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Topics referred to by the same term
Infinite tree may refer to: Tree (data structure), a data structure simulating a single-rooted, directed hierarchy (due to the requirement of computer-implementability
Infinite_tree
Mathematical structure
an infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an extension of top-down finite-tree automata
Infinite-tree_automaton
Class of algorithms
as breadth-first search, can also be used to traverse infinite trees, see below. Traversing a tree involves iterating over all nodes in some manner. Because
Tree_traversal
Partial order with well-ordered predecessors
κ {\displaystyle \kappa } -Aronszajn tree and a κ {\displaystyle \kappa } -Suslin tree. In fact, for any infinite cardinal κ {\displaystyle \kappa } ,
Tree_(set_theory)
Set that is not a finite set
then its union is infinite. The power set of an infinite set is infinite. Any superset of an infinite set is infinite. If an infinite set is partitioned
Infinite_set
Way of representing the hierarchical nature of a structure in a graphical form
node. The root is the starting node. But the converse is not true: infinite tree structures may or may not have a root node. The names of relationships
Tree_structure
2021 video game
Halo Infinite is a 2021 first-person shooter game developed by 343 Industries and published by Xbox Game Studios. It is the sixth mainline installment
Halo_Infinite
Method used in automata theory to represent tree structures using arithmetical sequences
successors. If every node of a tree has finitely many successors, then it is called a finitely, otherwise an infinitely branching tree. A path π is a subset of
Tree_(automata_theory)
Study of abstract machines and automata
words. Infinite input: An automaton that accepts infinite words (ω-words). Such automata are called ω-automata. Tree input: The input may be a tree of symbols
Automata_theory
Mathematical object for the lambda calculus
semantics of the lambda calculus, Böhm trees, Lévy-Longo trees, and Berarducci trees are (potentially infinite) tree-like mathematical objects that capture
Böhm_tree
sometimes identified with trees, specifically as a {0,1}-labeled tree {0,1}*; {0,1}* forms a complete infinite binary tree. For formula complexity, the
S2S_(mathematics)
Generalization of depth-first search trees
normal spanning trees, especially in the context of infinite graphs. All depth-first search trees and all Hamiltonian paths are Trémaux trees. In finite graphs
Trémaux_tree
Graph defined from a mathematical group
4-regular infinite tree. It is a key ingredient in the proof of the Banach–Tarski paradox. More generally, the Bethe lattice or Cayley tree is the Cayley
Cayley_graph
Algorithmic process of solving equations
single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite tree terms. Similarly, the semantic first-order unification problem { a⋅x
Unification (computer science)
Unification_(computer_science)
Israeli mathematician and computer scientist (1931–2026)
very shortly before by Cobham and Edmonds). In 1969, Rabin introduced infinite-tree automata and proved that the monadic second-order theory of n successors
Michael_O._Rabin
Undirected, connected, and acyclic graph
within distance 2 of a central path subgraph. A regular tree of degree d is the infinite tree with d edges at each vertex. These arise as the Cayley graphs
Tree_(graph_theory)
State machine for tree structures
bottom-up DFTA, but not by a top-town DFTA. Infinite-tree automata extend top-down automata to infinite trees, and can be used to prove decidability of
Tree_automaton
Tabletop role-playing game
the World Tree, a gigantic - possibly infinite - tree, with multiple trunks, branches tens of miles thick, and thousands long. World Tree was nominated
World Tree (role-playing game)
World_Tree_(role-playing_game)
Theorem in combinatorics generalizing Ramsey's theorem to infinite trees
mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure
Milliken's_tree_theorem
2022 video game
Torchlight: Infinite is an action role-playing game and the fourth game in the Torchlight series. It is developed and published by Chinese company XD Inc
Torchlight:_Infinite
Set-theoretic tree with uncountable branches
generally if κ {\displaystyle \kappa } is an infinite cardinal, then a κ {\displaystyle \kappa } -Kurepa tree is a tree of height κ {\displaystyle \kappa } with
Kurepa_tree
Algorithm component in computer science
Programming. 2: 143–149. Joxan Jaffar; Peter J. Stuckey (1986). "Semantics of Infinite Tree Logic Programming". Theoretical Computer Science. 46: 141–158. doi:10
Occurs_check
2023 video game
praising the mission tree system and use of Star Trek lore. Polygon indicated that, like in Stellaris (the game Star Trek: Infinite is based on), warfare
Star_Trek:_Infinite
Tree which includes all vertices of a graph
