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Total

Total may refer to:

Mathematics

Total order

A total order, also known as a linear order, is a binary relation ≤ on a set S that satisfies four axioms: reflexivity (for all a in S, a ≤ a), antisymmetry (for all a, b in S, if a ≤ b and b ≤ a then a = b), transitivity (for all a, b, c in S, if a ≤ b and b ≤ c then a ≤ c), and totality (for all a, b in S, either a ≤ b or b ≤ a).^[1] This structure ensures that every pair of elements in S is comparable, extending the concept of a partial order by requiring full comparability.^[2] The totality axiom distinguishes total orders from partial orders, where some elements may be incomparable.^[3] Key properties of a total order include the ability to arrange all elements of S into a sequence where each precedes or succeeds every other, often visualized as a chain or line. Reflexivity ensures self-comparison, while antisymmetry and transitivity prevent cycles and ensure consistency in ordering. For distinct elements a and b, exactly one of a < b (strict order, defined as a ≤ b and a ≠ b) or b < a holds, reinforcing the linear nature of the relation.^[1] Classic examples include the set of integers ℤ or real numbers ℝ equipped with the standard ≤ relation, where every pair of numbers can be compared directly.^[1] Another example is the lexicographical order on strings, such as dictionary ordering, which totals the elements based on sequential character comparisons.^[2] Total orders find applications in sorting algorithms, where comparators must enforce a total ordering to arrange elements without ambiguity, as seen in implementations like those in standard libraries that require reflexive, antisymmetric, and transitive comparisons.^[4] In decision theory, total orders model complete preference relations, ensuring agents can rank all alternatives consistently, which underpins expected utility calculations and avoids intransitivities in choice axioms.^[5] In topology, total orders generate the order topology on a set, where basis elements are open intervals (a, b) = {x | a < x < b}, along with rays (-∞, b) and (a, ∞), providing a natural uniformity on linearly ordered spaces like the real line. The concept of total order emerged in the late 19th century within order theory, primarily through investigations by mathematicians such as Richard Dedekind and Ernst Schröder, who explored linear orders as foundational to set structures and arithmetic continuity.^[6]

Total function

In mathematics, a total function from a set A to a set B is a mapping f: A \to B such that for every element x \in A, there exists exactly one element f(x) \in B, meaning it is defined everywhere on its specified domain without any undefined points.^[7] This contrasts with a partial function, where the effective domain may be a proper subset of the intended domain, allowing some inputs to remain undefined.^[8] The notation f: A \to B conventionally denotes a total function unless otherwise specified, emphasizing that the domain A is fully covered.^[7] Examples of total functions include the identity function on the natural numbers, defined by \mathrm{id}_\mathbb{N}(n) = n for all n \in \mathbb{N}, which maps each natural number to itself.^[9] Another is a constant function c_b: A \to B where c_b(x) = b for some fixed b \in B and all x \in A, ensuring a uniform output regardless of input.^[10] These illustrate how total functions provide complete coverage, unlike partial analogues such as division on integers, which is undefined at zero. In computability theory, total recursive functions play a central role as the subclass of partial recursive functions that are defined for all inputs in their domain, corresponding to algorithms that always terminate and produce an output.^[11] They encompass all primitive recursive functions—built from basic operations like zero, successor, and projection via composition and primitive recursion—and extend to more complex cases via minimization, as formalized by Kleene in 1936.^[11] Seminal examples include addition and multiplication on natural numbers, which are total recursive, while the Ackermann-Péter function demonstrates a total recursive function that grows faster than any primitive recursive one, highlighting the hierarchy within computability.^[11] This class is crucial for Church's thesis, equating total recursive functions with effectively computable ones that halt universally.^[11] A key property is that any total function with a finite domain is computable, as one can enumerate the domain and hardcode the mappings in a finite algorithm, ensuring termination on all inputs.^[12] In category theory, total functions align with the notion of morphisms, which are total by definition, and natural transformations serve as "total" assignments of such morphisms to each object in a category, preserving structure across functors.

