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As

Arsenic is a chemical element with the symbol As and atomic number 33. Classified as a metalloid, it displays properties intermediate between those of metals and nonmetals, appearing as a brittle, steel-gray solid in its stable gray allotrope at standard conditions. Arsenic occurs naturally in the Earth's crust at an average concentration of about 1.5 to 2 milligrams per kilogram, primarily in sulfide minerals such as arsenopyrite and realgar, often extracted as a byproduct of copper and lead refining. In industrial applications, arsenic compounds serve as n-type dopants in manufacturing, particularly for and cells, and as additives in alloys like lead-acid batteries and to enhance strength and resistance. Historically, arsenic-based pesticides such as dominated agriculture until phased out due to environmental persistence and risks, though its compounds retain niche roles in and . Medically, has demonstrated efficacy in treating , leveraging its ability to induce cancer cell , marking a rare therapeutic pivot from its notorious toxic legacy. Inorganic arsenic compounds rank among the most potent poisons, disrupting via ATP inhibition and causing acute symptoms like gastrointestinal distress, neuropathy, and cardiovascular collapse upon or inhalation, with chronic exposure linked to lesions, peripheral , and elevated cancer risks including , , and malignancies. Elemental itself exhibits low , but environmental —predominantly from in regions like —affects millions, prompting global remediation efforts despite debates over naturally occurring versus sources. Its dual role as both industrial asset and health hazard underscores causal trade-offs in extraction and application, with regulatory limits now enforced to mitigate population-level exposures.

Mathematics, science, and technology

Computing

, with the chemical symbol As, is integral to technologies underpinning modern . High-purity arsenic metal (99.9999% or greater) is refined for producing III-V compound semiconductors such as (GaAs), (InAs), and (InGaAs), which are employed in high-performance transistors, integrated circuits, and optoelectronic devices critical for . These materials exhibit higher than , enabling faster and higher operating frequencies in microprocessors, radio-frequency amplifiers, and photonic components used in data centers and high-speed systems. In silicon-based , arsenic functions as an n-type to introduce free electrons into the crystal lattice, forming the basis for n-channel transistors and logic elements in complementary metal-oxide-semiconductor () integrated circuits that power central processing units (CPUs), graphics processing units (GPUs), and memory chips. (AsH₃) gas is deployed in epitaxial growth processes like to achieve atomic-scale precision in doping silicon wafers, with concentrations typically on the order of 10¹⁵ to 10¹⁸ atoms per cubic centimeter for optimal conductivity. This doping enhances carrier concentration without significantly altering the bandgap, supporting the scalability of in transistor density up to the 5-nanometer nodes prevalent in 2025 computing architectures. Emerging applications leverage arsenic's topological properties for advanced computing paradigms. Princeton researchers in 2024 demonstrated hybrid topological materials incorporating arsenic, which exhibit robust edge states resistant to defects, potentially enabling fault-tolerant quantum bits (qubits) and low-dissipation logic gates for quantum and neuromorphic computing. Such developments address limitations in conventional silicon, where scattering losses limit performance at terahertz frequencies, though supply chain vulnerabilities for arsenic—predominantly sourced from China—pose risks to global computing manufacturing. Despite toxicity concerns in handling, arsenic's efficacy in these roles remains unmatched by substitutes in high-volume production as of 2025.

