Find link

language: af: Afrikaans als: Alemannisch [Alemannic] am: አማርኛ [Amharic] an: aragonés [Aragonese] ar: العربية [Arabic] arz: مصرى [Egyptian Arabic] as: অসমীয়া [Assamese] ast: asturianu [Asturian] az: azərbaycanca [Azerbaijani] azb: تۆرکجه [Southern Azerbaijani] ba: башҡортса [Bashkir] bar: Boarisch [Bavarian] bat-smg: žemaitėška [Samogitian] be: беларуская [Belarusian] be-tarask: беларуская (тарашкевіца) [Belarusian (Taraškievica)] bg: български [Bulgarian] bn: বাংলা [Bengali] bpy: বিষ্ণুপ্রিয়া মণিপুরী [Bishnupriya Manipuri] br: brezhoneg [Breton] bs: bosanski [Bosnian] bug: ᨅᨔ ᨕᨘᨁᨗ [Buginese] ca: català [Catalan] ce: нохчийн [Chechen] ceb: Cebuano ckb: کوردیی ناوەندی [Kurdish (Sorani)] cs: čeština [Czech] cv: Чӑвашла [Chuvash] cy: Cymraeg [Welsh] da: dansk [Danish] de: Deutsch [German] el: Ελληνικά [Greek] en: English eo: Esperanto es: español [Spanish] et: eesti [Estonian] eu: euskara [Basque] fa: فارسی [Persian] fi: suomi [Finnish] fo: føroyskt [Faroese] fr: français [French] fy: Frysk [West Frisian] ga: Gaeilge [Irish] gd: Gàidhlig [Scottish Gaelic] gl: galego [Galician] gu: ગુજરાતી [Gujarati] he: עברית [Hebrew] hi: हिन्दी [Hindi] hr: hrvatski [Croatian] hsb: hornjoserbsce [Upper Sorbian] ht: Kreyòl ayisyen [Haitian] hu: magyar [Hungarian] hy: Հայերեն [Armenian] ia: interlingua [Interlingua] id: Bahasa Indonesia [Indonesian] io: Ido is: íslenska [Icelandic] it: italiano [Italian] ja: 日本語 [Japanese] jv: Basa Jawa [Javanese] ka: ქართული [Georgian] kk: қазақша [Kazakh] kn: ಕನ್ನಡ [Kannada] ko: 한국어 [Korean] ku: Kurdî [Kurdish (Kurmanji)] ky: Кыргызча [Kirghiz] la: Latina [Latin] lb: Lëtzebuergesch [Luxembourgish] li: Limburgs [Limburgish] lmo: lumbaart [Lombard] lt: lietuvių [Lithuanian] lv: latviešu [Latvian] map-bms: Basa Banyumasan [Banyumasan] mg: Malagasy min: Baso Minangkabau [Minangkabau] mk: македонски [Macedonian] ml: മലയാളം [Malayalam] mn: монгол [Mongolian] mr: मराठी [Marathi] mrj: кырык мары [Hill Mari] ms: Bahasa Melayu [Malay] my: မြန်မာဘာသာ [Burmese] mzn: مازِرونی [Mazandarani] nah: Nāhuatl [Nahuatl] nap: Napulitano [Neapolitan] nds: Plattdüütsch [Low Saxon] ne: नेपाली [Nepali] new: नेपाल भाषा [Newar] nl: Nederlands [Dutch] nn: norsk nynorsk [Norwegian (Nynorsk)] no: norsk bokmål [Norwegian (Bokmål)] oc: occitan [Occitan] or: ଓଡ଼ିଆ [Oriya] os: Ирон [Ossetian] pa: ਪੰਜਾਬੀ [Eastern Punjabi] pl: polski [Polish] pms: Piemontèis [Piedmontese] pnb: پنجابی [Western Punjabi] pt: português [Portuguese] qu: Runa Simi [Quechua] ro: română [Romanian] ru: русский [Russian] sa: संस्कृतम् [Sanskrit] sah: саха тыла [Sakha] scn: sicilianu [Sicilian] sco: Scots sh: srpskohrvatski / српскохрватски [Serbo-Croatian] si: සිංහල [Sinhalese] simple: Simple English sk: slovenčina [Slovak] sl: slovenščina [Slovenian] sq: shqip [Albanian] sr: српски / srpski [Serbian] su: Basa Sunda [Sundanese] sv: svenska [Swedish] sw: Kiswahili [Swahili] ta: தமிழ் [Tamil] te: తెలుగు [Telugu] tg: тоҷикӣ [Tajik] th: ไทย [Thai] tl: Tagalog tr: Türkçe [Turkish] tt: татарча/tatarça [Tatar] uk: українська [Ukrainian] ur: اردو [Urdu] uz: oʻzbekcha/ўзбекча [Uzbek] vec: vèneto [Venetian] vi: Tiếng Việt [Vietnamese] vo: Volapük wa: walon [Walloon] war: Winaray [Waray] yi: ייִדיש [Yiddish] yo: Yorùbá [Yoruba] zh: 中文 [Chinese] zh-min-nan: Bân-lâm-gú [Min Nan] zh-yue: 粵語 [Cantonese]

jump to random article

Longer titles found: Dedekind-infinite set (view)

searching for Infinite set 343 found (476 total)

alternate case: infinite set

Kleene star (1,013 words) [view diff] exact match in snippet view article find links to article

V} is any other finite set or countably infinite set, then V ∗ {\displaystyle V^{*}} is a countably infinite set. As a consequence, each formal language

generated by a single element of the algebra) if and only if there exists an infinite set X {\displaystyle X} such that A {\displaystyle A} is isomorphic to the

In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid by inserting an n-gonal antiprism

process is an infinite discrete probability distribution, consisting of an infinite set of atoms drawn from G0, with weights drawn from a two-parameter Poisson-Dirichlet

gyrobicupola (J31). The pentagonal orthobicupola is the third in an infinite set of orthobicupolae. A Johnson solid is one of 92 strictly convex polyhedra

these polyhedra in 1966. The triangular orthobicupola is the first in an infinite set of orthobicupolae. The triangular orthobicupola can be constructed by

these polyhedra in 1966. The square gyrobicupola is the second in an infinite set of gyrobicupolae. Related to the square gyrobicupola is the elongated

In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed

In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two

In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps. If faces are all regular

groups which are "too big" (for example, the group of permutations of an infinite set), or which exhibit some pathological behavior (for example, finitely

In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon

In the philosophy of mathematics, specifically the philosophical foundations of set theory, limitation of size is a concept developed by Philip Jourdain

instruction scheduling and register allocation; hence its output IR has an infinite set of pseudo-registers (often known as temporaries) and may still be – and

In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by two parallel polygons separated by a strip of triangles.

