completeness has been proved is the
Hilbert's_program
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either
Classification of finite simple groups
Classification_of_finite_simple_groups
Characteristic of some logical systems
syntactically complete. Syntactical completeness can also refer to another unrelated concept, also called Post completeness or Hilbert–Post completeness. In this
Completeness_(logic)
Form of logic that allows quantification over predicates
hypothesis does not hold. This theory consists of a finite theory characterizing the real numbers as a complete Archimedean ordered field plus an axiom saying
Second-order_logic
Algebraic structure
a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements. As with any field, a finite field
Finite_field
Computation model defining an abstract machine
into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that
Turing_machine
Area of mathematical logic
trivial, since every proof can have only a finite number of antecedents used in the proof. The completeness theorem allows us to transfer this to satisfiability
Model_theory
Mathematical group based upon a finite number of elements
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical
Finite_group
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic
Kruskal's_tree_theorem
Discrete analog of a derivative
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often
Finite_difference
Existence of values making formula true
model if and only if it has a finite model. This question is important in the mathematical field of finite model theory. Finite satisfiability and satisfiability
Satisfiability
Type of category in mathematics
{\mathcal {E}}} such that: E {\displaystyle {\mathcal {E}}} is finitely complete (it has all finite limits). Equivalently, it has a terminal object, binary products
Elementary_topos
State of being limited or ended
Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered
Finiteness
Branch of logic
model theory that fail for finite structures under finite model theory include the compactness theorem, Gödel's completeness theorem, and the method of
Finite_model_theory
Non-contradiction of a theory
in a particular deductive logic, the logic is called complete.[citation needed] The completeness of the propositional calculus was proved by Paul Bernays
Consistency
In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of
List_of_finite_simple_groups
Mathematics of real numbers and real functions
from the rational numbers by their completeness. Roughly speaking, the real numbers have no gaps. This completeness can be formalized in several equivalent
Real_analysis
Whether a decision problem has an effective method to derive the answer
system, especially in the context of first-order logic where Gödel's completeness theorem establishes the equivalence of semantic and syntactic consequence
Decidability_(logic)
Type of theory in mathematical logic
characterizing the model's structure. In first-order logic, only theories with a finite model can be categorical, due to the upward Löwenheim–Skolem theorem. Higher-order
Categorical_theory
Finite collection of distinct objects
In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically
Finite_set
Impossible task in computing
proven to be impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of First-order logic, a statement is universally valid if and
Entscheidungsproblem
theorem implies that Gödel's completeness theorem (that is fundamental to first-order logic) does not hold in the finite case. Also it seems counter-intuitive
Trakhtenbrot's_theorem
Order whose elements are all comparable
the completeness of X: If the order topology on X is connected, X is complete. X is connected under the order topology if and only if it is complete and
Total_order
Unsolved problem in computer science
many equivalent ways of describing NP-completeness. Let L be a language over a finite alphabet Σ. L is NP-complete if, and only if, the following two conditions
P_versus_NP_problem
Theorem in mathematical logic
states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory
Compactness_theorem
Number representing a continuous quantity
structures have a notion of completeness; the description in § Completeness is a special case. (We refer to the notion of completeness in uniform spaces rather
Real_number
Subset of incomparable elements
More generally, counting the number of antichains of a finite partially ordered set is #P-complete. Let S {\displaystyle S} be a partially ordered set.