Health and medicine

Arsenic, with chemical symbol As, exerts significant toxic effects on human health, primarily through disruption of cellular metabolism and enzyme function via binding to sulfhydryl groups. Inorganic arsenic, the most toxic form, is classified as a Group 1 carcinogen by the International Agency for Research on Cancer, with chronic exposure associated with increased risks of skin, lung, bladder, and liver cancers. Long-term ingestion from contaminated groundwater, affecting over 140 million people globally as of 2022, also leads to non-cancerous outcomes including melanosis, hyperkeratosis, peripheral vascular disease, and diabetes mellitus. Acute , typically from of doses exceeding 100-300 mg, manifests within hours as severe gastrointestinal distress—, profuse , watery (often described as "rice-water" stools), and —followed by , , and potential multi-organ failure if untreated. of gas, a byproduct of industrial processes involving and acids, causes , , and renal failure, with symptoms including , dyspnea, and appearing 2-24 hours post-exposure. involves supportive care, including with (BAL) or succimer for severe cases, alongside gastric if is recent. The for inorganic is approximately 1-3 mg/kg body weight in adults. Chronic low-level exposure, prevalent in regions like and where arsenic exceeds 10 μg/L—the World Health Organization's guideline value—produces insidious symptoms emerging after months to years, such as , anorexia, , and sensory neuropathy with symmetric "stocking-glove" distribution. Dermatological hallmarks include diffuse , raindrop-like , and palmar-plantar hyperkeratoses, which precede malignancy in up to 10% of cases. Cardiovascular effects encompass blackfoot disease (peripheral artery occlusive disease) and , while neurological impacts involve cognitive deficits and . No specific exists for chronic poisoning; management focuses on exposure cessation and symptom palliation, with reserved for high urinary arsenic levels. In therapeutic contexts, arsenic trioxide (As₂O₃), administered intravenously, serves as a frontline agent for acute promyelocytic leukemia (APL), a subtype of acute myeloid leukemia comprising 5-10% of cases, by promoting degradation of the PML-RARα oncoprotein and inducing apoptosis in leukemic cells. Combined with all-trans retinoic acid (ATRA), it yields complete remission rates exceeding 90% in newly diagnosed low-risk APL patients, as demonstrated in a 2013 multicenter trial, while avoiding anthracycline-based chemotherapy and reducing relapse risk to under 5%. The U.S. Food and Drug Administration approved arsenic trioxide in 2000 for relapsed/refractory APL, expanding to frontline use by 2018 for low-risk cases. Common adverse effects include QT interval prolongation (requiring electrolyte monitoring), differentiation syndrome (fever, dyspnea, pulmonary infiltrates), and electrolyte imbalances, necessitating hospitalization during induction. Dosing typically involves 0.15 mg/kg daily until remission, followed by consolidation cycles. Investigational applications extend to other solid tumors and leukemias, though efficacy remains limited outside APL. Historical medicinal uses, such as Fowler's solution for syphilis in the 19th century, have been supplanted due to toxicity, underscoring arsenic's narrow therapeutic index.

Natural sciences

Arsenic is a chemical element with the symbol As and atomic number 33, classified as a metalloid in group 15 of the periodic table. It exists primarily as a steel-gray, brittle, crystalline semimetal that tarnishes upon exposure to air and oxidizes rapidly when heated to form arsenous oxide. Naturally occurring arsenic is monoisotopic, composed entirely of the stable isotope 75As, with a relative atomic mass of 74.922. In , is ubiquitous in the at concentrations averaging 1.5 to 2 mg/kg, often bound in minerals such as (FeAsS) and löllingite (FeAs2), or as sulfides like realgar (As4S4) and orpiment (As2S3). It enters the through natural processes including volcanic emissions, of arsenic-bearing rocks, and of deposits, as well as anthropogenic activities like and use. contamination arises from reductive dissolution of iron oxides in aquifers, mobilizing into potable water sources, with elevated levels documented in regions such as , , and parts of the . Biogeochemically, arsenic cycles through oxidation states from -3 to +5, with inorganic forms dominating in oxic environments and organic species like methylarsenic acids formed via microbial biomethylation in anoxic sediments. Certain prokaryotes, such as Sulfurospirillum arsenophilum, respire (AsV) as a terminal , while others reduce to (AsIII) for or energy generation, influencing its mobility in soils and aquatic systems. Inorganic compounds exhibit high acute and chronic , disrupting by inhibiting and contributing to , with the identifying a reference concentration of 10 µg/L in to mitigate risks of lesions, cardiovascular disease, and cancers of the , , and . Despite its , trace may play a role in some eukaryotic , though essentiality remains unestablished and debated due to confounding deficiencies in controlled studies.