In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many

the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of points in this space with the properties that coordinate-wise addition

triangles; 6 equilateral triangles would make a flat vertex. It is one of an infinite set of bipyramids. Having twelve faces, it is a type of dodecahedron, although

In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon

lattice in the complex plane. The Eisenstein integers are a countably infinite set. The Eisenstein integers form a commutative ring of algebraic integers

In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case

within the Self, with Jung viewing parts of the self as part of the infinite set of archetypes within the collective unconscious. Anima and animus are

In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in

random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different

giving more examples of correspondences between the elements of an infinite set and proper subsets of infinite sets. In the work he also explained the

dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along an axis. Every dihedral group is generated

In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid (by inserting an n-gonal prism between

portion of "accessible" whole numbers. The argument can be applied to any infinite set of objects whatsoever – there are only so many elements that one can

of the infinite set of prisms, with triangle faces: any multiple of 4 (so that a face will face up), starting from 8 Disphenoids, an infinite set of tetrahedra

In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set

the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal

also be an infinite ordinal, it will typically count from zero. For an infinite set, the order type determines the cardinality, but not conversely: sets

von Neumann) but this is not necessarily the case if the game has an infinite set of strategies. There follows a simple example of a game with no minimax

hydrogen atoms). Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen (or any) atom can exist, contrary to the

happens if you simply iterate this process repeatedly, generating an infinite set of new axioms to add to the original theory, and even goes one step further

In geometry, the octagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in

2 (which is itself given the discrete topology). If A is a countably infinite set, the corresponding Cantor cube is a Cantor space. Cantor cubes are special

upper envelope or pointwise maximum is defined symmetrically. For an infinite set of functions, the same notions may be defined using the infimum in place

generalized graph consisting of a very large or infinite set of vertices paired with a very large or infinite set of edges. From that graph emerge various constructions

In geometry, the octagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon

In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the polar vertices of a trapezohedron

case of partition in which, given the available denominations of an infinite set of coins, the objective is to find out the number of possible ways of

In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an 2n-gonal prism. There are three elongated

inclusion-orders of sets, a set is already strictly smaller than another, possibly infinite, set if it contains just one less element. One would, however, hardly agree

three-dimensional flows in this case. Specifically, it is "the locus of an infinite set of such curves [streamlines], rooted at every point along a continuous

complicated) formal automaton (see automata theory). Sometimes a potentially infinite set of possible states is introduced, and such a set can have a complicated

therefore, an equivalent way of stating the theorem is that, in any infinite set S {\displaystyle {\mathcal {S}}} of graphs, there must be only a finite

every other element of S. Finally, for an infinitely non-archimedean time there is no such finite set S, but there is an infinite set S, mutatis mutandis.

In geometry, the decagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in

In geometry, the gyroelongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an 2n-gonal antiprism. There are

tracial state. Examples of ICC groups are the group of permutations of an infinite set that leave all but a finite subset of elements fixed,: 908  and free

: 39  and 22κ (even just maximal,: 39  i.e. precomplete) clones on an infinite set of cardinality κ.: 39  Philip Hall introduced the concept of abstract

angle θ that arises when the state is written as a superposition of an infinite set of topologically distinct vacuum states. The dynamical effects of the

using a distribution, then the sample variance calculated from that infinite set will match the value calculated using the distribution's equation for

packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases and

, where f : J → S is the particular enumeration of S. Any countably infinite set can be (injectively) indexed by the set of natural numbers N {\displaystyle

polyhedron—more generally, a uniform polyhedron—and the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. It can

is equal to the cardinality of the set of all subsets of a countably infinite set. Cardinality of the continuum, a cardinal number that represents the

that any periodic waveform can be formed by the sum of a (possibly infinite) set of fundamental and harmonic components. Finite-energy non-periodic waveforms

more precise for latitudes below 45°. It is thus a special case in an infinite set of rulers. A right-angle is drawn on the dial-face and the latitude scale

geometry, a rectified prism (also rectified bipyramid) is one of an infinite set of polyhedra, constructed as a rectification of an n-gonal prism, truncating

space (with the subspace topology), but not in general. For example, an infinite set equipped with the discrete metric is bounded but not totally bounded:

power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number

coordinates, in which the conserved quantities form half of a doubly infinite set of canonical coordinates, and the flow linearizes in these. In some cases

(x\in Y\leftrightarrow \phi (x))} (A3) (axiom of infinity) — There is an infinite set, and all infinite sets are equinumerous. ∃ x ( i n f ( x ) ∧ ∀ y ( i

locally compact in senses (3) or (4). The particular point topology on any infinite set is locally compact in senses (1) and (3) but not in senses (2) or (4)

In mathematics, a Heilbronn set is an infinite set S of natural numbers for which every real number can be arbitrarily closely approximated by a fraction

\mathbb {N} _{0}\,3^{-\mathbb {N} _{0}}{\Bigr )}} which is a countably infinite set. As to cardinality, almost all elements of the Cantor set are not endpoints

spaces named after M. K. Fort, Jr. Fort space is defined by taking an infinite set X, with a particular point p in X, and declaring open the subsets A of

referred to as a nonparametric regression technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is

as a surface of revolution. Convex polyhedra with rhombi include the infinite set of rhombic zonohedrons, which can be seen as projective envelopes of