Totality in mathematical logic

In mathematical logic, totality refers to the property of a predicate or axiom that holds universally across all possible structures or models, ensuring that the defined concepts are complete and applicable without exceptions. This is particularly evident in total inductive definitions, where a set is constructed as the least fixed point of a monotone operator, guaranteeing that the associated predicate is satisfied for every element in the structure while being the smallest such set closed under the defining rules.^[13] A key concept is the role of totality axioms in set theory and proof theory. In set theory, the axiom schema of replacement serves as a totality principle by asserting that if a definable class function maps elements of a set to unique outputs, then the image of that set under the function is itself a set, thereby ensuring comprehensive existence for all sets in the universe without gaps in the hierarchy.^[14] In proof theory, totality axioms, such as the totality axiom in applicative theories (Tot: ∀x ∀y (xy ↓), meaning every application of terms is defined), provide a foundation for total computation and enable the derivation of strong induction principles, making these theories proof-theoretically equivalent to systems like Peano arithmetic.^[15] Examples illustrate totality's application in formal systems. In Peano arithmetic, the recursive axioms for addition—x + 0 = x and x + S(y) = S(x + y)—and for multiplication—x · 0 = 0 and x · S(y) = (x · y) + x—define these operations as total functions on natural numbers, with the induction schema proving their universality across all arguments.^[16] However, in higher-order logic, totality statements face undecidability issues; for instance, asserting the totality of rapidly growing functions like the Ackermann function leads to undecidable propositions, as the logic's expressiveness allows encoding of the halting problem, rendering such universal claims non-provable within the system.^[17] The historical development of totality in mathematical logic ties closely to Hilbert's program in the early 20th century, which aimed to establish the consistency of mathematics through finitary methods while avoiding impredicative totalities over infinite domains. Gödel's incompleteness theorems of 1931 demonstrated that no sufficiently strong consistent formal system can prove its own consistency or the totality of its primitive recursive functions exhaustively, undermining the program's goal of absolute foundational security and shifting focus toward ordinal analysis in proof theory.^[18] Totality in logic thus relates briefly to the computability notion of total functions, emphasizing defined behavior for all inputs without delving into domain specifics.

Business and Economics

Energy and Oil Companies

TotalEnergies SE is a French multinational integrated energy company headquartered in Courbevoie, near Paris. It was founded on March 28, 1924, as the Compagnie française des pétroles (CFP), established by the French government to secure the country's energy independence through domestic and international oil exploration and production.^[19] The company began operations with its first oil production in Iraq in 1927, marking its early entry into global upstream activities.^[19] The company's modern structure emerged from significant mergers in the late 1990s and early 2000s. In 1999, CFP—then operating as Total—merged with the Belgian oil company Petrofina (Fina) to form TotalFina, creating a stronger presence in refining and marketing.^[19] This was followed in 2000 by the acquisition of the French oil firm Elf Aquitaine, resulting in the entity TotalFinaElf, which was later simplified to Total S.A. in 2003; these consolidations positioned Total as one of the world's largest integrated oil and gas majors, with expanded operations in exploration, production, refining, and chemicals.^[19] A notable upstream milestone was in 2017, when Total signed an agreement to acquire an additional 21.57% stake in Uganda's Lake Albert oil project from Tullow Oil, enhancing its interests in East Africa's emerging hydrocarbon resources amid ongoing discoveries in the region.^[20] In 2021, the company rebranded to TotalEnergies SE to emphasize its strategic pivot toward a broader multi-energy portfolio, including a commitment to achieve carbon neutrality in its operations by 2050 in line with the 2015 Paris Agreement.^[19] This shift has involved scaling up investments in low-carbon solutions, such as solar, wind, and hydrogen projects, while maintaining core oil and gas activities; for instance, TotalEnergies plans to grow overall energy production (oil, gas, and electricity) by approximately 4% annually through 2030, alongside emissions reductions.^[21] In 2025, it continued this transition through acquisitions like the VSB Group for European wind and solar development and a pipeline of UK solar and battery projects totaling 350 MW capacity.^[22] Globally, TotalEnergies produces around 2.5 million barrels of oil equivalent per day (as of the first three quarters of 2025), primarily from upstream operations in Africa, the Middle East, and Europe, with a growing share from liquefied natural gas (LNG) and renewables.^[23] As of November 2025, TotalEnergies has a market capitalization of approximately $149 billion, reflecting its diversified portfolio and disciplined approach to energy markets.^[24] Key subsidiaries include TotalEnergies Exploration & Production (focused on upstream oil and gas), TotalEnergies Marketing & Services (handling downstream distribution and services), and TotalEnergies Renewables & Power (driving low-carbon electricity generation).^[25] The company operates in about 120 countries, balancing traditional fossil fuel production with initiatives like hydrogen development and renewable power purchase agreements, such as a 15-year deal in 2025 to supply Google's data centers.^[26]

