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OO

In mathematics, $0^0 denotes zero raised to the power of zero, an expression recognized as an indeterminate form primarily in the context of limits, where the value depends on the specific functions approaching zero and cannot be resolved to a single number without additional information.^[1]^[2] This indeterminacy arises because limits of the form \lim f(x)^{g(x)} as f(x) \to 0 and g(x) \to 0 can yield different results along various paths, such as approaching 1 along x^x as x \to 0^+ but potentially other values otherwise.^[3] Despite this, in discrete mathematics, algebra, and applications like power series and the binomial theorem, $0^0 is conventionally assigned the value 1 to preserve the validity and simplicity of formulas, such as the constant term in Taylor expansions or the empty product in combinatorics.^[4] This convention avoids special cases in theorems where exponents reach zero, ensuring continuity with the rule that any non-zero number to the power zero equals 1 and zero to a positive power equals zero.^[5] The debate over a universal definition persists, with analysts favoring leaving it undefined to reflect limit behavior, while practitioners in other fields prioritize the definitional choice for computational consistency.^[6]

Computing and Technology

Object-oriented programming

Object-oriented programming (OOP) is a programming paradigm organized around objects rather than functions and logic, where objects are instances of classes that bundle data fields and methods together to represent real-world entities or concepts.^[7] This approach emphasizes modeling software as collections of interacting objects, each encapsulating state and behavior, to promote modularity and reusability in code design.^[8] OOP emerged as a response to the limitations of procedural programming in handling complex, data-centric systems, particularly simulations and large-scale applications.^[9] The origins of OOP trace to the development of Simula at the Norwegian Computing Center in Oslo, where Ole-Johan Dahl and Kristen Nygaard created Simula I between 1962 and 1965, initially for discrete event simulation, introducing classes and objects as core constructs.^[9] Simula 67, released in 1967, formalized these ideas into the first language with full object-oriented features, including inheritance precursors via class hierarchies.^[10] Alan Kay, drawing from Simula and sketchpad graphics, conceived Smalltalk in 1966-1967 at the University of Utah and later at Xerox PARC, with initial implementations in the early 1970s; Smalltalk pioneered pure OOP by treating everything as an object and emphasizing message-passing for interaction.^[11] These foundational languages influenced subsequent adoption, with Bjarne Stroustrup's C++ (first released 1985) extending C with OOP capabilities for systems programming, marking widespread commercial viability.^[11] Central to OOP are four principles: encapsulation, which bundles data and methods within objects while restricting direct access to internal state via access modifiers, enhancing data integrity; inheritance, allowing classes to derive properties and behaviors from parent classes to promote code reuse and hierarchical organization; polymorphism, enabling objects of different classes to be treated interchangeably through method overriding or interfaces, supporting flexible code; and abstraction, which hides implementation details behind simplified interfaces to focus on essential features.^[8] ^[12] These principles facilitate modeling complex relationships, as in Simula's simulation objects inheriting simulation behaviors.^[9] Prominent languages supporting OOP include Simula and Smalltalk as pioneers; C++ for performance-critical applications; Java, released by Sun Microsystems in 1995, enforcing pure OOP with automatic memory management; Python, which integrates OOP seamlessly since version 1.0 in 1994; and C#, introduced by Microsoft in 2000 for .NET ecosystems.^[13] ^[14] Others like Ruby (1995) emphasize dynamic OOP for web development.^[14] OOP offers advantages such as improved code reusability through inheritance, reducing development time in large projects by up to 30-50% in empirical studies of modular systems; better maintainability via encapsulation, which localizes changes; and scalability for modeling domains like graphics or enterprise software.^[15] ^[16] However, it incurs disadvantages including increased complexity and overhead for simple tasks, where procedural approaches suffice with lower memory and CPU demands—OOP objects can consume 2-10 times more resources due to indirection and virtual method tables; a steeper learning curve from abstract concepts; and risks of over-engineering, as deep inheritance hierarchies lead to fragile base class problems, prompting alternatives like composition over inheritance in modern practices.^[17] ^[15] These trade-offs arise causally from OOP's emphasis on abstraction layers, which, while beneficial for extensibility, introduce runtime costs and debugging challenges not present in linear procedural code.^[15]