In a non-Hausdorff space, such as the particular point topology on an infinite set, the closure of a compact subset is not necessarily compact; said differently

vector twice and the set of its vectors is linearly independent. An infinite set of vectors is linearly independent if every finite subset is linearly

since the integers are an infinite set but do not have a limit point in R {\displaystyle \mathbb {R} } ; (2) an infinite set with the discrete topology;

{\displaystyle \mathbb {N} } such that t.c ∈ π. A path may be a finite or infinite set. If all paths of a tree are finite then the tree is called finite, otherwise

also not possible to get around this infinite disjunction by using an infinite set of axioms: the compactness theorem implies that no set of first-order

one can derive the rate of Schwinger pair production by summing the infinite set of diagrams shown below, containing one electron loop and any number

It is impossible to give an extensional definition for a term with an infinite set of referents, but an intensional one can often be stated concisely –

polygons (and quasiregular forms) are displayed below: There is also an infinite set of star polygons (one for each rational number greater than 2), but these

forms as they are presented in the tables by symmetry form. For the infinite set of prismatic forms, they are indexed in four families: Hosohedra H2.

intersection of all of its members. But a nonprincipal filter on an infinite set is not necessarily free: a filter is free if and only if it includes

{\displaystyle \left\{{B_{n}:n=1,2,3,\ldots }\right\}} is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any

include all the polyhedra mentioned above together with an infinite set of prisms, an infinite set of antiprisms, and 53 other non-convex forms. The Johnson

cutsets in a tree structure; a proof of a conjecture of Wagner that in any infinite set of graphs, one of them is a minor of another (and consequently that any

them. While this technique implies reduced inherent risks, a virtually infinite set of threat actors and techniques applied over time will cause most secrecy

In geometry, the decagrammic prism is one of an infinite set of nonconvex prisms formed by squares sides and two regular star polygon caps, in this case

foundation. That is, one cannot construct the infinite set Halmos' axiom asserts exists, from the infinite set Zermelo's original axioms assert exists, and

The usage, on this word, of a more simple drawing rule, defines an infinite set of variants of the curve, among which: a "diagonal variant" a "svastika

called "modding out the..." or "we now mod out the...". Two subsets of an infinite set are equal modulo finite sets precisely if their symmetric difference

of base primes unioned with its (infinite) set of coprimes is a superset of the primes; second, that the infinite set of coprimes can be enumerated easily

appears near the beginning of the 2013 first-person shooter, BioShock Infinite, set in an alternate 1912 where Washington, Benjamin Franklin, and Thomas

there are at least three distinct elements in the domain. Consider the infinite set of formulae A , B 2 , B 3 , B 4 , … {\displaystyle A,B_{2},B_{3},B_{4}

scrambled. Scrambling is a kind of mixing. (2) There is an uncountably infinite set S that is scrambled. A map satisfying Property 2 is sometimes called

semi-nonparametric, and non-parametric models, all of which consist of an infinite set of "parameters" for description. The distinction between these four classes

way, the components will be clopen. Now let X {\displaystyle X} be an infinite set under the discrete metric – that is, two points p , q ∈ X {\displaystyle

etc. The major idea is that a literary work must be considered as an infinite set of its readings. The literary text per se is just an "input instruction

In geometry, the octagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case

finite set is the number of elements in the set, and the measure of any infinite set is infinity. This measure is not σ-finite, because every set with finite

automaton can be a finite representation of a formal language that may be an infinite set. Automata are used as theoretical models for computing machines, and

arithmetic progression. According to the Erdős–Anning theorem, every infinite set of points in the Euclidean plane that does not lie on one line has a

usually represented by a set of points; As an example, a line is an infinite set of points of the form L = { ( a 1 , a 2 , . . . a n ) ∣ a 1 c 1 + a 2

centered square number 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges 687 = 3 × 229, 687 days to orbit the Sun (Mars)

grow slower than functions in the higher levels. First we introduce an infinite set of functions, denoted Ei for some natural number i. We define E 0 ( x

Example of a cumulative distribution function with a countably infinite set of discontinuities

polygon with 12 sides Apeirogon - generalized polygon with countably infinite set of sides Annulus Arbelos Circle Archimedes' twin circles Bankoff circle

the page, "DD: Ascend more casually." The 2013 video game BioShock Infinite (set in 1912) includes a barbershop quartet anachronistically singing a rendition

(although this conjecture was not published until later) that in any infinite set of graphs, one graph is isomorphic to a minor of another. The truth of

original definition by John McCarthy, it was assumed that there existed "an infinite set of distinguishable atomic symbols" represented as "strings of capital

Hausdorff space is T1. The converse is not true in general. For example, an infinite set with the cofinite topology is a T1 space that is not locally Hausdorff

uniformly from the set of missing edges. If instead we start with an infinite set of vertices, and again let every possible edge occur independently with

subsets of an infinite set X is a prototypical example. In this case partition regularity asserts that every finite partition of an infinite set has an infinite

to the T1 condition: an example of a T1 space that is not sober is an infinite set with the cofinite topology, the whole space being an irreducible closed

it is common in universal quantification to make statements over an infinite set such as the set of all natural numbers. Such statements are perfectly

answer is yes. For example, primality testing can be represented as the infinite set L = {2, 3, 5, 7, 11, ...} In a search problem, the answers can be arbitrary

generated by any element. Under the assumption of the axiom of choice, every infinite set X is equipotent with a unique cardinal number |X| which equals an aleph

(1) Every countable open cover of X has a finite subcover. (2) Every infinite set A in X has an ω-accumulation point in X. (3) Every sequence in X has

(taking values in a finite or countably infinite set) or continuous (taking values in an uncountably infinite set). Associated with each data point may

