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inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty. In descriptive set theory, an inductive set of
Inductive_set
Axiom of Zermelo-Fraenkel set theory
call a set built this way an inductive set. A natural language formulation of this axiom may read as: "There exists a set 𝐈 such that the empty set is an
Axiom_of_infinity
Axiomatic set theories based on the principles of mathematical constructivism
The latter has a classically equivalent inductive substitute. So a genuinely intuitionistic development of set theory requires the rewording of some standard
Constructive_set_theory
Learning logic programs from data
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples
Inductive_logic_programming
System of mathematical set theory
existence of two sets, the infinite inductive set y, and the null set ∅ . {\displaystyle \varnothing .} ∅ {\displaystyle \varnothing } is a set simply because
Morse–Kelley_set_theory
Number used for counting
function. Such sets are said to be inductive. The intersection of all inductive sets is still an inductive set. This intersection is the set of the natural
Natural_number
Axiomatic set theory devised by W.V.O. Quine
trivially true, since the universal set V {\displaystyle V} would be an inductive set. Since inductive sets always exist, the set of natural numbers N {\displaystyle
New_Foundations
Generalization of "n-th" to infinite cases
set membership ( ∈ {\displaystyle \in } ). The set ω ≡ N {\displaystyle \omega \equiv \mathbb {N} } is usually defined as the smallest inductive set
Ordinal_number
Assumptions for inference in machine learning
The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs
Inductive_bias
Type of wireless power transfer
Inductive charging, also known as wireless charging or cordless charging, is a type of wireless power transfer. It uses electromagnetic induction to provide
Inductive_charging
Branch of mathematics that studies sets
set may be regarded as a homotopy 0-type, with universal properties of sets arising from the inductive and recursive properties of higher inductive types
Set_theory
Data type that refers to itself in its definition
contrast, a static array's size requirements must be set at compile time. Sometimes the term "inductive data type" is used for algebraic data types which
Recursive_data_type
Inductive reasoning aptitude (also called differentiation or inductive learning ability) measures how well a person can identify a pattern within a large
Inductive_reasoning_aptitude
Data structure for storing non-overlapping sets
into "buckets", according to their rank. We define the buckets' ranges inductively, as follows: Bucket 0 contains vertices of rank 0. Bucket 1 contains
Disjoint-set_data_structure
Statement supporting a conclusion
make the conclusion more reasonable or increase its probability, such as inductive, abductive, and analogical arguments. Defective arguments, called fallacies
Premise
set Analytic set C-measurable set Projective set Inductive set Infinity-Borel set Suslin set Homogeneously Suslin set Weakly homogeneously Suslin set
List of properties of sets of reals
List_of_properties_of_sets_of_reals
properties inductive 1. An inductive set is a set that can be generated from a base set by repeatedly applying a certain operation, such as the set of natural
Glossary_of_set_theory
Electrical transmission without physical connection
fields using inductive coupling between coils of wire, or by electric fields using capacitive coupling between metal electrodes. Inductive coupling is
Wireless_power_transfer
Telecommunications device
direct connection of the transmitter to the line, while the receiver was inductively coupled. In local battery configurations, when the local loop was too
Telephone
Set of elements in any of some sets
{\displaystyle A\cup B=\bigcup \{A,B\}} . Then, finite unions can be defined inductively as: ⋃ i = 1 0 A i = ∅ , and ⋃ i = 1 n A i = ( ⋃ i = 1 n − 1 A i ) ∪
Union_(set_theory)
Type theory created by Thierry Coquand
variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction)
Calculus_of_constructions
Mathematical theory
Solomonoff's theory of inductive inference in philosophy is a method of evaluating scientific models according to their description length. According
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
Statistical technique for producing prediction sets
data, while inductive algorithms compute it on a subset of the training set. Inductive Conformal Prediction was first known as inductive confidence machines
Conformal_prediction
Question of whether inductive reasoning leads to definitive knowledge