OpenOffice

Apache OpenOffice is a free and open-source office productivity suite consisting of applications for word processing, spreadsheets, presentations, graphics, databases, and mathematical equations.^[18] It originated as the community-driven continuation of OpenOffice.org, which Sun Microsystems open-sourced in October 2000 from its proprietary StarOffice product developed since 1992.^[19] The project was transferred to the Apache Software Foundation in 2011 following Oracle's acquisition of Sun, aiming to foster collaborative development under Apache governance.^[18] The suite supports the OpenDocument Format (ODF) as its native file standard, ensuring interoperability and long-term accessibility, while also providing compatibility with Microsoft Office formats such as .docx, .xlsx, and .pptx through import/export filters.^[19] Key components include Writer for document creation with advanced formatting and PDF export; Calc for data analysis with pivot tables and charting; Impress for slide-based presentations; Draw for vector illustrations and flowcharts; Base for relational database management; and Math for rendering complex formulas.^[18] These tools run on Windows, macOS, Linux, and other platforms, with extensions available for enhanced functionality like grammar checking or barcode generation.^[20] Development of Apache OpenOffice has proceeded incrementally since its incubation at Apache, with version 4.1.0 released as the last major update in April 2014, introducing improvements in user interface consistency and ODF conformance.^[18] Subsequent releases, up to 4.1.15 in December 2023, have focused primarily on bug fixes and minor security patches rather than new features, reflecting a smaller volunteer contributor base compared to contemporaneous projects.^[20] In 2010, prior to the Apache transition, a significant portion of OpenOffice.org developers forked the codebase to create LibreOffice, citing accelerated innovation needs; LibreOffice has since diverged with more frequent releases, enhanced Microsoft compatibility, and additional tools like dedicated charting modules.^[21] As of 2025, Apache OpenOffice remains downloadable and functional for basic productivity tasks but is critiqued for slower evolution and unresolved vulnerabilities in some analyses, prompting recommendations for alternatives in security-sensitive environments.^[22]

Modeling and Transportation

OO gauge

OO gauge is a model railway standard employing a fixed track gauge of 16.5 mm to represent prototype standard-gauge railways, primarily in the United Kingdom, at a scale of 4 mm to 1 foot (equivalent to a ratio of approximately 1:76.2).^[23] This configuration uses the same track width as HO scale models but with larger body proportions to better approximate British rolling stock dimensions, resulting in a slight understatement of the gauge relative to the scale—the prototype's 4 ft 8+1/2 in (1,435 mm) track width scales to about 18.8 mm in true 4 mm proportions.^[24] The notation "OO" (or sometimes "00") derives from its position as half the size of O gauge, historically part of a progression from larger scales like 1 and 2.^[25] The scale originated in the interwar period through experimentation in the UK, with early adoption by manufacturers seeking affordable alternatives to bulkier O gauge models; Hornby Trains commercialized it in 1938, launching products like the 0-6-0 locomotive to capitalize on demand for smaller, more accessible layouts.^[25] Development accelerated post-World War II, from 1945 to 1975, as production resumed and standards solidified under enthusiast groups, though wartime restrictions had limited progress between 1939 and 1945.^[26] Unlike finescale alternatives such as EM gauge (18.2 mm track) or P4 (18.83 mm), which prioritize geometric accuracy, OO's use of commercially available 16.5 mm track facilitated mass production and widespread hobbyist adoption, despite the inherent scale-gauge compromise that can affect realism in wheel flanges and close coupling.^[24] OO gauge remains the dominant scale for British outline modeling in the UK, outselling alternatives like N gauge due to extensive availability of ready-to-run locomotives, wagons, and accessories tailored to era-specific liveries and detailing.^[27] Leading manufacturers include Hornby, which pioneered the scale and continues as the market leader with annual releases, alongside Bachmann (via its Branchline range), Heljan for diesel and electric prototypes, and newer entrants like Accurascale focusing on high-fidelity steam and freight models.^[28]^[29] In 2025, over 120 new OO gauge items were announced, including 72 locomotives (33 steam, 39 diesel/electric) and 56 pieces of rolling stock, reflecting sustained investment amid digital command control (DCC) integration and improved etching techniques.^[30] Its compatibility with HO track enables international sourcing but underscores its niche appeal outside British-themed layouts, where HO's finer 1:87 scale prevails.^[31]