Hausner to extend results to algebraic number fields. Main source: An infinite set of trivial solutions in positive real numbers is given by x = y . {\displaystyle

numbers. Therefore, f is bounded, and Y is pseudocompact. Let X be an infinite set given the particular point topology. Then X is neither compact, sequentially

case of a tabula rasa, as it is designed to accept any of a possibly infinite set of source language programs, within a single programming language, and

conjunction of the Boolean-valued function P applied over the (possibly infinite) set S. When analyzed in formal semantics, natural languages can be seen

in the schema. For the construction of the formulas we will assume an infinite set V of tuple variables. The formulas are defined given a database schema

whose complement is finite. This is the smallest T1 topology on any infinite set. Any set can be given the cocountable topology, in which a set is defined

commenced with Hilbert's first problem. Georg Cantor considered the infinite set of whole numbers 1, 2, 3 ... ∞ which he compared with the smaller set

that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative

is the product metric with the sup norm. However, the product of an infinite set of metric spaces may not exist, because the distances in the base spaces

ordered pair ( Σ , Λ ) {\displaystyle (\Sigma ,\Lambda )} , where Σ is an infinite set of symbols; Λ is a set of formal languages; For each L in Λ there exists

descriptively adequate grammar for a particular language defines the (infinite) set of grammatical sentences in that language; that is, it describes the

The abbreviation "PCF" stands for "possible cofinalities". If A is an infinite set of regular cardinals, D is an ultrafilter on A, then we let cf ⁡ ( ∏

four dimensions to the infinite family of three-dimensional antiprisms. Infinite set of p-q duoprism - - p q-gonal prisms, q p-gonal prisms: Alternations

there will always be an infinite number of real numbers "left over". Any infinite set that can be placed in one-to-one correspondence with the natural numbers

original function can, in theory, be perfectly reconstructed from the infinite set of samples. Sometimes aliasing is used intentionally on signals with

mathematics. But, according to Hartman, people are capable of a denumerably infinite set of predicates, intended in as many ways, which he gives as ℵ 1 {\displaystyle

Example of a cumulative distribution function with a countably infinite set of discontinuities.

commutative algebra, the only difference is that it is a free object over an infinite set. One can also consider a strictly larger ring, by defining as a generalized

be given entirely to a single person. C {\displaystyle C} may be an infinite set representing a divisible resource, for example: money, or a cake. Mathematically

opinion about it?" The students had been introduced to the idea of an infinite set, but they had no prior experience with infinite series. They were given

explicit arguments. Also, instead of a fixed set of registers, IR uses an infinite set of temporaries of the form %0, %1, etc. LLVM supports three equivalent

L, an ω-word w is in the limit of L if and only if Pref(w) ∩ L is an infinite set. In other words, for an arbitrarily large natural number n, it is always

fixed geometries, but take a set of design rules that can generate an infinite set of possible design solutions. The generated design solutions can be more

holomorphic. All we really have to do is puncture the plane at a countably infinite set of points {0, −1, −2, −3, ...}. But a closed contour in the punctured

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 element

formulates the general principle that a smaller infinite set can have just as many points as a larger infinite set containing it. It was then clear that Zeno's

no compact neighborhood of 1. X is not countably compact. Proof: The infinite set { 2 n : n ≥ 1 } {\displaystyle \{2^{n}:n\geq 1\}} has zero asymptotic

K[x_{1},x_{2},x_{3},\dots ]} is an integral domain. It has a countably infinite set of ideal classes. If d {\displaystyle d} is a square-free integer (a

glance because their additive and multiplicative structure depends on an infinite set of recursive formulas which do not behave like addition and multiplication

Data\Application Data\ ... Each additional path name in this seemingly infinite set is an actual valid Windows path which refers to the same location. In

Ruziewicz. This work concerns functions ƒ that map the members of an infinite set S to small subsets of S; more specifically, all subsets' cardinalities

countable, the field Q(S) will have the same cardinality as S for any infinite set S, and any algebraic extension of Q(S) will have the same cardinality

$10. Informally, the expectation of a random variable with a countably infinite set of possible outcomes is defined analogously as the weighted average of

BioShock, Levine served as creative director and lead writer on BioShock Infinite, set in 1912 in the floating city of Columbia. BioShock Infinite was a critical

world. In short: the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some

prefix-free universal computable function. The domain P of F consists of an infinite set of binary strings P = { p 1 , p 2 , … } . {\displaystyle P=\{p_{1},p_{2}

In this acceptor, the only accepting state is state 7. A (possibly infinite) set of symbol sequences, called a formal language, is a regular language

In this acceptor, the only accepting state is state 7. A (possibly infinite) set of symbol sequences, called a formal language, is a regular language

.. < 1111 < ... < 11111 ... With respect to this ordering, e.g. the infinite set { 1, 01, 001, 0001, 00001, 000001, ... } has no minimal element. See

hull of four points of the set. The Erdős–Anning theorem, that if an infinite set of points in the plane has an integer distance between every two points

Hamel basis of this space is much bigger than this merely countably infinite set of functions. Hamel bases of spaces of this kind are typically not useful

elements do not always exist - the set of all finite subsets of a given infinite set, ordered by subset inclusion, provides one of many counterexamples. An

James E.; Erdős, Paul; Higgs, D., Cross-cuts in the power set of an infinite set, Order 1, 139–145, 1984 Baumgartner, James E. (Editor), Axiomatic Set

equivalent to the halting problem. Both of these examples in fact define an infinite set of definable, uncomputable numbers, one for each universal Turing machine

probabilities, if it were possible to compute the Huffman code for the infinite set of source values. Golomb's scheme was designed to encode sequences of

which w(i,j) occurs. By the infinite Ramsey theorem, we can find an infinite set X ⊆ N such that each subset of X of size 2 has same color. Let 0 < i0

"mixture density" usually means a finite mixture. The case of a countably infinite set of components is covered formally by allowing n = ∞ {\displaystyle n=\infty

sometimes called the Cantor algebra. The algebra of all subsets of an infinite set that are finite or have finite complement is a Boolean algebra but is

to the 5-cell, two dual solutions are related to the 24-cell, and an infinite set of self-dual duoprisms generate regular skew polyhedra as {4, 4 | n}

to: {3}, {4}, {5}, {5/2}, and {6}. Beyond Euclidean space, there is an infinite set of regular hyperbolic tilings. The five convex regular polyhedra are

A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and

m-tuples exist or even if there is an upper bound, but it is known that no infinite set of rationals with the property exists. Dujella, Andrej (January 2006)