known as "inductive inferences". David Hume, who first formulated the problem in 1739, argued that there is no non-circular way to justify inductive inferences
Problem_of_induction
Method of logical reasoning
Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but
Inductive_reasoning
transitive set strictly totally ordered by set membership" and thus is absolute. "x = ω (the first infinite ordinal)" is equivalent to "x is an inductive set containing
Standard_model_(set_theory)
Mathematical proposition equivalent to the axiom of choice
Bourbaki, a partially ordered set is called inductive if each chain has an upper bound in the set (in particular, the set is then nonempty). Then the lemma
Zorn's_lemma
Concept in mathematical logic
hereditary set is interesting only in a context in which there may be urelements. The inductive definition of hereditary sets presupposes that set membership
Hereditary_set
Invariant of topological spaces
topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension
Inductive_dimension
Subset of artificial intelligence
identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner to make predictions. Inductive logic programming
Machine_learning
Production of voltage by a varying magnetic field
Induction cooking Induction motors Induction sealing Induction welding Inductive charging Inductors Magnetic flow meters Mechanically powered flashlight
Electromagnetic_induction
Determining the probability of future events based on past events
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical
Inductive_probability
Process mining algorithm
Inductive miner belongs to a class of algorithms used in process discovery. Various algorithms proposed previously give process models of slightly different
Inductive_miner
Set theory concept
set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the empty set is
Von_Neumann_universe
Defining elements of a set in terms of other elements in the set
recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some
Recursive_definition
Abstract data type for storing distinct values
element from a set without removing it; see msg106593 regarding standard name Ruby Feature #4553: Add Set#pick and Set#pop Inductive Synthesis of Functional
Set_(abstract_data_type)
Form of mathematical proof
Despite its name, mathematical induction differs fundamentally from inductive reasoning as used in philosophy, in which the examination of many cases
Mathematical_induction
First article on transfinite set theory
This proof comes from his 1879 proof, which contains a more complex inductive proof that demonstrates several properties of the intervals generated
Cantor's first set theory article
Cantor's_first_set_theory_article
System of mathematical set theory
B\subseteq B} is another way of expressing that B is transitive. The inductive hypothesis then informs us that ∀ a ∈ A ∃ b ( a ∈ b ∧ ⋃ b ⊆ b ) {\displaystyle
Kripke–Platek_set_theory
Magnetic perturbation of imperfectly coupled transformers
{\displaystyle L_{M}} is magnetizing inductance k {\displaystyle k} is inductive coupling coefficient Measuring basic transformer inductances & coupling
Leakage_inductance
Approximation of a mathematical set
based on a set of rules that describe the scope of the category. The choice of such rules is not unique, and therein lies the issue of inductive bias. See
Rough_set
System of mathematical set theory
{\displaystyle \phi } into an equivalent formula that simplifies the inductive part of the proof. For example, the only logical symbols in the transformed
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Process of using data analysis for predicting population data from sample data
assumption for covariate information. Objective randomization allows properly inductive procedures. Many statisticians prefer randomization-based analysis of
Statistical_inference
Process of drawing correct inferences
upon learning that penguins are birds that do not fly. Inductive reasoning starts from a set of individual instances and uses generalization to arrive
Logical_reasoning
Topological space of dimension zero
contained in exactly one open set of this refinement. A topological space is zero-dimensional with respect to the small inductive dimension if it has a base
Zero-dimensional_space
Proof assistant and programming language
programming language. It is based on the calculus of constructions with inductive types. It is a free and open-source software project hosted on GitHub
Lean_(proof_assistant)
Mathematical constructs and creation rules
In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type
Inductive_type