Antichain
Concept in mathematical logic
adequate. From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of
Functional_completeness
Group without normal subgroups other than the trivial group and itself
for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple
Simple_group
Generalized alphabetical order
used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences
Lexicographic_order
as the "content completeness problem". The problem stems from the greater expressiveness of natural language relative to the finite enumeration of concepts
Content_completeness_problem
Type of finite-state machine in automata theory
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its
Nondeterministic finite automaton
Nondeterministic_finite_automaton
Theories in mathematical logic
properties: it is complete, decidable, finitely axiomatizable, and so on. The only problem is that it has no models at all. By Gödel's completeness theorem, it
List_of_first-order_theories
Model of computation over real numbers
Quantum finite automaton Blum, Lenore; Shub, Mike; Smale, Steve (1989). "On a Theory of Computation and Complexity over the Real Numbers: NP-completeness, Recursive
Blum–Shub–Smale_machine
Commutative group (mathematics)
groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. An abelian
Abelian_group
PSPACE-complete". Theoretical Computer Science. 123 (2): 329–340. doi:10.1016/0304-3975(94)90131-7. Hearn; Demaine (2002). "PSPACE-Completeness of Sliding-Block
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Study of discrete mathematical structures
can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deal with finite sets, particularly
Discrete_mathematics
Term in logic and deductive reasoning
special sense of completeness, in which the class of models (up to isomorphism) is restricted to the intended one. The original completeness proof applies
Soundness
Limitative results in mathematical logic
with semantic completeness, which means that the set of axioms proves all the semantic tautologies of the given language. In his completeness theorem (not
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Formal semantics for non-classical logic systems
corresponding class of L than to prove its completeness, thus correspondence serves as a guide to completeness proofs. Correspondence is also used to show
Kripke_semantics
Complexity class used to classify decision problems
MA: Cengage Learning. Sections 7.3–7.5 (The Class NP, NP-completeness, Additional NP-complete Problems). ISBN 978-1-133-18779-0. Complexity Zoo: NP American
NP_(complexity)
Axiom of set theory
II-finite, III-finite, IV-finite, V-finite, VI-finite and VII-finite. I-finiteness is the same as normal finiteness. IV-finiteness is the same as Dedekind-finiteness
Axiom_of_choice
Property of a partially ordered set
property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness. It can be used to prove many
Least-upper-bound_property
Mathematical model describing how an output of a function is computed given an input
models, functional models, and concurrent models. Sequential models include: Finite-state machines Post machines (Post–Turing machines and tag machines). Pushdown
Model_of_computation
Collection of mathematical objects
{\displaystyle \emptyset } ) and the latter has no elements at all. A set is finite if there exists a natural number n {\displaystyle n} such that the first
Set_(mathematics)
Alternative to Tarskian semantics
of any finite subset of it (and hence it is not deducible from it). It follows immediately that both compactness and the strong completeness theorem
Truth-value_semantics
Mathematical proposition equivalent to the axiom of choice
tell about Zorn's lemma?" Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic. Moreover, Zorn's lemma (or one of its equivalent
Zorn's_lemma
Consistency of the axioms of arithmetic
but a stronger system with a second-order completeness axiom. The system Hilbert asked for a completeness proof of is more like second-order arithmetic
Hilbert's_second_problem
Verb form that can complete an independent clause by itself
English imperative). A finite transitive verb or a finite intransitive verb can function as the root of an independent clause. Finite verbs are distinguished
Finite_verb
of abstract algebra, a signalizer functor is a mapping from a potential finite subgroup to the centralizers of the nontrivial elements of an abelian group
Signalizer_functor
Infinite cardinal number
_{0}} : Every finite set of natural numbers has a maximum, which is also a natural number, and finite unions of finite sets are finite. An example application
Aleph_number
Numerical analysis technique
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis
Finite-difference time-domain method
Finite-difference_time-domain_method
Basic framework of mathematics
only semi-decidable as given by the completeness theorem). 1955: Pyotr Novikov showed that there exists a finitely presented group G such that the word
Foundations_of_mathematics
Study of abstract machines and automata
with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine
Automata_theory
Model of (first-order) Peano arithmetic that contains non-standard numbers
arithmetic, is neither provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic
Non-standard model of arithmetic
Non-standard_model_of_arithmetic
Benjamin (2013). "Godel's Completeness Theorem and Deligne's Theorem". arXiv:1309.0389 [math.LO]. "Deligne completeness theorem". nLab. Grothendieck
Coherent_topos
When a finite set S of relations yields polynomial-time or NP-complete problems
sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of