Retail and Telecommunications Businesses

Total Access Communication Public Company Limited, operating as DTAC, is a leading Thai telecommunications provider founded on August 31, 1989, by the Bencharongkul family to deliver wireless services in the 800 MHz and 1800 MHz spectrum bands. The company has grown to offer comprehensive services, including mobile voice and data networks, broadband internet, digital content, and enterprise solutions, serving urban and rural customers throughout Thailand with a focus on affordable connectivity and network reliability. In 2023, DTAC merged with True Corporation Public Company Limited in a $8.6 billion deal supported by major stakeholders Charoen Pokphand Group and Telenor, forming Thailand's largest telecom operator and enabling enhanced 5G rollout and service integration. As of the first quarter of 2025, the combined entity maintains a subscriber base of 48.8 million, underscoring its dominant market position with over 30 million mobile users contributing to revenue growth amid rising data demand. In the business context of retail and telecommunications, the concept of total revenue serves as a fundamental metric for evaluating financial performance, defined as the aggregate income from all sales activities and calculated using the formula:

\text{Total Revenue} = \text{Price} \times \text{Quantity}

This equation captures the core relationship between pricing strategies and sales volume, allowing companies like telecom providers to optimize tariffs for services such as broadband subscriptions while retailers assess bulk purchasing impacts on overall earnings. For instance, in telecommunications, total revenue growth post-merger for entities like True-DTAC has been driven by increased quantity of high-value 5G subscribers, despite competitive pricing pressures. Retail and telecommunications businesses bearing the "Total" name, such as DTAC, operate within highly competitive landscapes intensified by digital transformations since 2020, including accelerated e-commerce adoption in retail and the shift to 5G and cloud services in telecom. These sectors have grappled with supply chain disruptions, heightened cybersecurity threats, and the need for substantial investments in digital infrastructure to retain customers amid economic uncertainty and regulatory changes on data privacy. In Thailand's telecom market, for example, post-merger integration challenges have included spectrum allocation disputes and efforts to reduce churn through personalized digital experiences, while global retail trends highlight the ongoing pivot to omnichannel models to counter online giants. Unlike energy conglomerates that diversify across sectors, these consumer-facing operations prioritize agile adaptation to technological shifts for sustained growth.

Arts and Entertainment

Music Groups and Artists

Total is an American R&B girl group formed in 1994 in Plainfield, New Jersey, consisting of founding members Kima Raynor, Keisha Spivey, and Pamela Long.^[27] The trio signed to Bad Boy Records in 1994, becoming one of the label's earliest acts alongside The Notorious B.I.G. and Craig Mack, and debuted with background vocals on tracks like "Juicy" before releasing their self-titled debut album in 1996.^[28] Their sound blended contemporary R&B with hip-hop influences, earning them recognition as pioneers in the "new jack swing" evolution during the mid-1990s.^[27] The group's breakthrough came with the hit single "Can't You See," featuring The Notorious B.I.G., from their debut album Total, which peaked at number 13 on the Billboard Hot 100 and became a staple in hip-hop/R&B crossovers.^[29] Other notable singles from the album included "No One Else" (featuring Da Brat) and "Kissin' You," contributing to the record's platinum certification by the RIAA.^[30] Their second album, Kima, Keisha, and Pam (1998), featured tracks like "What About Us?" and "Trippin'," but received mixed reviews and lower commercial success amid shifting trends in R&B.^[29] Despite this, Total maintained a presence through collaborations and soundtrack contributions, solidifying their role in Bad Boy's golden era.^[31] The group went on hiatus in the early 2000s, with members pursuing solo endeavors—Pamela Long transitioning to gospel music—effectively disbanding by 2001, though they reunited for performances in 2014–2016 and from 2024 onward, including the Bad Boy Family Reunion Tour and ongoing 2025 tours such as the Room 112 Tour.^[32]^[31]^[33] Total's cultural impact lies in bridging R&B harmonies with hip-hop production, influencing subsequent girl groups and the fusion sound that dominated late-1990s urban music, without overlap into solo artist territories.^[34]