Models of computation
inductive inference (the "limiting recursive functionals" and "trial-and-error predicates", respectively). These models enable some nonrecursive sets
Hypercomputation
Finest topology making some functions continuous
mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set X , {\displaystyle X,} with respect to a family of functions
Final_topology
Large dummy load for testing electric power transmission systems
metering to show voltage and current. An inductive load includes inductive (lagging power factor) loads. An inductive load consists of an iron-core reactive
Load_bank
Area of automatic programming
Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses
Inductive_programming
Statement that all non empty subsets of positive numbers contains a least element
This also means that, in axiomatic set theory, the definition of the natural numbers as the smallest inductive set, N = { x ∈ S ∣ 0 ∈ S ∧ ∀ n ∈ S , n
Well-ordering_principle
Industrial Automation Software
Inductive Automation is a supplier of web-based industrial automation software based in Folsom, California, US. The Ignition SCADA platform is the company's
Inductive_Automation
Investigative process
of the application of inductive reasoning. However, Bacon's method of induction is much more complex than the essential inductive process of making generalisations
Baconian_method
Alternative foundation of mathematics
natural numbers. Proofs on inductive types are made possible by induction. Each new inductive type comes with its own inductive rule. To prove a predicate
Intuitionistic_type_theory
Study of the Bible
a message from God which has direct relevance to their daily lives. Inductive Bible study is a means of studying and exegeting a biblical passage. Richard
Bible_study_(Christianity)
equivalent to saying that the preordered set is the opposite of a closed preordered set. Inductive preordered sets satisfy Zorn's lemma and the Bourbaki–Witt
Closed_preordered_set
2025 novel by Suzanne Collins
on the Reaping to express Hume's philosophy of the distinction between inductive and deductive reasoning. As conveyed through Haymitch and Lenore Dove's
Sunrise_on_the_Reaping
Programming paradigm
the query is then given by the fraction of the successes. Probabilistic inductive logic programming aims to learn probabilistic logic programs from data
Probabilistic logic programming
Probabilistic_logic_programming
Special case of colimit in category theory
placing the final topology on the underlying set-theoretic direct limit. An ind-scheme is an inductive limit of schemes. Direct limits are linked to
Direct_limit
exists an inductive set) of ZFC of other set theories could not be married to ST. ST reveals how type theory can be made very similar to axiomatic set theory
ST_type_theory
Heuristics in automated theorem proving
Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as
Rippling
Mathematical result or axiom on order relations
(Bourbaki-Witt) at Zorn's lemma What we call a tower here is the same as an s-inductive set there. That proof is exactly the same as the proof of Zorn's lemma in
Hausdorff_maximal_principle
Inference seeking the simplest and most likely explanation
is expressed in terms such as "best available" or "most likely". While inductive reasoning draws general conclusions that apply to many situations, abductive
Abductive_reasoning
Simple radio receiver circuit for AM reception
pulses from the carrier frequency in it, which are blocked by the high inductive reactance and do not pass well through the coils of early date earphones
Crystal_radio
Type of mass spectrometry that uses an inductively coupled plasma to ionize the sample
Inductively coupled plasma mass spectrometry (ICP-MS) is a type of mass spectrometry that uses an inductively coupled plasma to ionize the sample. It
Inductively coupled plasma mass spectrometry
Inductively_coupled_plasma_mass_spectrometry
Recurrence relations of binomial coefficients in Pascal's triangle
\choose n-r}\qquad {\text{ for }}n,r\in \mathbb {N} ,\quad n\geq r.} The inductive and algebraic proofs both make use of Pascal's identity: ( n k ) = ( n
Hockey-stick_identity
Paradox arising from an incorrect proof
horses have the same color") was valid for n = 1 {\displaystyle n=1} . The inductive step proved here implies that since the rule is valid for n = 1 {\displaystyle
All_horses_are_the_same_color
Concept in mathematical logic and set theory
The language is extended to add a constant set symbol A. A formula in the extended language is inductively defined to be Σ n 1 , A {\displaystyle \Sigma
Analytical_hierarchy
algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes
Ind-scheme
Inductive logic game
Around the Rose, a similar inductive reasoning puzzle where the "secret rule" is always the same. The game can be played with any set of colorful playing pieces
Zendo_(game)
Study of correct reasoning
sciences are ampliative arguments. They are divided into inductive and abductive arguments. Inductive arguments are statistical generalizations, such as inferring
Logic
Philosophical study of knowledge
form of empiricism and explained knowledge of general truths through inductive reasoning. Charles Peirce (1839–1914) thought that all knowledge is fallible
Epistemology
_{1}^{\infty }K_{n}} as a union of compact sets K n {\displaystyle K_{n}} . Then inductively choose open sets V n ⊃ V n − 1 ¯ ∪ K n {\displaystyle V_{n}\supset
Exhaustion_by_compact_sets
Concept in set theory
inductive dimension (as are all spaces whose base consists of clopen sets.) The above definitions of open and closed sets provide the first two sets Σ
Baire_space_(set_theory)
Topological vector space
topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive system ( X n , i n m ) {\displaystyle (X_{n},i_{nm})} of
LF-space
Powder metallurgy process
within the induction coil. The advantage here is that the pressure and the inductive power are completely independent. Even powders with a liquid phase are
Hot_pressing
American inventor of algorithmic probability and artificial intelligence researcher
algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder of algorithmic information
Ray_Solomonoff
An Inductive pump is a magnetically regulated positive displacement pump used to pump liquids and gases. It is capable of handling many corrosive chemicals
Inductive_pump
Generalized sphere of dimension n (mathematics)
identifying the boundary of an n {\displaystyle n} -cube with a point, or (inductively) by forming the suspension of an ( n − 1 ) {\displaystyle (n-1)} -sphere
N-sphere
Theorem in group theory
showed that the McKay conjecture reduces to the checking of a so-called inductive McKay condition for each finite simple group. This opens the door to a
McKay_conjecture
Concept in philosophy of science
credited to Aristotle. For example, in Prior Analytics, he proposed an inductive syllogism, which served to establish the primary and immediate proposition
Inductionism
Functional programming language
after Thierry Coquand. The main way of defining data types in Agda is via inductive data types which are similar to algebraic data types in non-dependently
Agda_(programming_language)
positive and negative examples of some concept and a set of background-knowledge predicates, FOIL inductively generates a logical concept definition or rule
First-order_inductive_learner
Software platform
Ignition is an Integrated Software Platform for SCADA systems released by Inductive Automation in January 2010. Ignition features an OPC-UA server with an
Ignition_SCADA
Large countably-infinite ordinal number
iterated inductive definitions, and of K P ℓ 0 {\displaystyle KP\ell _{0}} , a fragment of Kripke–Platek set theory extended by an axiom stating every set is
Buchholz's_ordinal
Approach to the foundations of mathematics
necessarily finite. For mathematical purposes, the axiom "There exists an inductive set" would suffice. The following statements, while in the nature of axioms
Scott–Potter_set_theory
Large countable ordinal
February 2023. S. Feferman, "The proof theory of classical and constructive inductive definitions. A 40 year saga, 1968-2008." (2008), p.7. Accessed 21 February
Bachmann–Howard_ordinal
Mathematical theory of data types
calculus of inductive constructions, while Lean is based on dependent type theory. Type theory was created to avoid paradoxes in naive set theory and formal
Type_theory
Attempt to persuade or to determine the truth of a conclusion
predictions are inductive since the future is uncertain. An inductive argument is said to be strong or weak. If the premises of an inductive argument are
Argument
Crucial skill in all different fields of work and life
operations. Inductive reasoning compiles information and data to establish a general assumption that is suitable to the situation. Inductive reasoning commences
Analytical_skill
Professor of computer science
complexity to the study of inductive inference" was one of the first works to apply complexity theory to the field of inductive inference. Angluin joined
Dana_Angluin
Study of general and fundamental questions
not guarantee that the conclusion is true. One form is inductive reasoning. It starts from a set of individual cases and uses generalization to arrive