Schaefer's_dichotomy_theorem
Philosophy of mathematics that accepts only finite objects
not cause a problem regarding finite objects. This led to Hilbert's program of proving both consistency and completeness of set theory using finitistic
Finitism
Algebraic structure providing a semantics of Łukasiewicz logic
determines so-called infinite-valued Łukasiewicz logic. Chang's (1958, 1959) completeness theorem states that any MV-algebra equation holding in the standard MV-algebra
MV-algebra
Logical principle
to the study of concrete operations on finite or potentially (but not actually) infinite structures; completed infinite totalities … were rejected, as
Law_of_excluded_middle
Algebraic structure with an associative operation and an identity element
monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for
Monoid
Maximal proper filter
implies that the completeness of any powerset ultrafilter is at least ℵ 0 {\displaystyle \aleph _{0}} . An ultrafilter whose completeness is greater than
Ultrafilter_on_a_set
Size of a possibly infinite set
(bijection) between the elements of the two sets. The cardinality of a finite set can be identified with a natural number, which can be found simply by
Cardinal_number
Problem in computer science
of a journey through such a cycle. For nondeterministic finite automata (restricted to finite memory), it is also decidable whether the machine halts
Halting_problem
Ordered listing of items in collection
elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There
Enumeration
Type of mathematical object
general linear groups. Complete connected group schemes are in some sense opposite to affine group schemes, since the completeness implies all global sections
Group_scheme
Overview of and topical guide to algorithms
Karp — NP-completeness and combinatorial optimization Stephen Cook — Cook–Levin theorem and NP-completeness Leonid Levin — NP-completeness and computational
Outline_of_algorithms
Formal language that can be expressed using a regular expression
be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after
Regular_language
Presburger introduces Presburger arithmetic and proving its decidability and completeness. 1928 - Hilbert and Wilhelm Ackermann propose the Entscheidungsproblem:
Timeline of mathematical logic
Timeline_of_mathematical_logic
NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states
NFA_minimization
Glossary of terms used in branch of mathematics
relation. Complete semilattice. The notion of a complete semilattice is defined in different ways. As explained in the article on completeness (order theory)
Glossary_of_order_theory
Generalization of the discrete Fourier transform
the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform
Fourier transform on finite groups
Fourier_transform_on_finite_groups
from any finitely complete category. It is used to form the effective topos and other realizability toposes. Let C be a category with finite limits. Then
Exact_completion
Belief in a deity that is not omnipotent
Theistic finitism, also known as finitistic theism or finite godism, is the belief in a deity that is limited. It has been proposed by some philosophers
Theistic_finitism
Partial order with joins
partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially
Semilattice
Mathematical set containing no elements
modelled by the empty set. When speaking of the sum of the elements of a finite set, one is inevitably led to the convention that the sum of the elements
Empty_set
Concept in model theory
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding. Equivalently, every first-order
Model_complete_theory
Set of elements in any of some sets
one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set. The notation for
Union_(set_theory)
Manifold of dimension 3 equipped with a hyperbolic metric
discrete group of isometries (a Kleinian group). Hyperbolic 3-manifolds of finite volume have a particular importance in 3-dimensional topology as follows
Hyperbolic_3-manifold
Concept in mathematical logic
sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. Complete theories are closed under a number of conditions
Complete_theory
Yes-or-no question that cannot ever be solved by a computer
stated as follows: Given the description of an arbitrary program and a finite input, decide whether the program finishes running or will run forever.
Undecidable_problem
Concept in logic
theory, a finite game (sometimes called a founded game or a well-founded game) is a two-player game that is assured to end after a finite number of moves
Finite_game
Topological group that is in a certain sense assembled from a system of finite groups
2018-12-26. Nikolov, Nikolay; Segal, Dan (2007). "On finitely generated profinite groups. I: Strong completeness and uniform bounds. II: Products in quasisimple
Profinite_group
Set theory concept
2\uparrow \uparrow n} elements using Knuth's up-arrow notation. So the finite stages of the cumulative hierarchy cannot physically be written down explicitly
Von_Neumann_universe
Type of vector space in math
Kainth (2023). For the completeness of Euclidean space, see Definition 4.37 and Example 4.38, p. 108; for the equivalence of completeness with the property
Hilbert_space
Function that preserves distinctness
theorem.) If both X {\displaystyle X} and Y {\displaystyle Y} are finite with the same number of elements, then f : X → Y {\displaystyle f:X\to Y}
Injective_function
Mathematical object in category theory
into Y {\displaystyle Y} . Let C {\displaystyle {\mathcal {C}}} be a finitely complete category (we denote the terminal object by 1 {\displaystyle 1} ).