Over and out

"Over and out" is a phrase frequently employed in films, television, and casual speech to denote the conclusion of a radio transmission, yet it contravenes established radiotelephony protocols by conflating mutually exclusive signals.^[32]^[33] In standard procedure, "over" signifies that the speaker has completed their message and awaits a response, whereas "out" indicates the transmission's full termination with no reply expected or desired. The dual usage creates redundancy and confusion, as one cannot logically both invite continuation and declare closure simultaneously. This misuse proliferates in non-professional contexts but is explicitly discouraged in military, aviation, and maritime operations, where procedural words (prowords) ensure clarity amid potential interference or urgency.^[34] For instance, U.S. Marine Corps training materials emphasize that "over" and "out" possess opposing meanings and must never combine, a principle echoed in emergency responder guidelines from the International Telecommunication Union (ITU). Naval history accounts trace the phrase's erroneous adoption to entertainment portrayals rather than authentic ship-to-ship or air-to-ground exchanges, where precise diction prevents misinterpretation in high-stakes environments.^[32] Proper radio discipline, formalized in protocols like those of the U.S. Department of Defense and international aviation standards, prioritizes brevity and unambiguity; transmissions end solely with "over" during dialogue or "out" at conclusion.^[34] Amateur radio operators and auxiliary communications groups reinforce this by mandating exclusive use of one term per exchange to maintain operational efficiency. Despite its inaccuracy, "over and out" persists in civilian mimicry of military lingo, underscoring a broader cultural detachment from technical precision in communications training.^[33]

Biology and Science

Oo- prefix

The oo- prefix is a combining form in biological and medical terminology denoting an egg or structures related to egg production and development. It derives from the Ancient Greek ṓion (ὠόν), meaning "egg," which is cognate with Latin ovum and stems from the Proto-Indo-European root ōwyó-, associated with avian and reproductive eggs.^[35] This element entered modern scientific nomenclature through classical Greek influences on Latin and later European languages, particularly in the 19th century as microscopy advanced reproductive biology studies.^[36] In biology, oo- commonly prefixes terms describing female gametes, ovarian processes, or egg-containing structures, such as oocyte (a precursor to the mature ovum), oogenesis (the formation and maturation of eggs in the ovary), and oophorectomy (surgical removal of an ovary).^[37] For instance, oocyte refers to the primordial cell that develops into an ovum via meiosis, a process first detailed in mammalian reproduction by researchers like Walther Flemming in the 1880s.^[38] The prefix distinguishes egg-related concepts from broader reproductive terms, emphasizing cellular or embryonic origins, as seen in oogonium (an early-stage ovarian germ cell proliferating before meiosis).^[39] Usage extends to botany and mycology for analogous structures, like oospore (a thick-walled zygote in certain algae and fungi formed from egg-like gametes), highlighting conserved reproductive motifs across eukaryotes.^[35] While interchangeable with ov- or ovi- in some contexts (both from similar Indo-European roots for "egg"), oo- prevails in precise histological and cytological terms to evoke the Greek etymon directly, avoiding ambiguity in compound words.^[37] This convention aids clarity in peer-reviewed literature, such as studies on infertility where oocyte quality is quantified by metrics like spindle integrity, with viability rates below 70% in advanced maternal age often linked to aneuploidy.^[40]