Philosophy
Property of a mathematical space
the term "functionally open". An inductive dimension may be defined inductively as follows. Consider a discrete set of points (such as a finite collection
Dimension
Generalization of Turing computability
ordinal in terms of smaller ordinals in an effective way. The following inductive definition is typical; it uses a pairing function ⟨ ⋅ , ⋅ ⟩ {\displaystyle
Hyperarithmetical_theory
Passive two-terminal electrical component that stores energy in its magnetic field
saturable reactor exploits saturation of the core as a means of stopping the inductive transfer of current via the core. The winding resistance appears as a
Inductor
Generalization of ordinary algorithms that compute more than Turing machines
present and future."(Davis 2006: 128) Davis disputes Burgin's claims that sets at level Δ 2 0 {\displaystyle \Delta _{2}^{0}} of the arithmetical hierarchy
Super-recursive_algorithm
Form of reasoning
non-deductive or ampliative reasoning. For ampliative arguments, such as inductive or abductive arguments, the premises offer weaker support to their conclusion:
Deductive_reasoning
{ID}}_{\nu }} are referred to as "the formal theories of ν-times iterated inductive definitions". IDν extends PA by ν iterated least fixed points of monotone
Theories of iterated inductive definitions
Theories_of_iterated_inductive_definitions
Method for resonantly powering electric vehicles
Moving field inductive power transfer or MFIPT is a technique for powering electric vehicles while driving along the road. The MFIPT technology is an
Moving field inductive power transfer
Moving_field_inductive_power_transfer
INDUCTIVE SET
INDUCTIVE SET
Boy/Male
Muslim
Intuitive
Girl/Female
Tamil
Bhagavath | பாகவாத
Name of Goddess Saraswati Devi inspired, Intuitive, And creative, Goddess Durga
Bhagavath | பாகவாத
Male
Japanese
(1-妖一, 2-陽一, 3-洋一, 4-与一) Japanese name YOICHI means "bewitching/seductive first (son)," 2) "clear/sun/pride first (son)," 3) "foreign/ocean first (son)," and 4) "participating first (son)."
Girl/Female
Indian
Name of Goddess Saraswati Devi inspired, Intuitive, And creative, Goddess Durga
Girl/Female
French, German, Latin, Spanish
Smooth; Seductive; Flattering; Blond
Girl/Female
Tamil
Bhagavathi | பாகாவாதி
Name of Goddess Saraswati Devi inspired, Intuitive, And creative, Goddess Durga
Bhagavathi | பாகாவாதி
Boy/Male
Indian
People with this Name Tend to be Very Inspired Intuitive and Creative
Boy/Male
Arabic, Muslim
Intuitive
Girl/Female
Afghan, African, American, Arabic, Danish, Egyptian, Finnish, Hebrew, Hindu, Indian, Jamaican, Modern, Muslim, Swahili, Swedish, Tamil
Dark Beauty; Wine; Intoxication; Night Beauty; Born at Night; Seductive
Female
Chinese
flattering and seductive.
Boy/Male
Indian, Telugu
Very Knowledge; Intuitive; Creative; Their Aim is to Improve the World and can be Quite Altruistic; Strive to See the Big Picture and Achieve Their Dreams; Inspired by Goddess Sarasvati
Girl/Female
Indian
Name of Goddess Saraswati Devi inspired, Intuitive, And creative, Goddess Durga
Girl/Female
American, Arabic, Australian, Christian, English, French, Greek, Hebrew, Indian, Persian, Sanskrit
Dark Haired Beauty; Night; Divine Play; From the Island; Night Beauty; Lovelorn; Seductive
Girl/Female
African, American, Arabic, Assamese, Australian, British, Danish, English, French, German, Greek, Hebrew, Hindu, Indian, Iranian, Jamaican, Latin, Muslim, Parsi, Persian, Polish, Sanskrit, Sindhi, Swahili, Tamil
Good; Night; Feminine of Lyle; Seductive; Dark Beauty; Lily; Purity; Pleasure; Sport; Pastime; Delicate; Playful; Divine Drama
Girl/Female
American, Arabic, Australian, British, Danish, English, Greek, Hebrew, Latin
Night; Night Beauty; Feminine of Lyle; From the Island; Variant of Delilah; Form of Lilac; Bluish; Languishing; Lovelorn; Seductive
Girl/Female
Hindu, Indian
Knowledgeable; Inspired; Intuitive; Creative
Girl/Female
African, American, Arabic, Danish, Finnish, French, German, Hebrew, Indian, Iranian, Irish, Italian, Muslim, Parsi, Sindhi, Swedish, Tamil
Dark as Night; Black; Night; Night Beauty; Nocturnal; Dark-haired Beauty; Lovelorn; Seductive; Name of a Saint; Dark Haired
Girl/Female
American, Arabic, Hebrew
Night; Lovelorn; Seductive
Girl/Female
Indian, Punjabi, Sikh
People with this Name Tend to be Very Inspired; Intuitive; And Creative; They Strive to See the Big Picture and Achieve Their Dreams
Girl/Female
African, Arabic, Australian, French, German, Hebrew, Indian, Kenyan, Spanish, Swahili, Tamil
Gentle; Delicate; Gentleness is her Soul; Lovelorn; Seductive
INDUCTIVE SET
INDUCTIVE SET
Girl/Female
Anglo Saxon
Best.