listing all spanning trees in polynomial time per tree. Every finite connected graph has a spanning tree. However, for infinite connected graphs, the
Spanning_tree
Topics referred to by the same term
multiplication algorithm suitable for hand calculation Bethe lattice, a regular infinite tree structure used in statistical mechanics Bravais lattice, a repetitive
Lattice
2021 studio album by Deafheaven
Pumpkins and Porcupine Tree. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream publications, Infinite Granite received
Infinite_Granite
Function defined on formal languages in computer science
language can be viewed as a (potentially infinite) boolean-labelled tree (see also tree (set theory) and infinite-tree automaton). Each possible string w ∈
Brzozowski_derivative
Mathematical tree
Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees. More generally, for any infinite cardinal κ, a κ-Suslin tree is a tree of height
Suslin_tree
Mathematical concept
{\displaystyle G} is its own uniform tree. If G {\displaystyle G} contains at least 1 cycle, its uniform tree is an infinite tree. Leighton's Graph Covering Theorem
Uniform_tree
Mathematical result on infinite trees
useful special case of the lemma is that every infinite tree contains a vertex of infinite degree or an infinite simple path. If it is locally finite, it meets
Kőnig's_lemma
Method in probability theory
edge of G with probability 1−p, independently. The infinite complete binary tree T is an infinite tree where one vertex (called the root) has two neighbors
Second_moment_method
Regular infinite tree structure used in statistical mechanics
mathematics, the Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have the same number of neighbors
Bethe_lattice
Mathematical arithmetic dynamics function
absolute Galois group of a field and the automorphism group of an infinite, regular, rooted tree. The study of arboreal Galois representations of goes back to
Arboreal Galois representation
Arboreal_Galois_representation
Group of transformations under which the object is invariant
group of its Cayley graph; the free group is the symmetry group of an infinite tree graph. Cayley's theorem states that any abstract group is a subgroup
Symmetry_group
Mathematical game played on a directed graph
78 (1991) Zielonka, W (1998). "Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees". Theor. Comput. Sci. 200 (1–2):
Parity_game
Partition result about finite products of infinite trees
Halpern–Läuchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for set theory in which the
Halpern–Läuchli_theorem
letting Kn be the complete binary tree of depth n.) These ends can be thought of as the "leaves" of the infinite tree. In the end compactification, the
End_(topology)
2008 video game
Infinite Undiscovery (インフィニット アンディスカバリー, Infinitto Andisukabarī) is a 2008 action role-playing game developed by Microsoft Game Studios Japan and tri-Ace
Infinite_Undiscovery
Programming idiom
In computer programming, an infinite loop (or endless loop) is a sequence of instructions that, as written, will continue endlessly, unless an external
Infinite_loop
Theorem in algebra
obtained alternate or simplified proofs of the Muller–Schupp theorem. Infinite tree automaton Word problem (mathematics) Formal language David E. Muller
Muller–Schupp_theorem
Proof method in mathematical logic
programming, such as infinite trees, lazy predicates, and concurrent communicating predicates. Co-LP has applications to rational trees, verifying infinitary
Coinduction
Algorithm to search the nodes of a graph
position for White. Implicit trees (such as game trees or other problem-solving trees) may be of infinite size; breadth-first search is guaranteed to find
Breadth-first_search
Fractal with infinite genus
Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number
Cantor_tree_surface
Diagram used in various mystical traditions
referred to as the "kabbalistic tree of life" to distinguish it from the tree of life that appears alongside the tree of the knowledge of good and evil
Tree_of_life_(Kabbalah)
Index of articles associated with the same name
{\displaystyle k} apeirogonal tiling form a Bethe lattice, a regular infinite tree. Apeirogonal antiprism Apeirogonal prism Apeirohedron Mosseri, R.; Sadoc
Apeirogonal_tiling
Tree in the Garden of Eden
for the tree, being finite, could not grant infinite life. Hence after a period of time, the man and woman would need to eat again from the tree or else
Tree_of_life_(biblical)
British actor
for his roles in the films Breaking and Entering (2006), Nick & Norah's Infinite Playlist (2008), A Star Is Born (2018), as well as the television series
Rafi_Gavron
Mathematical concept for comparing objects
Since X {\displaystyle X} contains no infinite bad sequence, the tree T X {\displaystyle T_{X}} contains no infinite path starting at the root. Therefore
Well-quasi-ordering
Ordered binary tree of rational numbers