Geography

Oo, Indonesia

Oo is a rural village (desa) in Kulawi Selatan District, Sigi Regency, Central Sulawesi Province, Indonesia.^[41] The regency, established in 2008 by partitioning southern areas from Donggala Regency, encompasses diverse terrain including mountainous regions near Lore Lindu National Park.^[42] Situated at coordinates approximately 1°35′01″ S, 120°01′36″ E and an elevation of 493 meters, the village lies in a tropical environment prone to seasonal flooding from nearby rivers like the Mewe.^[42] Local livelihoods center on agriculture, plantations, and small-scale crafts such as rattan weaving, supported by community training programs from the Sigi Regency Cooperative, Small and Medium Enterprises Office.^[43] The area has faced environmental challenges, including floods that have inundated homes, displaced families, and damaged approximately 1 hectare of farmland in affected incidents.^[44] In response to infrastructure needs, the village received central government aid in April 2024 for electrical installations and metering to improve access to electricity.^[45] Residents include migrant workers employed abroad, particularly in Malaysia, with instances of government-facilitated repatriations for deceased individuals highlighting labor migration patterns from the community.^[46] The village maintains basic facilities, such as primary schools, amid its remote setting in Central Sulawesi's interior.^[47]

Oô, France

Oô is a commune in the Haute-Garonne department of the Occitanie region in southwestern France, located in the Pyrénées Luchonnaises at an elevation of approximately 1,000 meters on the left bank of the Neste d'Oô river.^[48] It borders Spain to the south and serves as an access point to high mountain valleys and peaks, including the Pic de Perdiguère at 3,222 meters.^[48] The commune's terrain ranges from 954 to 3,215 meters in elevation, encompassing rugged Pyrenean landscapes with glacial features. The local economy relies on tourism, driven by the Lac d'Oô—a 42-hectare lake at 1,507 meters altitude that ranks as the second-most visited site in the French Pyrenees—and traditional pastoral activities such as sheep herding.^[48] Five lakes in the area, including Lac d'Oô, support hydroelectric power generation, with a barrage constructed at the lake in 1921.^[49] As of 2021, Oô had a population of 103 residents, reflecting a stable, low-density rural community of about 3.17 inhabitants per square kilometer.^[50] Historically, Oô functioned as a waypoint on the Camino de Santiago pilgrimage route (Way of St. James).^[48] Key heritage sites include the Tour du Castet, a 10th-11th century watchtower classified as a historical monument in 1950, and the Romanesque Church of Saint-Jacques from the 12th century, featuring a 17th-century baroque polychrome retable with statues of the Virgin and Child, Saint James, and Saint Roch, as well as the Pierre d'Oô—a mysterious marble bas-relief measuring 111 cm by 40 cm by 26 cm.^[48] The name "Oô" derives from Gascon, meaning "lake," applied to the river and thus evoking "lake of the lake" for the nearby body of water, historically known as Lac de Séculjo.^[51]

Arts, Entertainment, and Culture

O.O (Nmixx song)

"O.O" (stylized in all caps) is the debut single by South Korean girl group NMIXX, released on February 22, 2022, as the title track of their single album Ad Mare by JYP Entertainment.^[52] The seven-member group at debut—comprising Haewon, Lily, Sullyoon, Jinni, BAE, Jiwoo, and Kyujin—introduced a sound blending intense rock verses with explosive EDM choruses, reflecting JYP's experimental approach to K-pop following the success of acts like Twice.^[52] ^[53] The track was penned by a large team of writers including Dr. JO and Chanti, with composition and arrangement handled by producers such as Brian U, ENAN, and MarkAlong, resulting in a genre-mashing structure that shifts abruptly from aggressive sirens and guitar riffs to high-energy drops.^[54] ^[55] This hybrid style aimed to capture a "fierce aura," as described in promotional materials, but drew criticism for its perceived lack of cohesion and overambitious experimentation.^[56] ^[57] The accompanying music video opens with a shipwreck amid fog, symbolizing the album's nautical theme (Ad Mare translates to "To the Sea" in Latin), before transitioning to synchronized choreography showcasing the members' powerful vocals and dance precision.^[58] It garnered over 40 million YouTube views within five days, highlighting strong initial buzz despite polarized fan reactions.^[59] Reception among critics was divided: some lauded its bold energy and vocal delivery as innovative for a rookie group, while others faulted the song's fragmented transitions and absence of a unified vision, with one review calling it "attention-grabbing but messy."^[57] ^[59] Ad Mare achieved commercial success, selling 227,399 copies in its first week on Hanteo Chart—the highest debut-week figure for a K-pop girl group at the time—and earning a silver plaque for exceeding 200,000 units.^[60] The single also charted modestly internationally, peaking at number 19 on Billboard's Hot Trending Songs and entering the Global 200.^[61]

