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Statements

Subject Item: dbr:Calculus
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Subject Item: dbr:Power_law
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Subject Item: dbr:Projectively_extended_real_line
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Subject Item: dbr:Propagator
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Subject Item: dbr:Quantum_limit
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Subject Item: dbr:Quantum_logic
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Subject Item: dbr:Schwarz_lantern
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Subject Item: dbr:Entropy_rate
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Subject Item: dbr:Meissel–Mertens_constant
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Subject Item: dbr:Method_of_normals
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Subject Item: dbr:Metric_derivative
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Subject Item: dbr:Q-analog
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Subject Item: dbr:Quadratic_growth
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Subject Item: dbr:Radiometry
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Subject Item: dbr:Timeline_of_mathematics
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Subject Item: dbr:Christiaan_Huygens
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Subject Item: dbr:Chrysippus
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Subject Item: dbr:Circumference
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Subject Item: dbr:Clearance_(pharmacology)
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Subject Item: dbr:Ehrling's_lemma
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Subject Item: dbr:Envelope_(mathematics)
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Subject Item: dbr:Fresnel_equations
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Subject Item: dbr:Fréchet_space
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Subject Item: dbr:Gaetano_Fichera
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Subject Item: dbr:Gilles_de_Roberval
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Subject Item: dbr:Glaisher–Kinkelin_constant
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Subject Item: dbr:Glossary_of_areas_of_mathematics
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Subject Item: dbr:Glossary_of_calculus
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Subject Item: n47:_A–L
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Subject Item: dbr:Multiple_integral
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Subject Item: dbr:Constant_problem
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Subject Item: dbr:Continuous_predicate
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Subject Item: dbr:Controversy_over_Cantor's_theory
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Subject Item: dbr:Convergence_proof_techniques
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Subject Item: dbr:Thomas_Bradwardine
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Subject Item: dbr:Thomas_precession
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Subject Item: dbr:Peano_curve
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Subject Item: dbr:Oscillation_(mathematics)
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Subject Item: dbr:Approximation
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Subject Item: dbr:Arithmetization_of_analysis
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Subject Item: dbr:Leibniz's_notation
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Subject Item: dbr:Leibniz_integral_rule
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Subject Item: dbr:Limit_(math)
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Subject Item: dbr:Limit_(mathematic)
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Subject Item: dbr:Limit_(mathematics)
rdf:type: owl:Thing
rdfs:label: Limite (mathématiques) Limeso نهاية (رياضيات) Límite (matemática) Границя Granica (matematyka) Предел (математика) 极限 (数学) 極限 Limite Limiet Limite (matematica) Όριο (μαθηματικά) Gränsvärde Limit (mathematics) Limita 극한 Límit Limite Limit (matematika) Teorainn (matamaitic)