Subobject_classifier
Statistics term
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to
Completeness_(statistics)
Set of functions used to represent the electronic wave function
Vaara have proposed completeness-optimized basis sets, where the exponents are obtained by maximization of the one-electron completeness profile instead of
Basis_set_(chemistry)
Statement that is taken to be true
interpretation". Gödel's completeness theorem establishes the completeness of a certain commonly used type of deductive system. Note that "completeness" has a different
Axiom
Type of mathematical space
property of finite sets is that every cover of a finite set by subsets has a finite subcover: one may choose, for each point of the finite set, a member
Compact_space
travel, tourism, insurance
FINITE COMPLETENESS
FINITE COMPLETENESS
Boy/Male
Hindu, Indian
Very Intelligent
Boy/Male
Celtic Irish
Handsome.
Boy/Male
Hindu
Unassuming, Knowledgeable, Modest, Venus, Requester
Male
Portuguese
Portuguese form of Latin Philippus, FILIPE means "lover of horses."
Girl/Female
Hindu
Humble, Unassuming, Obedience, Knowledge, Venus, Requester
Girl/Female
Indian
Infinite, Divine
Male
English
Variant spelling of English Finnian, FINIAN means "little white one."
Boy/Male
Hindu, Indian
Smart
Girl/Female
Hindu
Modesty, Education
Girl/Female
French
May Jehovah add. Addition (to the family). A feminine form of Joseph.
Boy/Male
Hindu
Girl/Female
Indian
Modest
Boy/Male
Indian, Sanskrit
Decent; Domesticated
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu, Traditional
Modest; The Most Lovable
Surname or Lastname
English
English : habitational name (reflecting the pronunciation of the place name) for someone from Finchale in Durham, named from Old English finc ‘finch’ + halh ‘nook or corner of land’.English : possibly a metonymic occupational name or topographic name from Middle English fenkel ‘fennel’. Compare Fennell.Respelling of German Finkel.
Girl/Female
Tamil
Infinite, Divine
Boy/Male
Indian, Telugu
Good Look
Girl/Female
Hindu, Indian
Daughter of Mahavir Jain
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Modesty; Good Behaviour
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Latin, Malayalam, Marathi, Spanish, Tamil, Telugu, Traditional
Polite Sweet; Requester Knowledge; Kindness
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
n.
See Yenite.
a.
To make fine; to dress finically.
n.
The joiner work and other finer work required for the completion of a building, especially of the interior. See Inside finish, and Outside finish.
n.
An infinite quantity or magnitude.
n.
See Conite.
a.
Unlimited or boundless, in time or space; as, infinite duration or distance.
n.
Fixedness; as, fixity of tenure; also, that which is fixed.
a.
Serving to define or restrict; limiting; determining; as, the definite article.
a.
Of or pertaining to a minute or minutes; occurring at or marking successive minutes.
v. t.
To give occasion for; as, to invite criticism.
n.
That which is infinite; boundless space or duration; infinity; boundlessness.
v. t.
To kindle or set on fire; as, to ignite paper or wood.
adv.
In a finite manner or degree.
a.
Attentive to small things; paying attention to details; critical; particular; precise; as, a minute observer; minute observation.
a.
Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.
p. pr. & vb. n.
of Fine
a.
Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.
n.
The Infinite Being; God; the Almighty.
v. t.
To invite or ask.
a.
Having certain or distinct; determinate in extent or greatness; limited; fixed; as, definite dimensions; a definite measure; a definite period or interval.
travel, tourism, insurance