Songs, Albums, and Other Media

In music, several notable songs bear the title "Total" or closely related variants, often exploring themes of completeness, destruction, or emotional intensity. One prominent example is "Total Eclipse of the Heart," a power ballad written by Jim Steinman and performed by Bonnie Tyler, released in 1983 as the lead single from her album Faster Than the Night. The song's lyrics depict a tumultuous relationship marked by longing and despair, with iconic lines like "Turn around, every now and then I get a little bit lonely and you're never coming 'round," emphasizing isolation and unrequited love. It achieved massive commercial success, topping the Billboard Hot 100 for four weeks and selling over 6 million copies worldwide, certified gold by the RIAA.^[35]^[36] Other songs titled "Total" include tracks by various artists across genres. For instance, the R&B group Total released a self-titled debut album in 1996 on Bad Boy Records, featuring singles like "Can't You See" (with The Notorious B.I.G.), which peaked at No. 13 on the Billboard Hot 100 and blended hip-hop soul with smooth harmonies. The album itself, Total, reached No. 23 on the Billboard 200, showcasing the group's vocal interplay on tracks exploring romance and resilience. Beyond music, "Total" appears in influential other media, particularly in science fiction and gaming. The 1990 film Total Recall, directed by Paul Verhoeven and starring Arnold Schwarzenegger, adapts Philip K. Dick's short story "We Can Remember It for You Wholesale," delving into themes of identity, false memories, and corporate dystopia on a colonized Mars. The narrative questions reality through the protagonist's implanted vacation memories that unravel into a rebellion plot, grossing over $261 million worldwide and earning acclaim for its action and philosophical depth. A 2012 remake directed by Len Wiseman, featuring Colin Farrell and Kate Beckinsale, updates the visuals with advanced CGI while retaining core sci-fi motifs of mind manipulation and political intrigue, though it received mixed reviews for lacking the original's satirical edge, earning $198 million at the box office. In gaming, the Total War series, developed by Creative Assembly and published by Sega since 2000, revolutionized strategy titles by merging turn-based grand strategy—managing empires, economies, and diplomacy—with real-time tactical battles involving thousands of units. The inaugural entry, Shogun: Total War, set in feudal Japan, emphasized historical accuracy in warfare mechanics like unit formations and terrain effects, selling over a million copies and establishing the franchise's blend of depth and spectacle, with subsequent titles expanding to eras like Rome and the Napoleonic wars.^[37]

Sports

Tactical Concepts in Team Sports

In team sports, particularly football (soccer) and rugby union, "total" tactics represent innovative philosophies that prioritize fluidity, versatility, and collective involvement over rigid positional structures. These approaches emerged in the mid-20th century as responses to evolving game dynamics, emphasizing proactive pressing, seamless positional interchanges, and universal skill sets among players to maintain control and exploit spaces dynamically. Originating in Europe, they transformed how teams organize on the field, influencing strategies that blend attack and defense into a unified system.^[38] Total Football, a hallmark of Dutch soccer in the 1970s, was pioneered by coach Rinus Michels at Ajax Amsterdam starting in 1965, with Johan Cruyff as its emblematic player and later advocate. The system's core principles include positional interchange, where players fluidly swap roles to disrupt opponents and create numerical advantages; high-intensity pressing to regain possession quickly in advanced areas; and the demand for technical proficiency, fitness, and tactical awareness from all outfield players, enabling the team to adapt the pitch's "size" by expanding it in attack and compressing it in defense. Under Michels, Ajax implemented this to secure four Eredivisie titles (1966, 1967, 1968, 1970) and the 1971 European Cup, showcasing triangular passing patterns and proactive movement. The Netherlands national team, coached by Michels and led by Cruyff, epitomized Total Football at the 1974 FIFA World Cup, reaching the final with victories over Argentina (4-0) and Brazil (2-0) through relentless pressing and fluid attacks, though they fell 2-1 to West Germany in the title match. Cruyff's vision further propagated the tactic at Barcelona, where he later coached, embedding it as a foundational influence on possession-based play.^[38] In rugby union, Scottish coach Jim Telfer developed a forward-dominated strategy in the 1980s, drawing inspiration from New Zealand's dynamic style to promote continuous phase play and eliminate fixed positions. Telfer's philosophy centered on ferocious rucking and mauling to maintain momentum, with back-row forwards deeply involved in both attack and defense to drive forward phases without pauses, requiring high work rates, tackling efficiency, and ball-carrying versatility from the entire pack. As forwards coach for Scotland, Telfer applied these tenets to orchestrate the nation's first Grand Slam in 59 years during the 1984 Five Nations, emphasizing relentless forward dominance and quick ball recycling to wear down opponents. His approach influenced the British and Irish Lions tours, including the 1997 series win in South Africa, and resonated with the All Blacks' implementations in the late 1980s and 1990s, where similar fluid back-row integration and phase continuity powered their dominance, as seen in extended possession sequences during the 1987 Rugby World Cup victory. Telfer's no-nonsense training regimens, such as intensive scrum drills, underscored the tactic's reliance on disciplined, all-court execution.^[39]^[40] The evolution of these total tactics in the modern era, particularly post-2020, has integrated data analytics to refine hybrid models that balance fluidity with precision. In football, clubs like Manchester City under Pep Guardiola—himself a Cruyff disciple—use metrics such as expected goals (xG) and pressing intensity (PPDA) to optimize positional rotations and high-pressing triggers, adapting Total Football's principles to counter data-informed defenses through AI-driven simulations of interchange patterns. Rugby teams, including the All Blacks and Scottish squads, employ wearable tech and video analytics to quantify ruck speed, phase efficiency, and back-row contributions, enabling post-2020 adjustments like targeted substitutions based on fatigue models to sustain continuous play amid fixture congestion. These data-enhanced hybrids have improved performance in elite competitions. Such integrations preserve the tactical essence of total philosophies while addressing contemporary demands for sustainability and opponent scouting.^[41]