rdfs:comment: Dalam matematika, konsep limit digunakan untuk menjelaskan perilaku suatu fungsi saat peubah bebasnya mendekati suatu titik tertentu, atau menuju tak hingga; atau perilaku dari suatu barisan saat indeks mendekati tak hingga. Limit dipakai dalam kalkulus (dan cabang lainnya dari analisis matematika) untuk membangun pengertian kekontinuan, turunan dan integral. Dalam pelajaran matematika, limit biasanya mulai dipelajari saat pengenalan terhadap kalkulus, dan untuk memahami konsep limit secara menyeluruh bukan sesuatu yang mudah. Границя — одне з основних понять математики, яке означає, що деякий об'єкт, змінюючись, нескінченно наближається до певного сталого значення. Точний зміст отримує лише при наявності коректного визначення поняття близькості між елементами (точками) множини, в якій вказана величина набуває значення. Основні поняття математичного аналізу — неперервність, похідна, інтеграл — визначають через границю. En la matematiko la limeso aŭ limvaloro estas kvanto difinita laŭ certa regulo, kiu varias depende de tio ĉu temas pri limeso de funkcio aŭ limeso de vico, kaj ĉu temas pri limeso ĉe punkto aŭ limeso ĉe malfinio. La intuitiva ideo de ĉiuj tiuj difinoj de limeso estas ke ĝi estas la punkto al kiu iu kvanto alproksimiĝas. Ekzemple la vico (1/n) (do 1, 1/2, 1/3, ...) alproksimiĝas al 0 kiam n "alproksimiĝas" al malfinio. Granica – pojęcie używane w matematyce określające zachowania funkcji, a w szczególności ciągu, gdy ich wartości zbliżają się do pewnej wartości lub dążą do nieskończoności. Granice używane są w rachunku różniczkowo-całkowym i innych działach analizy matematyczej do definiowania pochodnych i ciągłości. Pojęcia te stosuje się głównie przy określaniu granic ciągów (zob. granica ciągu) i funkcji (zob. granica funkcji); jednak można te definicje połączyć i uogólnić na dowolne przestrzenie topologiczne, używając ciągów uogólnionych lub filtrów. 极限（英語：Limit）是數學分析或微積分的重要基础概念，连续和导数的都是通过极限来定义的。極限分為描述一个序列的下標愈來越大时的趋势（序列極限），或是描述函数的自变量接趨近某個值的时函数值的趋势（函數極限）。函数极限可以推广到网中，而数列的极限则与范畴论中的极限和有向极限密切相关。 In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as which reads " of tends to as tends to ". Преде́л — одно из основных понятий математического анализа, на него опираются такие фундаментальные разделы анализа, как непрерывность, производная, интеграл, бесконечные ряды и др. Различают предел последовательности и предел функции. Понятие предела на интуитивном уровне использовалось ещё во второй половине XVII века Ньютоном, а также математиками XVIII века, такими как Эйлер и Лагранж. Первые строгие определения предела последовательности дали Больцано в 1816 году и Коши в 1821 году. Sa mhatamaitic, luach a ndruideann athróg leis. Mar shampla, féadfaidh an athróg a bheith cothrom le suim líon téarmaí i seicheamh, mar seo: Sn = 1/1 + 1/2 + 1/4 + 1/2n. De réir mar a théann n i méid (is é sin, n →∞), druideann S le luach 2. Mar shampla eile, féadfaidh athróg y a bheith spleách ar athróg eile x, agus féadfaidh sí druidim le teorainn de réir mar a dhruideann x le luach ar leith. Abair gur y = 2 + 1/x, druideann sé le luach 2 de réir mar a théann x i méid. Tá coincheap na teorann bunúsach i gcalcalas agus cuid mhaith brainsí den mhatamaitic. Sainmhínítear teorainn feidhme f(x), L, mas ann di, de réir mar a dhruideann x le luach ar leith x0, leis an riail seo a leanas, do gach ε > 0, δ > 0 ann ionas más | x-x0| < δ, go gciallaíonn sé sin gur |f(x)- L| < ε. Thug an matamaitice النهاية أو الغاية (بالإنجليزية: Limit)‏ أحد المفاهيم الأساسية في الرياضيات ، وبشكل خاص في التفاضل والتكامل والتحليل الرياضي، ويقصد بها أن متغير ما تابع لمتغير آخر تقترب قيمته اعتباطيا من ثابت ما لأن المتغير الآخر يتغير بطريقة محددة. تكمن أهمية النهاية في أنها تستعمل لتعريف مفاهيم أساسية أخرى في الرياضيات مثل: الاستمرارية والاشتقاقية والتكامل. Matematikan, limitea kontzeptu bat da segida edo funtzio baten joera adierazten duena, segida edo funtzio horren parametroak balio jakin batera hurbiltzen direnean. Kalkuluan (bereziki eta matematikoan) kontzeptu horrek erabiltzen da honako funtsezko kontzeptuak definitzeko: , jarraitutasuna, deribazioa eta integrazioa, besteak beste. Limitea funtzio baten aldagai independenteari baldintzaren bat jarri ondoren, funtzioa hurbiltzen den balioa da, beraz: Ett gränsvärde (limes) (matematisk symbol: lim) för en funktion beskriver funktionens