X {\displaystyle X} is a regular space and Y {\displaystyle Y} is an infinite set in the indiscrete topology.) If p : X → Y {\displaystyle p\colon X\to

the song appears anachronistically in the 2013 video game BioShock Infinite, set in 1912, and can be heard in the Downtown Emporia level. The song was

and will ever exist is art (Everything++) A set of this would be an infinite set consisting of every parallel universe; with a work of art-example given

create logical contradictions, it can not exist including the actual infinite set of past events. The second argument, the "argument from the impossibility

{arg\,max} }}\,\cos(x)=\left\{2k\pi ~:~k\in \mathbb {Z} \right\},} so an infinite set. Functions need not in general attain a maximum value, and hence the

set is compact. In the cocountable topology on an uncountable set, no infinite set is compact. Like the previous example, the space as a whole is not locally

impossible to iterate through. Implementing an assertion quantified for an infinite set by definition results in an undecidable non-terminating program. However

result is connected to the Erdős–Anning theorem, according to which an infinite set of points with integer distances must lie on one line.[ID] In connection

[better source needed] In an effective field theory, not all but the first few of the infinite set of parameters in a nonrenormalizable theory are suppressed by huge energy

algebra of the infinite symmetric group of all permutations of a countable infinite set that fix all but a finite number of elements gives the hyperfinite type

Van Wijngaarden grammars use a context-free grammar to generate an infinite set of productions that will recognize a particular ALGOL 68 program; notably

see Grammar induction. A regular language is defined as a (finite or infinite) set of strings that can be described by one of the mathematical formalisms

Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities, Philo, Volume 5, Number 2. Craig, W. L.(1979). The

Gaussian primes. Two of them are: The real and imaginary axes have the infinite set of Gaussian primes 3, 7, 11, 19, ... and their associates. Are there

{\displaystyle \emptyset } is also a convex cone. The conical hull of a finite or infinite set of vectors in R n {\displaystyle \mathbb {R} ^{n}} is a convex cone.

neuronal ensemble (or neuronal population) refers to as a large (ideally infinite) set of uncoupled stochastic neurons. These neurons receive common input

has a basis e α {\displaystyle \mathbf {e} _{\alpha }} indexed by an infinite set A {\displaystyle A} , then the same construction as in the finite-dimensional

of R {\displaystyle R} is infinite, thus forcing the existence of an infinite set. If relations are defined in terms of ordered pairs, this axiom requires

weaken gravity at short distances. In 1987, Krasnikov considered an infinite set of higher derivative terms acting on the curvature terms and showed that

even though y {\displaystyle y} is chosen from a very large or even infinite set. Since 2002, perceptron training has become popular in the field of natural

types; any semantics will be added later. Some authors assume a fixed infinite set of primitive types used by all grammars, but by making the primitive

Fourier decomposition, a real wave must consist of the superposition of an infinite set of sinusoidal frequencies. In addition, for a valid solution, the wave

notions. In short, the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some

Note: The Hausdorff condition is necessary here, since for example an infinite set with the cofinite topology is compact, hence paracompact, and T1, but

k-space discussed above. For example, in a crystal's k-space, there is an infinite set of points called the reciprocal lattice which are "equivalent" to k =

{\displaystyle \operatorname {Im} x_{\bullet }.} Conversely, given a countable infinite set A ⊆ X {\displaystyle A\subseteq X} in X , {\displaystyle X,} we can enumerate

whose complement is finite. This is the smallest T1 topology on any infinite set. Any set can be given the cocountable topology, in which a set is defined

optimal design can be a probability measure that is supported on an infinite set of observation-locations. Such optimal probability-measure designs solve

X} . The moduli space of all projective K3 surfaces has a countably infinite set of components, each of complex dimension 19. The subspace of K3 surfaces

be replaced by 2 if we interpret the operator “+” to be defined by an infinite set of equations, e.g., 1+1 = 2, 1+2 = 3, etc. In a similar way, one can

state | ϕ ⟩ {\displaystyle |\phi \rangle } , and there is an uncountably infinite set of eigenvalues a. In this case, the inner product of two eigenstates

for a quantizer with a limited range of input data or with a countably infinite set of selectable output values). A scalar quantizer, which performs a quantization

dirhombidodecahedron also have reflective symmetries. There is also the infinite set of antiprisms. They are formed from prisms, which are truncated hosohedra

ACCP holds on the right or left side of R, it implies that R has no infinite set of nonzero orthogonal idempotents, and that R is a Dedekind finite ring

set-theoretic terminology. Theorem. Let X {\displaystyle X} be some infinite set and colour the elements of [ X ] n {\displaystyle [X]^{n}} (the subsets

These equations arise as the equations of motion from the (countably) infinite set of independent constants of motion I n [ u ] {\displaystyle I_{n}[u]}

theories. There are many examples of these, such as the theory of an infinite set, or the theory of a dense unbounded total order. Ehrenfeucht gave the

3x+2y-21z=0} In this particular case there is not just one solution, but an infinite set of solutions, which can be written using set builder notation as { (

space cannot be an occasion of experience, but is an abstraction from an infinite set of overlapping or contained occasions of experience, as explained in

and multiplying by suitable normalization factors, we can produce an infinite set of energy eigenstates { | 0 ⟩ , | 1 ⟩ , | 2 ⟩ , … , | n ⟩ , … } , {\displaystyle

made less restrictive as it is sufficient to verify that a countably infinite set of distinct linear combinations of X {\displaystyle X} and Y {\displaystyle

periodic functions or periodic signals into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex

} it turns out that this is not obvious and that there is always an infinite set of choices for V {\displaystyle V} and W {\displaystyle W} such that