Units of measurement

The as, also known as the libra or Roman pound, was the primary unit of weight in ancient Rome, standardized at approximately 328.9 grams following reforms around 268 BC. This unit derived from earlier Italic measures and formed the foundation for weighing commodities, metals, and early coinage, with physical bronze weights inscribed as as or libra surviving from Republican-era sites. The as equated to roughly 0.722 avoirdupois pounds (0.329 kg), reflecting a duodecimal system where it divided into 12 uncae (singular uncia), each weighing about 27.3 grams. Subdivisions extended beyond the uncia to smaller fractions like the (1/6 as) and (1/4 as), used for precise mercantile and measurements, while multiples such as the (2 assēs) scaled up for bulk goods. This system emphasized practical balance-scale applications in markets and state treasuries, with the as influencing provincial standards across the until the adoption of Greek-influenced metrics in . Archaeological evidence, including lead and stone weights from and Ostia dated to the 1st–2nd centuries AD, confirms consistency in the as's despite minor regional variations. The as also underpinned Roman bronze coinage introduced circa 300–280 BC, where early aes rude bars and aes signatum ingots were valued by weight in assēs, evolving into struck coins nominally equaling one as of bronze—though debasement reduced actual mass to about 27 grams by the late Republic. This integration of weight and currency facilitated trade but led to inflationary reductions, such as the as uncialis reform of 217–215 BC, which halved the coin's weight to half an uncia while preserving the as as the abstract unit. By the Imperial era, the as coin persisted as a low-value denomination until Diocletian's reforms circa 294 AD, but the weight unit endured in legal and fiscal contexts.

Other uses in mathematics, science, and technology

As is the chemical symbol for arsenic, a metalloid element in group 15 of the periodic table with atomic number 33 and standard atomic weight of 74.921595(29). Arsenic occurs naturally in the Earth's crust at an average concentration of about 1.5 to 2 milligrams per kilogram, primarily in sulfidic ores such as arsenopyrite (FeAsS), and exists in four allotropes: gray (the stable metallic form), yellow, black, and brown. The element is semiconducting in its gray form, with a density of 5.73 g/cm³ at 20°C, melting point of 817°C (under 36 atm pressure), and boiling point of 614°C, though it sublimes readily at atmospheric pressure around 615°C. Arsenic's toxicity stems from its interference with cellular respiration by binding to sulfhydryl groups in enzymes, leading to applications in historical pesticides and rodenticides, though modern uses are limited due to health risks; it also finds industrial roles in alloys like lead-acid batteries and semiconductors such as gallium arsenide (GaAs) for LEDs and solar cells.

Language

Grammatical uses

"As" primarily functions as a , , or in . As a preposition, it introduces a to indicate the role, , or in which someone or something acts, such as "She works as a ." It can also denote manner or style, as in "He dressed as a pirate for the party," or , like "Treat it as confidential." In its role as a subordinating , "as" connects a to an independent one, often expressing reason ("As it was raining, we stayed indoors"), time ("She arrived as the meeting began"), or manner ("Do as I say"). For time clauses, it emphasizes of events, typically with simple or continuous forms in the subordinate , distinguishing it from "when" which may imply . In comparative or conditional senses, it appears in constructions like "as if" for hypothetical manner ("He acts as if he owns the place") or "as though" similarly. As an , "as" appears in equative comparisons with the structure "as + / + as," indicating , such as "This book is as interesting as that one," where the first "as" modifies the following or . It also features in phrases like "such as" to introduce examples ("Fruits such as "), functioning adverbially to specify instances without implying exhaustiveness. These uses can overlap or shift based on context, with "as" sometimes forming part of idiomatic expressions like "as well as" for addition ("Apples as well as oranges") or "as for" to introduce topics ("As for the budget, it's approved"). Distinguishing its part of speech requires analyzing syntactic position: prepositional when followed by a noun phrase without a verb, conjunctive when introducing a full clause.