värde när dess argument kommer tillräckligt nära en viss punkt eller växer sig oändligt (eller tillräckligt) stora. Gränsvärden används inom matematisk analys, bland annat för att definiera kontinuitet och derivata. För gränsvärden används notationen alternativt f(x) → A då x → a. Båda utläses som ”gränsvärdet av f(x) då x går mot a är lika med A” eller ”limes av f(x) …”, alternativt ”f(x) går mot A då x går mot a”, och innebär att när x är "nästan a" kommer f(x) att vara "nästan A". In matematica, il concetto di limite serve a descrivere l'andamento di una funzione all'avvicinarsi del suo argomento a un dato valore (limite di una funzione) oppure l'andamento di una successione al crescere illimitato dell'indice (limite di una successione). I limiti si utilizzano in tutti i rami dell'analisi matematica; sono usati ad esempio per definire la continuità, la derivazione e l'integrazione. Il concetto di limite di una funzione, più generale del limite di una successione, può essere generalizzato da quello di limite di un filtro. Με τον όρο «όριο» στα μαθηματικά, νοείται η διαρκής προσέγγιση ενός σημείου ή, διαφορετικά, η διαρκής μείωση μιας απόστασης, χωρίς όμως ποτέ αυτή να μηδενίζεται. Συνήθως, η έννοια του ορίου χρησιμοποιείται για να περιγραφεί η συμπεριφορά μιας συνάρτησης καθώς το της πλησιάζει κάποιο σημείο ή καθώς μεγαλώνει (αντίστοιχα μικραίνει) απεριόριστα. Η έννοια του ορίου συνάρτησης περιλαμβάνει και την έννοια του ορίου ακολουθίας όπου εκεί η έννοια του ορίου χρησιμοποιείται για να περιγράψουμε τη συμπεριφορά της ακολουθίας καθώς ο δείκτης της αυξάνεται απεριόριστα. En análisis real y complejo, el concepto de límite es la clave de toque que formaliza la noción intuitiva de aproximación hacia un punto concreto de una sucesión o una función, a medida que los parámetros de esa sucesión o función se acercan a un determinado valor. En el análisis los conceptos de series convergentes, derivada e integral definida se fundamentan mediante el concepto de límite. Para fórmulas, el límite se utiliza usualmente de forma abreviada mediante lim como en lim(an) = a o se representa mediante la flecha (→) como en an → a. Limita je matematická konstrukce vyjadřující, že se hodnoty zadané funkce nebo posloupnosti blíží libovolně blízko k nějakému bodu. Právě tento bod je pak označován jako limita. Tato skutečnost se u funkcí zapisuje a u posloupností . En matemàtiques, la noció de límit és força intuïtiva, malgrat la seva formulació abstracta. Amb l'objectiu de donar-ne una introducció simple, en aquest article es tracta només el cas de les successions de nombres reals i el cas de les funcions reals d'una variable real. Em matemática, o conceito de limite é usado para descrever o comportamento de uma função à medida que o seu argumento se aproxima de um determinado valor, assim como o comportamento de uma sequência de números reais, à medida que o índice (da sequência) vai crescendo, i.e. tende para infinito . Os limites são usados no cálculo diferencial e integral e em outros ramos da análise matemática para definir derivadas, continuidade de funções, soma de Riemann, integrais definidas e integrais impróprias. En analyse mathématique, la notion de limite décrit l’approximation des valeurs d'une suite lorsque l'indice tend vers l’infini, ou d'une fonction lorsque la variable se rapproche d’un point (éventuellement infini) au bord du domaine de définition. Si une telle limite existe dans l’ensemble d’arrivée, on dit que la suite ou la fonction est convergente (au point étudié). Si ce n’est pas le cas, elle est divergente, comme dans le cas de suites et fonctions périodiques non constantes (telle la fonction sinus en +∞). 数学においては、数列など、ある種の数学的対象をひとまとまりに並べて考えたものについての極限（きょくげん、英: limit）がしばしば考察される。直感的には、数の列がある値に限りなく近づくとき、その値のことを数列の極限あるいは極限値といい、この数列は収束するという。収束せず正の無限大、負の無限大、振動することを発散するという。極限を表す記号として、lim (英語: limit, リミット、ラテン語: limes)という記号が一般的に用いられる。例えば次のように使う: * * Het woord limiet is afkomstig van het Latijnse "limes", dat "grens" betekent. In de wiskunde kan het begrip limiet of grenswaarde goed gedemonstreerd worden met het volgende voorbeeld. De getallen uit de rij 1, 1/2, 1/4, 1/8, ... naderen steeds dichter de grenswaarde 0. Het getal 0 is dan ook de limiet van deze rij. Echter, ook 1, −1/2, 1/4, −1/8, ... heeft limiet 0, waarbij de term "grens" minder van toepassing is.