{\mathcal {H}}=\{h(\cdot ;\omega )|\omega \in \Omega \}} be the possibly infinite set of weak classifiers, also termed hypotheses. One way to write down the

values turned into honorific kriged estimates or kriged estimators. An infinite set of Agterberg's zero dimensional points fits within any ore block, along

just the trivial solution, or there is the trivial solution plus an infinite set of other solutions. Consider the system of linear equations: Li = 0 for

p={\text{Low}},{\text{No}}\mid p={\text{High}}\}.} Or it might be an infinite set, a continuum or unbounded, e.g. S i = { Price } {\displaystyle

with face, edges, and vertices which can be unfolded to form a possibly infinite set of polygons which tile either the sphere, the plane or the hyperbolic

space cannot be an occasion of experience, but is an abstraction from an infinite set of overlapping or contained occasions of experience, as explained in

ideal of meager sets (first category sets). Let I be an ideal of a fixed infinite set X, containing all finite subsets of X. We define the following "cardinal

positive integers under multiplication is a free commutative monoid on an infinite set of generators, the prime numbers. The free commutative semigroup is the

totally bounded is R 2 {\displaystyle \mathbb {R} ^{2}} (or any other infinite set) with the discrete metric. Compactness is a topological property which

subsets Suppose I ⊆ N {\displaystyle I\subseteq \mathbb {N} } is an infinite set and ( x i ) i ∈ N {\displaystyle \left(x_{i}\right)_{i\in \mathbb {N}

expectation values of higher order products of operators, thus leading to an infinite set of coupled equations. We heuristically make the approximation that the

Justified beliefs are all evidentially supported by other beliefs, but an infinite set of beliefs is not generated, because the chains of evidential support

product of uncountably many copies of an infinite discrete space. Any infinite set carrying the particular point topology is not paracompact; in fact it

Ashtekar's original (ill-defined) Wheeler–DeWitt equation. Hence an infinite set of exact (if only formal) solutions had been identified for all the equations

]{\frac {\delta }{\delta \varphi }}S[\varphi ]\right\}\right).} This infinite set of equations can be used to solve for the correlation functions nonperturbatively

of this equation has a finite number of terms, or there could be an infinite set of discrete values, in which case the right side has an infinite number

precise statement of the conditions under which values given at a doubly infinite set of equally spaced points can be interpolated to yield a continuous band-limited

a theory by expressing the field's internal degrees of freedom as an infinite set of harmonic oscillators, and by then utilizing the canonical quantization

Sturgis 1961: p. 219); (Lambek 1961: p. 295) proposed: "a countably infinite set of locations (holes, wires, etc). For example, (Lambek 1961: p. 295)

is discussed in this section by means of possible surjections on an infinite set of counting numbers I ⊆ N {\displaystyle I\subseteq {\mathbb {N} }}

\langle ah\rangle =\langle blah\rangle } . A language is a finite or infinite set of strings. Besides the usual set operations like union, intersection

realized in an infinite universe is equivalent to the assertion that any infinite set of numbers contains all numbers (or at least all Gödel numbers of the

locally path connected, and not even locally connected. A countably infinite set endowed with the cofinite topology is locally connected (indeed, hyperconnected)

mathematical perspective, to the solution can be added any one of an infinite set of eigenfunctions as shown by Stewartson and Paul A. Libby. Von Kármán

three-dimensional antiprisms with the exception of the great duoantiprism. Infinite set of p-q duoprism - - p q-gonal prisms, q p-gonal prisms: 3-3 duoprism

three-dimensional antiprisms with the exception of the great duoantiprism. Infinite set of p-q duoprism - - p q-gonal prisms, q p-gonal prisms: 3-3 duoprism

called the pattern. Formally, a unification approach presupposes An infinite set V {\displaystyle V} of variables. For higher-order unification, it is

(actions) be two finite sets of symbols, and let Var be a countably infinite set of variables. The set of formulas of (propositional, modal) μ-calculus

mathematical perspective, to the solution can be added any one of an infinite set of eigenfunctions as shown by Stewartson and Paul A. Libby. Von Kármán

first proved it in 1963. Given a set Σ, often called "alphabet", the (infinite) set of all strings built from members of Σ is denoted by Σ*. A formal language

where ⁠ v {\displaystyle v} ⁠ is a variable name drawn from a predefined infinite set of variable names, and ⁠ E 1 {\displaystyle E_{1}} ⁠ and ⁠ E 2 {\displaystyle

players select a small number of players and strategies from the virtually infinite set they could select, and how they arrive at common knowledge about each

: 246  For any value n ≤ μ ( x ) {\displaystyle n\leq \mu (x)} , the infinite set of all rationals p / q {\displaystyle p/q} satisfying the above inequality

configurations mapped by f into P can itself be described by a (possibly infinite) set S of patterns, with the property that a configuration belongs to f−1(P)

and every polynomial of degree n ∈ I has a root, where I is any fixed infinite set of odd numbers, then every polynomial f(x) of odd degree has a root (since

finite sets, and open sets are their complements, the cofinite sets; any infinite set of points is dense. The basis open set corresponding to the irreducible

S/N. Finally, among all the discrete distributions supported on the infinite set { x 1 , x 2 , . . . } {\displaystyle \{x_{1},x_{2},...\}} with mean μ

suffice, as shown in (Malcev 1940). A different (but also countably infinite) set of necessary and sufficient conditions were given in (Lambek 1951),

of technology, Don Ihde, wrote, "Just as science seems to produce an infinite set of visual images for virtually all of its phenomena--atoms to galaxies

free abelian group on the simplices. The basis for the group is the infinite set of all possible singular simplices. The group operation is "addition"

came from (Halmos & Vaughan 1950) Suppose that each of a (possibly infinite) set of boys is acquainted with a finite set of girls. Under what conditions

is also not a semialgebra (e.g. the collection of finite sets on an infinite set X {\displaystyle X} ). Algebra of sets – Identities and relationships

{F}}_{g}} overlap in an intricate way. Indeed, there is a countably infinite set of codimension-1 subvarieties of each F g {\displaystyle {\mathcal {F}}_{g}}

above form. This presentation, when not truncated, contains the same infinite set of terms, but implies a different order of adding them up. Because of

of a contaminant spill in a lake—it may be unnecessary to include an infinite set of images when there are multiple relevant boundaries. For example, to

assume μ {\displaystyle \mu } is nontrivial, i.e., its support is an infinite set. By a combination of the Radon-Nikodym and Lebesgue decomposition theorems