In number theory, the Stern–Brocot tree is an infinite complete binary tree whose vertices correspond one-for-one to the positive rational numbers, whose
Stern–Brocot_tree
Type of topological space
free, with one generator for each petal. The universal cover is an infinite tree, which can be identified with the Cayley graph of the free group. (This
Rose_(topology)
Well-quasi-ordering of finite trees
above. That is to say, given any infinite sequence T 1 , T 2 , … {\displaystyle T_{1},T_{2},\ldots } of rooted trees labeled in X {\displaystyle X} ,
Kruskal's_tree_theorem
Indian science fiction writer and editor
2016). "Indra Das: 'The artist's job is to provide the seed for an infinite tree of branching meanings, all flowering inside the hive mind of a collective
Indrapramit_Das
Family of higher-order functions
[1..13]) "(1+((2+3)+(((4+5)+(6+7))+((((8+9)+(10+11))+(12+13))+0))))" Infinite tree-like folding is demonstrated e.g., in recursive primes production by
Fold_(higher-order_function)
Variation of a finite automaton that runs on infinite input
(MSO) theory of natural numbers under successor. Infinite-tree automata extend ω-automata to infinite trees and can be used to prove decidability of S2S,
Ω-automaton
Collection of prefixes of finite sequences
shows that the empty sequence belongs to every tree. A branch through a tree T {\displaystyle T} is an infinite sequence of elements of X {\displaystyle X}
Tree_(descriptive_set_theory)
Use of functions that call themselves
recursive tree traversal). In recursive computer programming, omitting the base case or defining it incorrectly may result in unintended infinite recursion
Recursion_(computer_science)
Mathematical structure
Euclidean, buildings. An affine building of type Ã1 is the same as an infinite tree without terminal vertices. Although the theory of semisimple algebraic
Building_(mathematics)
Technique that interweaves different computations
sometimes referred to as dovetailers. Consider a tree that potentially contains a path of infinite length (but each node has only finitely many children):
Dovetailing (computer science)
Dovetailing_(computer_science)
Ten emanations in Kabbalah
of emanations from the infinite divine essence. This was necessary due to the inability of humanity to exist in God's infinite presence. God does not
Sefirot
String instrument
The Infinite Guitar is a modified electric guitar created by Michael Brook, as a way of allowing a note to be held with infinite sustain. It consists of
Infinite_Guitar
Conjecture in graph theory
k-uniform hypergraphs for k>2 (Kocay). Infinite graphs. If T is the tree where every vertex has countably infinite degree, then the union of two disjoint
Reconstruction_conjecture
given an infinite subtree of the binary tree 2 < ω {\displaystyle 2^{<\omega }} , it is possible to find an infinite path through the tree with particular
Low_basis_theorem
Hallway at the Massachusetts Institute of Technology
The Infinite Corridor is a 251-meter (823 ft) hallway that runs through the main buildings of the Massachusetts Institute of Technology, specifically parts
Infinite_Corridor
Concept in set theory
representation of the Baire space as the set of all infinite paths passing through the full tree ω<ω of finite sequences of natural numbers ordered by
Baire_space_(set_theory)
Finding an optimal algorithm for playing chess
combinatorial games of perfect information) such as Capablanca chess and infinite chess. In a weaker sense, solving chess may refer to proving which one
Solving_chess
Limited form of tree data structure
complete binary tree. A complete binary tree can be efficiently represented using an array. The infinite complete binary tree is a tree with ℵ 0 {\displaystyle
Binary_tree
Classic counterexample in topology
the infinite broom is a subset of the Euclidean plane that is used as an example distinguishing various notions of connectedness. The closed infinite broom
Infinite_broom
Theorem on triangulation graph colorings
follows from Musin's theorem. There is a similar lemma about finite and infinite trees and cycles. Mirzakhani and Vondrak study a weaker variant of a Sperner
Sperner's_lemma
Species of fig
mulberry family. It is also known as the bodhi tree, bo tree, peepul tree, peepal tree, pipala tree or ashvattha tree (in Bangladesh, India and Nepal). The sacred
Ficus_religiosa
Slovene writer (born 1932)
Grozde: »jaz sem neskončno drevo« (The Martyr Lojze Grozde: "I Am an Infinite Tree"), 2010 Berta Golob on the Biographical Lexicon of Famous People from
Berta_Golob
Antiquated theory in biology
He claimed that it was not unreasonable to believe that "they are infinite trees in only one seed," as he stated that we could already see chickens in
Preformationism
Independent video game
game world use shapes that are impossible in Euclidean geometry, like infinite trees, equidistants and horocycles, and straight lines which never cross.