rdfs:seeAlso: dbr:Cauchy_sequence
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dbo:abstract: Sa mhatamaitic, luach a ndruideann athróg leis. Mar shampla, féadfaidh an athróg a bheith cothrom le suim líon téarmaí i seicheamh, mar seo: Sn = 1/1 + 1/2 + 1/4 + 1/2n. De réir mar a théann n i méid (is é sin, n →∞), druideann S le luach 2. Mar shampla eile, féadfaidh athróg y a bheith spleách ar athróg eile x, agus féadfaidh sí druidim le teorainn de réir mar a dhruideann x le luach ar leith. Abair gur y = 2 + 1/x, druideann sé le luach 2 de réir mar a théann x i méid. Tá coincheap na teorann bunúsach i gcalcalas agus cuid mhaith brainsí den mhatamaitic. Sainmhínítear teorainn feidhme f(x), L, mas ann di, de réir mar a dhruideann x le luach ar leith x0, leis an riail seo a leanas, do gach ε > 0, δ > 0 ann ionas más | x-x0| < δ, go gciallaíonn sé sin gur |f(x)- L| < ε. Thug an matamaiticeoir cumasach Francach Augustin Louis Cauchy (1789-1857) an bealach seo le teorainn a shainmhíniú sna 1820idí mar chuid den chéad iarracht shásúil dianchur síos a dhéanamh ar an gcalcalas. Granica – pojęcie używane w matematyce określające zachowania funkcji, a w szczególności ciągu, gdy ich wartości zbliżają się do pewnej wartości lub dążą do nieskończoności. Granice używane są w rachunku różniczkowo-całkowym i innych działach analizy matematyczej do definiowania pochodnych i ciągłości. Pojęcia te stosuje się głównie przy określaniu granic ciągów (zob. granica ciągu) i funkcji (zob. granica funkcji); jednak można te definicje połączyć i uogólnić na dowolne przestrzenie topologiczne, używając ciągów uogólnionych lub filtrów. Granica zwykle zapisywana jest jako i jest odczytywana jako „granica od gdy dąży do równa się ”. Fakt, że funkcja zbliża się do granicy gdy dąży do jest czasami oznaczany strzałką w prawo jak w . En analyse mathématique, la notion de limite décrit l’approximation des valeurs d'une suite lorsque l'indice tend vers l’infini, ou d'une fonction lorsque la variable se rapproche d’un point (éventuellement infini) au bord du domaine de définition. Si une telle limite existe dans l’ensemble d’arrivée, on dit que la suite ou la fonction est convergente (au point étudié). Si ce n’est pas le cas, elle est divergente, comme dans le cas de suites et fonctions périodiques non constantes (telle la fonction sinus en +∞). Sous condition d’existence, le calcul des limites est simplifié par la compatibilité avec les opérations arithmétiques élémentaires, mais plusieurs formes indéterminées font obstacle à cette technique calculatoire. La comparaison de croissance permet de lever bien souvent ces indéterminations. La détermination d’une limite peut être raffinée par l’expression d’un équivalent (notamment dans le cas d’une limite nulle ou infinie), d’asymptotes obliques ou de branches paraboliques, voire de développement limité ou asymptotique. La limite d’une fonction en un point appartenant à son domaine de définition est liée à la caractérisation de sa continuité. Ce constat permet d’exprimer plus généralement la limite dans un cadre topologique à l’aide de la notion de voisinage. Elle peut même s’étendre hors de ce cadre avec la notion de filtre. Pour une fonction d’une variable à valeurs vectorielles, et notamment une courbe intégrale d’un champ de vecteurs (par exemple associé à l’espace des phases pour une équation différentielle ordinaire du second ordre), l’absence de limite est parfois compensée par l’existence d’un cycle limite. In matematica, il concetto di limite serve a descrivere l'andamento di una funzione all'avvicinarsi del suo argomento a un dato valore (limite di una funzione) oppure l'andamento di una successione al crescere illimitato dell'indice (limite di una successione). I limiti si utilizzano in tutti i rami dell'analisi matematica; sono usati ad esempio per definire la continuità, la derivazione e l'integrazione. Il concetto di limite di una funzione, più generale del limite di una successione, può essere generalizzato da quello di limite di un filtro. 