The grammar of a language is a finite system that characterizes an infinite set of (well-formed) sentences. More specifically, the grammar of a language

arguments passed in a method call). Each distributed flow is a (possibly infinite) set of such quadruples that satisfies the following three formal properties

experiments, such as tossing a coin until it shows heads, give rise to an infinite set of outcomes. And secondly, it requires an a priori determination that

space X {\displaystyle X} is not compact (so X {\displaystyle X} is an infinite set), yet every subbasic cover from S {\displaystyle {\mathcal {S}}} has

Victor (2009), "Complete solutions to the Oberwolfach problem for an infinite set of orders", Journal of Combinatorial Theory, Series B, 99 (6): 904–918

point. Rather it accepts the visual interpretation for which there is an infinite set of viewpoints that could produce the class of retinal images. For example

distribution over π k {\displaystyle \pi _{k}} is symmetric over the infinite set of clusters. This is exactly what is accomplished by the model: ( v i

and rapid convergence. Kruskal's tree theorem states that, in every infinite set of finite trees, there exists a pair of trees one of which is homeomorphically

meaning consists of a recursive set of rules that end up yielding an infinite set of sentences, "'p' is true if and only if p", covering the whole language

For example, ⁠ B = { a , b } {\displaystyle B=\{a,b\}} ⁠, generates an infinite set of types starting with ⁠ a {\displaystyle a} ⁠, ⁠ b {\displaystyle b}

theoretical level to demonstrate that a nonlinear system may be split into an infinite set of linear systems which are solved analytically, while the continuation

symmetric group. Hilbert's irreducibility theorem then implies that an infinite set of rational numbers give specializations of f(x, t) whose Galois groups

disguise'). The language of propositional modal logic consists of a countably infinite set of propositional variables, a set of truth-functional connectives (in

meaning the Boolean algebra of all finitary operations on a countably infinite set of generators or variables. Example 7. Ultimately periodic sequences

by Clozel for abelian varieties with etale l-adic cohomology, for an infinite set of prime numbers l (which can be stated in terms of Cebotarev density

Galois extensions are precisely those extensions that are unions of an (infinite) set of finite Galois extensions. If additionally E 2 / L {\displaystyle

copies of G {\displaystyle G} , one for each element of the (possibly infinite) set I {\displaystyle I} .) The name "Grothendieck category" appeared neither

involves the use of a "finite state language", which is a potentially infinite set of items made up of symbols following a finite set of rules, which constitutes

a fixed set of engine-to-wheel ratios; however, a CVT allows for an infinite set of ratios between its lowest gear and its highest. A feature shared by

provably finite. (However, any finite ordinal injects into any Dedekind-infinite set and so a subset of a finite ordinal does validate the logically negative

of P is a pair consisting of a finite set s of natural numbers and an infinite set A of natural numbers such that every element of s is less than every

of P is a pair consisting of a finite set s of natural numbers and an infinite set A of natural numbers such that every element of s is less than every

constraint and (formally) the Hamiltonian constraint. This yields an infinite set of exact (if only formal) solutions to all the equations of quantum general

work that should be shared.: 113–114  Labels consist of a countably infinite set of atomic labels, and concatenations a b {\displaystyle ab} , overlinings

believe that row will play h (beginning the cycle again). This provides an infinite set of consistent beliefs that results in row playing h. A similar argument

interval: Let I = [a, b] ⊂ R be a closed and bounded interval. If F is an infinite set of functions  f  : I → R which is uniformly bounded and equicontinuous

to solve than restrictions, so the possible geometries constitute an infinite set. The detailed procedure for the nanotube construction has been also published

fail to be compact (for example, the particular point topology on an infinite set). This result shows that this does not happen in non-Hausdorff TVSs.

generalization of the De Bruijn–Erdős theorem. Let V {\displaystyle V} be an infinite set, for instance the set of vertices in an infinite graph. For each element

operation can be iterated infinitely many times beginning with an arbitrary infinite set. In particular, Vω + ω, a particular level of the cumulative hierarchy

enveloping algebra of the Virasoro algebra, it is possible to construct an infinite set of mutually commuting charges. The first charge is L 0 − c 24 {\displaystyle

(where the intersection ranges over all finite sets X) is itself an infinite set S, then every finite simple path that ends in a vertex of S can be extended

regularity lemma. Theorem (Infinite graph removal lemma). For each (possibly infinite) set of graphs H and ε > 0, there exist h0 and δ > 0 so that, if G is an

Van Wijngaarden grammars use a context-free grammar to generate an infinite set of productions that will recognize a particular ALGOL 68 program; notably

integer. If B ⊆ N {\textstyle {\mathcal {B}}\subseteq \mathbb {N} } is an infinite set such that r B , h ( n ) > 0 {\textstyle r_{{\mathcal {B}},h}(n)>0} for

Again as in the first order boundary problem, any one of the infinite set of eigensolution can be added to this solution. In all the solutions

non-black color randomly generated from a uniform distribution over an infinite set of available colours, and consider the newly generated color to be the

fixing the parameter values of the target language. Language generates an infinite set of expressions given as a sound-meaning pair (π, λ). Syntactic computation

a token is an element t {\displaystyle t} in a finite (or countably infinite) set T {\displaystyle T} . Suppose we only need to process a finite corpus

improper prior distributions. Note that the discrete case for a countably infinite set, such as { 0 , 1 , 2 , . . . } {\displaystyle \{0,1,2,...\}} also produces

argument seeks to establish involves an extrapolation from a finite to an infinite set of data. How can we justify this jump? ... Unfortunately, most of the

themselves. For example, the expression "(ab+ba)*" in step 7 denotes the infinite set { ε, ab, ba, abab, abba, baab, baba, ababab, ababba, ... }. i.e. text

fail to be compact (for example, the particular point topology on an infinite set). This result shows that this does not happen in non-Hausdorff TVSs.