O_O emoticon

The O_O emoticon represents a facial expression of surprise, shock, confusion, or being dumbfounded, depicted by two wide-open eyes (O's) connected by an underscore to suggest an open mouth or intense stare.^[62] It emerged within early internet culture, particularly in chat rooms and Internet Relay Chat (IRC) channels, where ASCII characters were combined to mimic emotions beyond basic punctuation.^[63] Variations include lowercase o_o for a subtler tone and 0_0 substituting zeros for O's, maintaining the same core meaning of bewilderment or astonishment, though often typed interchangeably in casual digital exchanges.^[62] The o_O form, with differing case sizes, conveys skepticism or a raised eyebrow effect, implying one eye squinted in disbelief or curiosity.^[63] Documented usage in online slang repositories dates to at least January 2003, reflecting its adoption in pre-social media texting and forums to punctuate unexpected or absurd statements, such as responding to improbable claims with "O_O That's impossible."^[63] In contemporary texting and platforms like TikTok or Instagram, O_O persists as a quick visual cue for exaggerated reactions, distinct from emoji equivalents like 😲 due to its minimalist, text-native origins.^[62] Its simplicity allows broad accessibility across devices without graphical support, though overuse in ironic contexts can dilute its intensity to mere acknowledgment of oddity.

References

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0^0 is an ``indeterminate form''. When evaluating a limit of the form 0^0, then you need to know that limits of that form are called ``indeterminate forms''.
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Who wrote “O.O” by NMIXX? - Genius
“OO” by NMIXX was written by Dr. JO, ENAN (이난), Chanti, Brian U, 마카롱 (MarkAlong), Charlotte Wilson, EJAE, Awrii (THE HUB), Ayushy (THE HUB), Jan Baars
[55]
O.O - Song by NMIXX - Apple Music
Feb 22, 2022 · Composition & Lyrics. Brian U. Arranger, Vocal Arranger. ENAN. Arranger ... Production & Engineering. Chris Gehringer. Mastering Engineer. DJ ...Missing: writers | Show results with:writers
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NMIXX – O.O Lyrics - Genius
Feb 22, 2022 · After an exhausting wait, “O.O” showcases the fierce aura of NMIXX, as it also serves as the lead track to debut single-album, AD MARE. Staying ...
[57]
Song Review: NMIXX – O.O
Feb 22, 2022 · The reviewer finds "O.O" attention-grabbing but messy, with a cool rock verse, but lacking structure and a clear vision, and a rating of 7.
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NMIXX drop fierce music video for debut single 'O.O' - NME
Feb 22, 2022 · The visual opens at a scene of a shipwreck, as an ominous fog clears to reveal the members of the new girl group. They launch into a fierce ...Missing: facts | Show results with:facts
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Highly-anticipated girl group Nmixx leaves listeners... confused?
Mar 1, 2022 · In the spotlight from its inception, Nmixx's music video for "O.O" garnered over 40 million views in five days on YouTube. However, despite ...
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Nmixx sells over 200,000 copies of debut EP in first week
Mar 17, 2022 · The sales tracker gives out first-time plaques to artists who exceed a certain number of album sales during the first week of their release.<|control11|><|separator|>
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NMIXX's 'Young, Dumb, Stupid' Debuts Atop Hot Trending Songs ...
Mar 21, 2023 · It's NMIXX's second time on the weekly chart, following “O.O,” which peaked at No. 19 in March 2022. NMIXX reigns over Jao and Anitta's ...
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O_O | What Does O_O Mean? - Cyber Definitions
The emoticon O_O means 'Confused' or 'Dumbfounded.' This page explains how O_O is used in texting or on apps like TikTok or Instagram.
[63]
o_O - Urban Dictionary
o_O: Confused, stunned, or weirded out ... An emoticon that means Surprise Buttsecks. As you can see, the >(^_ is the surprise buttsecks-er behind (O_O) ...