极限（英語：Limit）是數學分析或微積分的重要基础概念，连续和导数的都是通过极限来定义的。極限分為描述一个序列的下標愈來越大时的趋势（序列極限），或是描述函数的自变量接趨近某個值的时函数值的趋势（函數極限）。函数极限可以推广到网中，而数列的极限则与范畴论中的极限和有向极限密切相关。 Het woord limiet is afkomstig van het Latijnse "limes", dat "grens" betekent. In de wiskunde kan het begrip limiet of grenswaarde goed gedemonstreerd worden met het volgende voorbeeld. De getallen uit de rij 1, 1/2, 1/4, 1/8, ... naderen steeds dichter de grenswaarde 0. Het getal 0 is dan ook de limiet van deze rij. Echter, ook 1, −1/2, 1/4, −1/8, ... heeft limiet 0, waarbij de term "grens" minder van toepassing is. Ett gränsvärde (limes) (matematisk symbol: lim) för en funktion beskriver funktionens värde när dess argument kommer tillräckligt nära en viss punkt eller växer sig oändligt (eller tillräckligt) stora. Gränsvärden används inom matematisk analys, bland annat för att definiera kontinuitet och derivata. För gränsvärden används notationen alternativt f(x) → A då x → a. Båda utläses som ”gränsvärdet av f(x) då x går mot a är lika med A” eller ”limes av f(x) …”, alternativt ”f(x) går mot A då x går mot a”, och innebär att när x är "nästan a" kommer f(x) att vara "nästan A". Границя — одне з основних понять математики, яке означає, що деякий об'єкт, змінюючись, нескінченно наближається до певного сталого значення. Точний зміст отримує лише при наявності коректного визначення поняття близькості між елементами (точками) множини, в якій вказана величина набуває значення. Основні поняття математичного аналізу — неперервність, похідна, інтеграл — визначають через границю. Με τον όρο «όριο» στα μαθηματικά, νοείται η διαρκής προσέγγιση ενός σημείου ή, διαφορετικά, η διαρκής μείωση μιας απόστασης, χωρίς όμως ποτέ αυτή να μηδενίζεται. Συνήθως, η έννοια του ορίου χρησιμοποιείται για να περιγραφεί η συμπεριφορά μιας συνάρτησης καθώς το της πλησιάζει κάποιο σημείο ή καθώς μεγαλώνει (αντίστοιχα μικραίνει) απεριόριστα. Η έννοια του ορίου συνάρτησης περιλαμβάνει και την έννοια του ορίου ακολουθίας όπου εκεί η έννοια του ορίου χρησιμοποιείται για να περιγράψουμε τη συμπεριφορά της ακολουθίας καθώς ο δείκτης της αυξάνεται απεριόριστα. Преде́л — одно из основных понятий математического анализа, на него опираются такие фундаментальные разделы анализа, как непрерывность, производная, интеграл, бесконечные ряды и др. Различают предел последовательности и предел функции. Понятие предела на интуитивном уровне использовалось ещё во второй половине XVII века Ньютоном, а также математиками XVIII века, такими как Эйлер и Лагранж. Первые строгие определения предела последовательности дали Больцано в 1816 году и Коши в 1821 году. Limita je matematická konstrukce vyjadřující, že se hodnoty zadané funkce nebo posloupnosti blíží libovolně blízko k nějakému bodu. Právě tento bod je pak označován jako limita. Tato skutečnost se u funkcí zapisuje a u posloupností . Dle toho, zda se uvažuje o funkci nebo o posloupnosti, hovoříme o limitě funkce nebo limitě posloupnosti. Pojem limity lze definovat na reálných číslech, obecnější definice má smysl na libovolném metrickém prostoru a ještě obecnější definice na libovolném topologickém prostoru. Tam, kde má smysl více definic, jsou tyto definice ekvivalentní (například reálná čísla jsou metrickým i topologickým prostorem). En análisis real y complejo, el concepto de límite es la clave de toque que formaliza la noción intuitiva de aproximación hacia un punto concreto de una sucesión o una función, a medida que los parámetros de esa sucesión o función se acercan a un determinado valor. En el análisis los conceptos de series convergentes, derivada e integral definida se fundamentan mediante el concepto de límite. En cálculo (especialmente en análisis real y matemático) este concepto se utiliza para