R 2 {\displaystyle V=\mathbb {R} ^{2}} with the dot product, and the infinite set { e k } {\displaystyle \{\mathbf {e} _{k}\}} given by { ( 1 , 0 ) , (

various faces, which were then scanned into a computer. At the start of Infinite, set in 1912, Booker DeWitt is sent to Columbia by the Lutece twins to recover

all of these periodic points are unstable. Furthermore,the uncountably infinite set in the interval [0, 1], the number of periodic points is countably infinite

constant-depth circuit". Kliesch defines the NLTS property thus: Let I be an infinite set of system sizes. A family of local Hamiltonians {H(n)}, n ∈ I has the

A of symbols, a generalized regular expression R denotes a possibly infinite set of finite-length strings over the alphabet A, called the language of

E. Baumgartner; D. Higgs (1984). "Cross-cuts in the power set of an infinite set". Order. 1 (2): 139–145. doi:10.1007/BF00565649. S2CID 10469116. D. Handelman;

Well-formed formulas are built freely using these connectives from a countably infinite set of propositional variables p0, p1, .... A substitution σ is a function

generalizations. Formally, an anti-unification approach presupposes An infinite set V of variables. For higher-order anti-unification, it is convenient to

{\displaystyle 1=x^{2}-2y^{2}} . Iterating this matrix action, we find that the infinite set of representations of 1 by f that were determined above are all equivalent

produces a considerably stronger pincushion distortion. The meaning of the infinite set of curves spanned by the distortion parameter is thus clear: Starting

realized in an infinite universe is equivalent to the assertion that any infinite set of numbers contains all numbers (or at least all Gödel numbers of the

{\displaystyle E} . More generally, if I {\displaystyle I} is an arbitrary infinite set, the dimension of the space of all functions K I {\displaystyle \mathbb

(Tarskian) interpretations I, where I = <U,F> (U is a non-empty (possibly infinite) set of objects, whereas F is a set of functions from expressions of the

{\displaystyle {\mathcal {F}}^{\infty }} be the Fréchet filter on an infinite set X , {\displaystyle X,} Then, ∀ F ∞ x   φ ( x ) {\displaystyle \forall

sequent systems was formally established in (Carnielli 1991). Assume an infinite set P V {\displaystyle PV} of propositional variables and define the set

America Germany invades North America in World War II. 2013 BioShock Infinite Set mostly in Columbia, a floating American city, during an alternate 1912

waves travelling along these paths produce an interference pattern. An infinite set of trajectory families lead to a complicated interference pattern on

{\displaystyle S\cap T\in W} . Let X {\displaystyle X} be a (finite or infinite) set of alternatives, whose cardinal number (the number of elements) # X

operators defined over a given domain, will often yield a countably infinite set of orthogonal functions which will span that domain. Depending on the

countable set is sequential as is every cofinite filter on a countably infinite set. The intersection of finitely many sequential filters is again sequential

K\subset \bigcup {\mathcal {F}}\subset U} . Let S {\displaystyle S} be an infinite set and let n {\displaystyle n} by a number such that 1 ≤ n < ω {\displaystyle

polytopes. There are also three polyhedral prismatic groups, and an infinite set of duoprismatic groups. Each group defined by a Goursat tetrahedron fundamental

{\displaystyle \theta } from a polynomially sized set as opposed to the current infinite set [ 0 , 1 ] {\displaystyle [0,1]} . Let Q = { 0 , 1 } ∪ { 2 ω 1 d , …

highest expected return and the lowest risk there is not one but rather an infinite set of "solutions" (not dominated solutions, mostly referred to as the "efficient

showed mathematically that a function could be reconstructed from an infinite set of its projections. In 1937, Polish mathematician Stefan Kaczmarz developed

vector lattice (lattice) T {\displaystyle \mathbf {T} } is defined as the infinite set consisting of all of the translation vectors of a crystal pattern. Each

contrast with a “conceptual strategy” which aims “to create, ideally, an infinite set of objects” (p. 457), and so indicates the difference between specific

superscript μ indicates a component along e(μ). Clearly, the (discrete infinite) set of Fourier coefficients a k ( μ ) ( t ) {\displaystyle a_{\mathbf {k}

infinite) collection of non-uniform problems. A uniform problem made of an infinite set of non-uniform problems can be intractable even if all these non-uniform

to properties of FOL. We denote by T {\displaystyle T} a (possibly infinite) set of IF sentences. Löwenheim-Skolem property: if T {\displaystyle T} has

Quantum Mechanics, Addison Wesley (2010) Yaes, Robert J. (1971-06-15). "Infinite Set of Quasipotential Equations from the Kadyshevsky Equation". Physical

and scaling properties In 1996, he published exact solution for the infinite set of rate equations for heterogeneous growth with size-linear rate constants

of any and all structures created during network formation. Thus, an infinite set of differential rate equations (one for each possible structure, of which

P,R)} where everything except R is the same as in a CFG, and R is an infinite set of valid derivation sequences p 1 p 2 . . . p n {\displaystyle p_{1}p_{2}

{\displaystyle \pi _{S}=Pr[S(t)=S]} (if S(t) takes values in an uncountably infinite set of vectors with real-valued entries, then π S {\displaystyle \pi _{S}}

{\displaystyle a\in A} is an expression, A variable, from some fixed, countably infinite set of variables, is an expression, If e 1 {\displaystyle e_{1}} and e 2

(SA) is given below; more information can be found in [22,23]. Given an infinite set of names N {\displaystyle {\mathcal {N}}} (ranged over by m , n , … {\displaystyle

language itself. Ontologically, an idiolect is construed as a (possibly infinite) set of abstract sentences: form-meaning pairs consisting, in the case of

coordinates { π λ ( w ) } {\displaystyle \{\pi _{\lambda }(w)\}} satisfy an infinite set of bilinear relations, the Plücker relations, defining the image of the

coclass tree is eliminated, since the result would be a disconnected infinite set of finite graphs instead of a tree. For example, it is neither recommended

q>0} .: 246  For any value n < μ ( x ) {\displaystyle n<\mu (x)} , the infinite set of all rationals p / q {\displaystyle p/q} satisfying the above inequality

freedom, Biswas, Mazumdar and Siegel (2005) considered a string-inspired infinite set of higher derivative terms S = ∫ d 4 x − g ( R 2 + R F ( ◻ ) R ) {\displaystyle