Girl/Female
Australian, Danish, French, German, Italian, Latin
Noble; Female Version of Patrick; Patrician; Well Born; Noblewoman
Surname or Lastname
English
English : variant spelling of Comley.
Male
English
Variant spelling of English Miles, MYLES means "son of Mile."
Female
Scandinavian
Short form of Scandinavian Kristina, STINA means "believer" or "follower of Christ."
Female
Portuguese
 Portuguese and Spanish form of Latin Mathilda, MATILDE means "mighty in battle." Compare with other forms of Matilde.
Boy/Male
Indian, Punjabi, Sikh
Within God
Girl/Female
Hindu, Indian
Hindu Goddess Parvati
Girl/Female
Indian
From gazelle
Girl/Female
Christian, German, Greek
Noble; Kind; Noble Sort
INDUCTIVE SET
INDUCTIVE SET
INDUCTIVE SET
INDUCTIVE SET
INDUCTIVE SET
a.
Leading to inferences; proceeding by, derived from, or using, induction; as, inductive reasoning.
n.
An expression which inveighs or rails against a person; a severe or violent censure or reproach; something uttered or written, intended to cast opprobrium, censure, or reproach on another; a harsh or reproachful accusation; -- followed by against, having reference to the person or thing affected; as an invective against tyranny.
a.
Not disposed to action or effort; not diligent or industrious; not busy; idle; as, an inactive officer.
a.
Not active; inert; esp., not exhibiting any action or activity on polarized light; optically neutral; -- said of isomeric forms of certain substances, in distinction from other forms which are optically active; as, racemic acid is an inactive tartaric acid.
a.
Not active; having no power to move; that does not or can not produce results; inert; as, matter is, of itself, inactive.
n.
The act or process of inducting or bringing in; introduction; entrance; beginning; commencement.
a.
Rendered electro-polar by induction, or brought into the opposite electrical state by the influence of inductive bodies.
a.
Inductive.
a.
Seeing clearly; as, an intuitive view; intuitive vision.
a.
Facilitating induction; susceptible of being acted upon by induction; as certain substances have a great inductive capacity.
n.
A process of demonstration in which a general truth is gathered from an examination of particular cases, one of which is known to be true, the examination being so conducted that each case is made to depend on the preceding one; -- called also successive induction.
a.
Received. reached, obtained, or perceived, by intuition; as, intuitive judgment or knowledge; -- opposed to deductive.
adv.
By induction or inference.
a.
Tending to lead astray; apt to mislead by flattering appearances; tempting; alluring; as, a seductive offer.
a.
Having the quality or power of conducting; as, the conductive tissue of a pistil.
a.
Pertaining to, or proceeding by, induction; inductive.
n.
The indicative mood.
a.
Operating by induction; as, an inductive electrical machine.
n.
A reductive agent.