Linguistic names

As refers to a nearly extinct Austronesian language of the Raja Ampat–South Halmahera subgroup, historically spoken in three villages—Asbaken, Mega, and Kabare—along the northwest coast of the in , . As of 1987, it had approximately 300 speakers across these locations, but by 2020, only five fluent speakers and two semi-speakers remained, all elderly and residing primarily in Asbaken, with everyday use limited to occasional discussions of . The language's ISO 639-3 code is asz, and its Glottocode is asss1237. The vitality of As is critically low, classified as moribund due to lack of intergenerational transmission; younger residents in Asbaken primarily speak Papuan Malay or standard Indonesian, with As reserved for interactions among the remaining elderly speakers. Linguistic documentation efforts, including surveys and recordings, have been conducted since the 1980s by researchers affiliated with SIL International and independent linguists, highlighting its phonological, grammatical, and lexical features distinct from neighboring Papuan languages. No standardized orthography or published grammars exist, though recent fieldwork has produced audio corpora and basic lexical inventories for preservation. The ethnic As population numbers around 45 individuals, concentrated in Asbaken, where cultural identity persists despite language shift.

Places

Europe

As is a municipality in the province of Limburg, Belgium, located in the northeastern part of the country bordering the Netherlands. The area features rural landscapes suitable for walking and cycling activities. Ås (often anglicized as As) is a municipality in Akershus county, Norway, approximately 30 km south of Oslo. It serves as the largest agricultural municipality in Akershus and hosts the Norwegian University of Life Sciences along with the Tusenfryd amusement park. The estimated population was 22,344 as of 2025, with a density of 220.6 inhabitants per km² over 101.3 km².

Americas and Oceania

No geographical locations named "As" are recorded in the Americas or Oceania within authoritative databases such as the United States Geological Survey's (GNIS), which catalogs over 2 million domestic features, or international equivalents for , , , , and . Comprehensive reviews of place names in these regions, including populated places, streams, and mountains, yield no matches for "As" as a standalone designation. This absence contrasts with occurrences in , such as the Norwegian municipality of Ås, suggesting "As" lacks prominence or historical adoption in New World or Pacific naming conventions influenced by indigenous, colonial (primarily , , English, and ), or settler languages. Minor or undocumented local features cannot be verified without primary surveys, but no evidence emerges from gazetteers or mapping resources.

Asia and Africa

In Asia, the Bala'as Mountains (also known as Jabal al-Bala'as) form a range in the eastern countryside of , Syria, extending toward province and serving as a in the region's arid terrain. These mountains have featured prominently in military operations due to their strategic elevation and isolation, with reports documenting insurgent activity and aerial strikes in the area as recently as 2024. In Africa, the As River (Afrikaans: As-rivier, sometimes mistranslated as Ash River) flows as a tributary of the Liebenbergsvlei River through the eastern Free State province of South Africa, originating near Bethlehem and supporting local ecosystems amid the region's grasslands. Its name derives from the Afrikaans term for "axle," linked to historical wagon transport rather than botanical ash trees, with a length contributing to seasonal flooding and white-water rafting opportunities. The river was dammed by the Sol Plaatje Dam in 1968 to regulate water flow for irrigation and urban supply, impounding approximately 58 million cubic meters at full capacity.