HyperRogue
Data structure
For example, the parent of 6 = 1102 is 8 = 10002. This conceptual tree is infinite, but only the part with indexes up to n {\displaystyle n} is stored
Fenwick_tree
English polymath (1642–1727)
the Newton-Cotes formulas for numerical integration. Newton's work on infinite series was inspired by Simon Stevin's decimals. He also initiated the field
Isaac_Newton
Kleene–Brouwer order is itself a well-ordering if and only if the tree has no infinite branch. It is named after Stephen Cole Kleene, Luitzen Egbertus Jan
Kleene–Brouwer_order
Subfield of set theory
Michael O. (1969). "Decidability of second order theories and automata on infinite trees" (PDF). Transactions of the American Mathematical Society. 141: 1–35
Determinacy
r=n-c} . It turned out that descendant trees of a particular kind, the so-called pruned coclass trees whose infinitely many vertices share a common coclass
Descendant tree (group theory)
Descendant_tree_(group_theory)
Retrieved January 20, 2026. DiVincenzo, Alex (January 8, 2026). "'The Infinite Husk' Trailer – Exiled Alien Consciousness Invades Earth in Sci-Fi Thriller"
List of American films of 2026
List_of_American_films_of_2026
Type of graph related to pursuit–evasion
graphs can even be infinite trees, with a finite number of edges per vertex. By Kőnig's lemma, such a tree must have an infinite path, and an omniscient
Cop-win_graph
American actor (born 1975)
ensure his availability for all appearances prior to and in the "Crisis on Infinite Earths" crossover. In July 2019, it was announced that Garrett would also
LaMonica_Garrett
Science and comedy radio show
The Infinite Monkey Cage is a BBC Radio 4 comedy and popular science series. Hosted by physicist Brian Cox and comedian Robin Ince, The Independent described
The_Infinite_Monkey_Cage
1987 studio album by U2
The Joshua Tree is the fifth studio album by the Irish rock band U2. It was produced by Daniel Lanois and Brian Eno, and was released on 9 March 1987 by
The_Joshua_Tree
Programming function applied recursively to its previous result
a) newtype Tree a = Tree {unNode :: Either a (Tree a, a, Tree a)} anaTree :: (tree_a -> Either a (tree_a, a, tree_a)) -> (tree_a -> Tree a) With these
Anamorphism
uncountably infinite graphs with only one end in which every spanning tree has infinitely many ends. If G {\displaystyle G} is an infinite grid graph,
End_(graph_theory)
Notion in combinatorial game theory
about repetition of position) the game tree is generally infinite. A decision tree is a subtree of the game tree, with each position labelled "player A
Game_complexity
Form of second-order logic
subsumes first-order logic. The monadic second-order theory of the infinite complete binary tree, called S2S, is decidable. As a consequence of this result,
Monadic_second-order_logic
French mathematician and computer scientist
publications also include: Bruno Courcelle (1983). "Fundamental Properties of Infinite Trees". Theoretical Computer Science. 25 (2): 95–169. doi:10.1016/0304-3975(83)90059-2
Bruno_Courcelle
Generalised alphabetical order
true that the set of all finite words is well-ordered; for example, the infinite set of words {b, ab, aab, aaab, ... } has no lexicographically earliest
Lexicographic_order
Form taken by the network of interconnections of a circuit
such as integrated circuits. Graphs can also be used in the analysis of infinite networks. The circuit diagrams in this article follow the usual conventions
Circuit_topology_(electrical)
Solving symbolic inequations
Alain Colmerauer (1984). "Equations and Inequations on Finite and Infinite Trees". In ICOT (ed.). Proc. Int. Conf. on Fifth Generation Computer Systems
Dis-unification
Tree-based ensemble machine learning methods
n}(\mathbf {x} ).} When the number of trees M {\displaystyle M} goes to infinity, then we have infinite random forest and infinite KeRF. Their estimates are close
Random_forest
Extension of ideas in combinatorics to infinite sets
extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and
Infinitary_combinatorics
German mathematician
including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of discrete mathematics at the University
Reinhard_Diestel
Infinite binary tree
In mathematical set theory, the Cantor tree is either the full binary tree of height ω + 1, or a topological space related to this by joining its points
Cantor_tree
Jewel The Afghan Whigs September 17 United States The Smashing Pumpkins Infinite Sadness tour Giant Lee Buffalo Silverchair September 18 October 3 United
List of entertainment events at Madison Square Garden
List_of_entertainment_events_at_Madison_Square_Garden
Infinitely detailed mathematical structure
Detailing added to make models appear more complex H tree – Right-angled fractal canopy Infinite regress – Philosophical problem Lacunarity – Term in
Fractal
list of episodes of the Korean reality-variety television comedy series Infinite Challenge (Korean: 무한도전; RR: Muhandojeon). The show's regular run ended
List of Infinite Challenge episodes
List_of_Infinite_Challenge_episodes
{\displaystyle [A]^{n}} is a barrier. (Nash-Williams, 1965) Finite products of infinite trees (Halpern–Läuchli, 1966) Piecewise syndetic sets (Brown, 1968) Call a
Partition_regularity
Solution to x*x + y*y + z*z = 3xyz
29, 433), (1, 233, 610), (2, 169, 985), (13, 34, 1325), ... There are infinitely many Markov numbers and Markov triples. There are two simple ways to obtain
Markov_number
On coloring infinite graphs
graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that, when
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
INFINITE TREE
INFINITE TREE
Boy/Male
Indian
Infinite.