definir los conceptos fundamentales de convergencia, continuidad, derivación, integración, entre otros. Si bien, el concepto de límite parece intuitivamente relacionado con el concepto de distancia, en un espacio euclídeo, es la clase de conjuntos abiertos inducidos por dicha métrica, lo que permite definir rigurosamente la noción de límite. El concepto se puede generalizar a otros espacios topológicos, como pueden ser las redes topológicas; de la misma manera, es definido y utilizado en otras ramas de la matemática, como puede ser la teoría de categorías. Para fórmulas, el límite se utiliza usualmente de forma abreviada mediante lim como en lim(an) = a o se representa mediante la flecha (→) como en an → a. En la matematiko la limeso aŭ limvaloro estas kvanto difinita laŭ certa regulo, kiu varias depende de tio ĉu temas pri limeso de funkcio aŭ limeso de vico, kaj ĉu temas pri limeso ĉe punkto aŭ limeso ĉe malfinio. La intuitiva ideo de ĉiuj tiuj difinoj de limeso estas ke ĝi estas la punkto al kiu iu kvanto alproksimiĝas. Ekzemple la vico (1/n) (do 1, 1/2, 1/3, ...) alproksimiĝas al 0 kiam n "alproksimiĝas" al malfinio. Dalam matematika, konsep limit digunakan untuk menjelaskan perilaku suatu fungsi saat peubah bebasnya mendekati suatu titik tertentu, atau menuju tak hingga; atau perilaku dari suatu barisan saat indeks mendekati tak hingga. Limit dipakai dalam kalkulus (dan cabang lainnya dari analisis matematika) untuk membangun pengertian kekontinuan, turunan dan integral. Dalam pelajaran matematika, limit biasanya mulai dipelajari saat pengenalan terhadap kalkulus, dan untuk memahami konsep limit secara menyeluruh bukan sesuatu yang mudah. Em matemática, o conceito de limite é usado para descrever o comportamento de uma função à medida que o seu argumento se aproxima de um determinado valor, assim como o comportamento de uma sequência de números reais, à medida que o índice (da sequência) vai crescendo, i.e. tende para infinito . Os limites são usados no cálculo diferencial e integral e em outros ramos da análise matemática para definir derivadas, continuidade de funções, soma de Riemann, integrais definidas e integrais impróprias. النهاية أو الغاية (بالإنجليزية: Limit)‏ أحد المفاهيم الأساسية في الرياضيات ، وبشكل خاص في التفاضل والتكامل والتحليل الرياضي، ويقصد بها أن متغير ما تابع لمتغير آخر تقترب قيمته اعتباطيا من ثابت ما لأن المتغير الآخر يتغير بطريقة محددة. تكمن أهمية النهاية في أنها تستعمل لتعريف مفاهيم أساسية أخرى في الرياضيات مثل: الاستمرارية والاشتقاقية والتكامل. En matemàtiques, la noció de límit és força intuïtiva, malgrat la seva formulació abstracta. Amb l'objectiu de donar-ne una introducció simple, en aquest article es tracta només el cas de les successions de nombres reals i el cas de les funcions reals d'una variable real. Matematikan, limitea kontzeptu bat da segida edo funtzio baten joera adierazten duena, segida edo funtzio horren parametroak balio jakin batera hurbiltzen direnean. Kalkuluan (bereziki eta matematikoan) kontzeptu horrek erabiltzen da honako funtsezko kontzeptuak definitzeko: , jarraitutasuna, deribazioa eta integrazioa, besteak beste. Limitea funtzio baten aldagai independenteari baldintzaren bat jarri ondoren, funtzioa hurbiltzen den balioa da, beraz: 数学においては、数列など、ある種の数学的対象をひとまとまりに並べて考えたものについての極限（きょくげん、英: limit）がしばしば考察される。直感的には、数の列がある値に限りなく近づくとき、その値のことを数列の極限あるいは極限値といい、この数列は収束するという。収束せず正の無限大、負の無限大、振動することを発散するという。極限を表す記号として、lim (英語: limit, リミット、ラテン語: limes)という記号が一般的に用いられる。例えば次のように使う: * * In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as (although a few authors may use "Lt" instead of "lim")and is read as "the limit of f of x as x approaches c equals L". The fact that a function f approaches the limit L as x approaches c is sometimes denoted by a right arrow (→ or ), as in which reads " of tends to as tends to ".
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