Religion

Mythology and deities

In Norse mythology, the term ás (Old Norse singular, plural æsir) refers to a god or member of the principal pantheon of deities, distinct from other supernatural beings. The Æsir are depicted as ruling from Asgard, one of the nine worlds, and embody attributes of sovereignty, war, wisdom, and order. Primary accounts derive from medieval Icelandic texts such as the Prose Edda by Snorri Sturluson (c. 1220) and the Poetic Edda (compiled c. 13th century from earlier oral traditions), which portray the Æsir as anthropomorphic figures involved in cosmic events like the creation of the world from the giant Ymir's body and the impending Ragnarök. Prominent Æsir deities include Odin, the Allfather, associated with poetry, prophecy, and battle strategy, who sacrificed an eye for wisdom at Mimir's well; Thor, wielder of the hammer Mjölnir, protector against giants and chaos; Frigg, Odin's wife and goddess of foresight and domesticity; Tyr, god of justice and heroic glory, who lost a hand binding the wolf Fenrir; and Baldr, symbol of beauty and purity, whose death foreshadows Ragnarök. These figures often intermarry and ally with humans or other beings, reflecting themes of fate, honor, and cyclical destruction. Loki, a shape-shifting trickster of partial giant heritage, is sometimes affiliated with the Æsir through blood-brotherhood with Odin, though his actions contribute to their downfall. The originated in a primordial conflict with the , a rival linked to fertility, prosperity, and magic (e.g., , , ). The war erupted after failed hostage exchanges, with the employing direct combat and the using seidr sorcery, ending in stalemate around the world's creation era. A truce involved mutual oaths of peace, spitting into a shared vessel to form the covenant, and integration: hostages Njord and joined the in , while emissaries Hoenir and Mimir went to Vanaheim, though Mimir's beheading strained relations. This merger symbolizes the blending of martial and agrarian divine aspects in the unified cosmos.

Religious concepts

In Old Norse, the term áss (plural æsir) designates a god or divine being, specifically those belonging to the pantheon in , representing a class of deities associated with authority, war, and cosmic order. This contrasts with the , another divine tribe linked to fertility, prosperity, and natural cycles, whose integration into the Aesir following a primordial conflict symbolizes the unification of divine powers in . The æsir include prominent figures such as , Thor, and Tyr, embodying principles of sovereignty and martial prowess central to pre-Christian worldview. Etymologically, áss traces to Proto-Germanic *ansuz, denoting an ancestral divine force or breath of life, with cognates in other Indo-European languages suggesting ancient conceptual links to vital spirits or ruling powers, such as Sanskrit ásu for life-force or spirit. In religious practice, invocation of the æsir occurred through rituals like blóts (sacrificial offerings) aimed at securing favor for battles, harvests, or voyages, reflecting a pragmatic theology where gods were petitioned as active patrons rather than abstract ideals. Contemporary Ásatrú, a reconstructionist reviving since the 1970s, centers on honoring the through communal rites, emphasizing ancestral ties, ethical conduct (as in the derived from Eddic sources), and ecological harmony, with practitioners numbering around 2,000 registered in alone as of recent counts. This modern adaptation interprets concepts as fostering personal resilience and communal solidarity, drawing from archaeological evidence of Viking-era idol worship and invoking divine for protection.

Art, entertainment, and media

Literature and publications

is a sports founded on December 6, 1967, in by Luis Montiel Balibrea, initially as a supplement to the general newspaper Ya. It expanded into a standalone daily publication emphasizing coverage alongside other sports, achieving widespread circulation with over 200,000 daily copies by the early 2000s and maintaining digital editions including AS USA for international audiences. as a Journal, published biannually in , adopts a thematic approach where each issue's title incorporates "as a Journal" followed by a specific focus, such as immersion in singular topics through interdisciplinary contributions from , , and essays. Launched to foster deep exploration of concepts, it invites submissions that align with the issue's , emphasizing creative and reflective content over conventional formats. As/Us operates as an online literary journal dedicated to global writers, releasing themed issues that address cultural and personal narratives, exemplified by its 2017 edition on sacred spaces acknowledging colonial histories and communal bonds. It prioritizes diverse voices through , , and visual elements, functioning as a for dialogue without strict genre boundaries.

Film, television, and music

"As" is the title of a song written, produced, and performed by Stevie Wonder, released on September 28, 1976, as the seventh track on his double album Songs in the Key of Life. The track features Wonder on vocals, keyboards, and drums, with contributions from musicians including Nathan Watts on bass; it exemplifies Wonder's fusion of soul, funk, and jazz elements, reaching philosophical themes of enduring love and cosmic unity. The song has been covered notably by Mary J. Blige with George Michael on the 1999 album Mary, blending R&B and pop interpretations. In film, As Is is a 1986 American television movie directed by Michael Lindsay-Hogg, adapting William M. Hoffman's play about a young gay man diagnosed with AIDS amid his relationships and friendships in 1980s New York City; it stars Robert Carradine, Jonathan Hadary, and Colleen Dewhurst, airing on Showtime and addressing early AIDS crisis realities with dramatic intensity. The film received a Peabody Award for its sensitive portrayal of the epidemic's human toll. Television series incorporating "As" include the British sitcom As Time Goes By (1992–2005), created by Bob Larbey and starring and as former lovers reuniting after decades apart, spanning nine series on with themes of romance, family, and aging. Another is the German action series A.S. (1995–1998), centered on a handling high-stakes cases, produced by RTL Television.