Boy/Male
Hindi
Infinite.
Boy/Male
Hindu
Infinite, Endless
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Infinite
Boy/Male
Tamil
Infinite visionary
Girl/Female
Indian, Telugu
Infinite
Boy/Male
Japanese
Infinite; endless.
Boy/Male
Tamil
Infinite God
Boy/Male
Tamil
Infinite, Endless
Girl/Female
Hindu, Indian
Infinite
Boy/Male
Hindu
Infinite God
Girl/Female
Hindu, Indian, Marathi
Infinite; Knowledge
Boy/Male
Indian
Infinite visionary
Girl/Female
Hindi
Infinite.
Girl/Female
Indian, Telugu
Infinite
Boy/Male
Tamil
Infinite, Endless
Girl/Female
Indian
Infinite, Divine
Girl/Female
Hindu, Indian, Marathi
Infinite; Matchless
Girl/Female
Tamil
Infinite, Divine
Boy/Male
Hindu
Infinite, Endless
INFINITE TREE
INFINITE TREE
Boy/Male
Tamil
Radhas husband, Another name of Lord Ganesh
Boy/Male
Australian, Egyptian, Greek
Name of a Pharaoh; Aggressive
Girl/Female
Assamese, Hindu, Indian, Marathi, Tamil
With Inner Beauty
Girl/Female
Tamil
Manuscripts of God
Girl/Female
African, Arabic, Australian, French, Hebrew, Muslim, Swahili
Flower; Beauty; Star
Girl/Female
Muslim
One who travels
Boy/Male
Arabic American
Much praised. One of many names of the prophet Muhammad.
Boy/Male
Tamil
Achiever, Devoted
Female
Spanish
Spanish feminine form of Latin Angelus, ANGÉLICA means "angel, messenger."
Girl/Female
Muslim
The saved
INFINITE TREE
INFINITE TREE
INFINITE TREE
INFINITE TREE
INFINITE TREE
n.
Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
pl.
of Infinity
n.
An infinitive form of the verb; a verb in the infinitive mood; the infinitive mood.
n.
The Infinite Being; God; the Almighty.
a.
Having no determined or certain limits; large and unmeasured, though not infinite; unlimited; as indefinite space; the indefinite extension of a straight line.
n.
That which is infinite; boundless space or duration; infinity; boundlessness.
n.
Infinite extent; unlimited space; immensity; infinity.
n.
The state or quality of being infinite; infinity; greatness; immensity.
n.
The quality or state of being infinite, or without limits; infiniteness.
n.
Endless or indefinite number; great multitude; as an infinity of beauties.
n.
That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.
a.
Unlimited or boundless, in time or space; as, infinite duration or distance.
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.
An infinity; an incalculable or very great number.
a.
Boundless; infinite.
n.
An infinite quantity or magnitude.
a.
Infinite; perpetual, as a canon whose end leads back to the beginning. See Infinite, a., 5.
a.
Not definite; not limited, defined, or specified; not explicit; not determined or fixed upon; not precise; uncertain; vague; confused; obscure; as, an indefinite time, plan, etc.
a.
Having certain or distinct; determinate in extent or greatness; limited; fixed; as, definite dimensions; a definite measure; a definite period or interval.
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.