mathematicians may call a set built this way an inductive set. Hint: In English, it reads: "There exists a set 𝐈 such that the empty set is an element of it...

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...

The latter has a classically equivalent inductive substitute. So a genuinely intuitionistic development of set theory requires the rewording of some standard...

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...

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...

Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples...

Inductive charging (also known as wireless charging or cordless charging) is a type of wireless power transfer. It uses electromagnetic induction to provide...

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...

existence of two sets, the infinite inductive set y, and the null set ∅ . {\displaystyle \varnothing .} ∅ {\displaystyle \varnothing } is a set simply because...

into "buckets", according to their rank. We define the buckets' ranges inductively, as follows: Bucket 0 contains vertices of rank 0. Bucket 1 contains...

Induction cooking Induction motors Induction sealing Induction welding Inductive charging Inductors Magnetic flow meters Mechanically powered flashlight...

Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but...

fields using inductive coupling between coils of wire, or by electric fields using capacitive coupling between metal electrodes. Inductive coupling is...

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...

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...

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...

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...

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...

{\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 ) ∪...

{\displaystyle A} . In axiomatic set theory, the natural numbers are defined as the smallest inductive set (i.e., set containing 0 and closed under the...

{\displaystyle L_{M}} is magnetizing inductance k {\displaystyle k} is inductive coupling coefficient Measuring basic transformer inductances & coupling...

hereditary set is interesting only in a context in which there may be urelements. The inductive definition of hereditary sets presupposes that set membership...

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...

Inductive reasoning aptitude (also called differentiation or inductive learning ability) measures how well a person can identify a pattern within a large...

variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction)...

Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest...

data, while inductive algorithms compute it on a subset of the training set. Inductive Conformal Prediction was first known as inductive confidence machines...

upon learning that penguins are birds that do not fly. Inductive reasoning starts from a set of individual instances and uses generalization to arrive...

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...

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...