Fictional characters and works

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Business and law

In , AS denotes aksjeselskap, the standard form for a private , which operates as a from its owners, limits liability to their , and requires a minimum of 30,000 kroner as stipulated by the Companies Act. Such companies must include "aksjeselskap" or "AS" in their official name upon registration with the Brønnøysund Register Centre. In , A/S signifies aktieselskab, a authorized to issue shares publicly, subject to registration with the Danish Business Authority and compliance with the Danish Companies Act, including requirements for a and audited for larger entities. This structure provides to shareholders while enabling broader capital raising compared to private forms like ApS.

Economic terms

The as (plural asses) served as the fundamental unit of weight and the lowest denomination of coinage in ancient economic systems, originating as a measure equivalent to one (), weighing approximately 327 grams of or alloy. Initially cast in irregular shapes known as aes rude before the Third Century BCE, it evolved into struck coins around the late fourth or early third century BCE, marking the transition from and weighed metal to standardized in the . This denomination underpinned early monetary valuation, with higher units like the (worth four asses) and (16 asses post-reform) derived from it, facilitating trade, taxation, and military payments across the expanding republic. Over time, the as underwent debasement to address fiscal strains, such as after the Second Punic War in 217 BCE, when its weight dropped from over 250 grams to around 37 grams by the late Republic, shifting composition from aes grave (heavy bronze) to lighter forms while retaining nominal value. Under the Empire, particularly from Augustus onward, it persisted as a minor bronze coin until the third century CE, when inflation and metal shortages led to further reductions and eventual supersession by other denominations like the sestertius and later the follis. Numismatic evidence, including hoards from Republican sites, confirms its role in everyday transactions, with designs often featuring deities like Janus or the prow of a ship (prow type) symbolizing naval power and commerce. In broader economic context, the as exemplified early fiduciary money principles, where intrinsic metal value diverged from face value due to state authority, influencing subsequent coinage systems; for instance, Carolingian reforms echoed its subdivisions in pounds, shillings, and pence. Archaeological finds, such as those from the Vesuvius region dated to 79 , reveal over 100 variants, underscoring its ubiquity despite periodic recalls and reminting to combat counterfeiting. Its decline by the late Empire reflected systemic monetary instability, with eroding small denominations' utility in favor of higher-value silver and .

Businesses and organizations

Companies

is a multinational online and beauty retailer headquartered in . Founded on 2 June 2000 by Nicholas Robertson and Quentin Griffiths, the company initially operated under the name "As Seen On Screen," focusing on apparel inspired by outfits featured in films and television shows targeted at young adults. By 2025, serves over 20 million active customers across more than 200 markets, offering products from approximately 850 third-party brands alongside its own-label ranges, with annual revenues exceeding £3 billion as of 2023. The company went public on the London Stock Exchange in October 2001, achieving rapid growth through expansion and acquisitions such as in 2021, though it has faced challenges including disruptions and competition from fast-fashion rivals like . ASOS employs around 3,300 people and is led by CEO José Antonio Ramos Calamonte as of 2024. Its business model emphasizes fast delivery, inclusive sizing, and digital marketing, positioning it as a key player in the global online apparel sector despite periodic profitability pressures from inventory management and economic downturns.

Non-profit and other organizations

No notable non-profit organizations are commonly abbreviated or named "AS" in standard disambiguations or acronym lists.) Various searches for acronyms, NGOs, charities, and non-profits yield no direct matches for "AS" as a primary designation for such entities, with results instead focusing on general definitions of non-profits or unrelated terms. In contexts like legal structures, "A/S" or "AS" typically denotes for-profit limited companies in Nordic countries (e.g., Aktieselskab in Danish), not non-profits, which are often structured as foundations (stiftelser) or associations without the "AS" suffix. Other potential overlaps, such as organizations related to American Samoa (ISO code AS), do not feature prominent non-profits specifically branded as "AS."

Education and research

Academic institutions

In American universities, "AS" frequently abbreviates the , an academic division overseeing disciplines such as , social sciences, natural sciences, , and languages. This usage standardizes internal references for course codes, department listings, and administrative purposes across institutions. For example, at , the operates under the AS designation, encompassing over 20 departments and serving approximately 6,000 undergraduates as of 2023. Similarly, employs AS to refer to its College of Arts, Media and Design alongside broader and sciences programs, integrating interdisciplinary with co-op experiences. Such abbreviations facilitate efficient cataloging in systems but vary by institution, with no standardization beyond local conventions. No standalone academic institutions are primarily known by the abbreviation "AS," distinguishing it from degree designations like Associate of Science (A.S.), which community colleges confer but do not adopt as institutional identifiers.

Research concepts

In probability theory, a random event occurs almost surely—often abbreviated as "a.s."—if it holds with probability 1 relative to the underlying probability measure, meaning the event's complement has measure zero. This concept distinguishes itself from certainty by allowing for negligible exceptions on sets of probability zero, which may be non-empty but unobservable in practice due to the continuous nature of many probability spaces. Researchers employ "almost surely" to describe outcomes in stochastic processes where absolute guarantees are impractical, such as in infinite sample spaces where pathological events occur with vanishing probability. A sequence of random variables X_n converges almost surely to a limit X if the probability that \lim_{n \to \infty} X_n = X equals 1, denoted X_n \to^{a.s.} X. This mode of convergence implies convergence in probability but not vice versa, providing a stronger notion essential for theorems like the strong law of large numbers, where sample averages converge to expected values almost surely under mild conditions. In empirical research involving Monte Carlo simulations or asymptotic analysis, almost sure convergence ensures reliability beyond weaker probabilistic guarantees, as deviations occur only on null sets that standard sampling avoids. The terminology underpins and modeling in fields like and , where "" qualifies statements about or amid infinite-dimensional spaces. For instance, in martingale theory, validates long-run predictions without requiring uniform bounds, highlighting its role in rigorous proof construction over approximations. Misapplication can lead to overconfidence in finite-sample results, as sets remain theoretically possible despite empirical absence.

Other uses

Historical and miscellaneous

The as (plural asses) was unit of weight and currency in , originating as a bronze ingot (aes rude) in the before evolving into cast and struck coins. Nominally weighing one pound (libra), equivalent to approximately 327 grams and subdivided into 12 unciae, the as functioned as a standard measure for trade and coinage until the late , when its weight was progressively reduced due to economic pressures. Early examples, known as aes signatum, featured unmarked bronze bars stamped with official symbols to guarantee value, transitioning to the republican as around 225 BC with designs like the ship's prow (prora) on the obverse, symbolizing naval power. By the , the coin shifted to and diminished in size, persisting until the AD amid and . In other contexts, as has denoted an in Scandinavian card games, deriving from influences on modern and Danish terminology for playing cards.

Abbreviations and symbols

As denotes the for , a element with in the periodic table. appears in various allotropic forms, including gray, yellow, and black, and is essential in semiconductors but toxic in higher exposures. In international standards, AS represents the code for , an unincorporated U.S. territory in the South Pacific. This code facilitates geographic and postal designations, such as in domain names (.as) and registrations. In , a.s. abbreviates "almost surely," indicating an event occurs with probability 1 under a given measure, distinct from "almost everywhere" in integration contexts. Other specialized uses include AS for "autonomous system" in routing protocols, identifying networks under single administrative control via BGP. In medicine, AS can signify , a valvular heart condition narrowing blood flow. These applications vary by field, with capitalization and context determining precise meaning.