Motorsport and Racing Events

The Total 24 Hours of Spa is an annual endurance racing event held at the Circuit de Spa-Francorchamps in Stavelot, Belgium, featuring GT3-specification cars in a 24-hour format. First staged in 1924 on public roads surrounding the circuit, it evolved into a dedicated track-based race by the 1950s. After a hiatus following the 1953 edition, it was revived in 1964 as a 24-hour event to test vehicle reliability and driver stamina under varying weather conditions.^[42]^[43] The event divides competitors into classes based on driver experience levels—Pro, Gold, Silver, Bronze, and Pro-Am—allowing professional, semi-professional, and gentleman drivers to compete separately while racing together on track.^[44] TotalEnergies, the energy company formerly known as Total, has served as the title sponsor since 2007, rebranded as the TotalEnergies 24 Hours of Spa ahead of the 2021 edition following its corporate name change. This long-term partnership underscores the company's commitment to motorsport, providing fuels, lubricants, and technical support to enhance performance and sustainability. The 2024 edition drew a record 67-car entry list, surpassing previous GT-era highs and highlighting the event's growing global appeal, with competitors from Europe, Asia, and the Americas. The overall winner was Comtoyou Racing Aston Martin Vantage AMR GT3 Evo, driven by Italian Mattia Drudi, Danish Nicki Thiim, and Danish Marco Sørensen. By 2025, the field expanded further to 75 cars, incorporating diverse manufacturers like Ferrari, Lamborghini, Porsche, and Mercedes-AMG. The 2025 overall winner was Grasser Racing Team Lamborghini Huracán GT3 Evo2, driven by Italian Mirko Bortolotti, German Luca Engstler, and South African Jordan Pepper.^[45]^[46]^[47] Safety has been a priority, particularly after multiple incidents during the 2020 edition, which was postponed due to the COVID-19 pandemic and run in October under shortened daylight conditions, leading to crashes exacerbated by poor visibility and track limits enforcement. Post-2020 enhancements include stricter track limits monitoring via GPS technology, mandatory technical pit stops for brake inspections after 11 hours, and improved lighting along key sections like Eau Rouge and Blanchimont to mitigate risks during night racing. These measures, combined with the FIA's introduction of the halo device in GT3 cars by 2021, have reduced incident severity and improved response times.^[48]^[49]^[50] The event features international driver lineups, with teams typically fielding three or four drivers from multiple nationalities to share stints and comply with rest regulations. For instance, the 2024 winning Comtoyou Racing Aston Martin included drivers from Italy, Denmark, and Denmark, exemplifying the multicultural composition that draws talent from Formula 1, IMSA, and regional series worldwide.^[51]^[52] Beyond Spa, TotalEnergies maintains historical ties to the 24 Hours of Le Mans through its Total Quartz lubricant brand and fuel supply agreements. Since 2018, the company has been the official fuel provider to the Automobile Club de l'Ouest (ACO), supplying Excelium racing fuels and Quartz lubricants to all entrants, a partnership rooted in decades of collaboration dating back to the 1990s with teams like Peugeot and Nissan.^[53]^[54]^[55] By 2022, TotalEnergies introduced 100% renewable fuels derived from waste and biomass for the entire Le Mans field, aligning with decarbonization goals. The event's evolution includes the Hypercar class, featuring hybrid powertrains since 2021, with TotalEnergies supporting hydrogen-electric prototypes; in 2025, hydrogen-powered prototypes and demonstrators, including fuel cell vehicles supplied by the company's mobile hydrogen stations, participated in support events.^[56]^[57]

Science and Technology

Optics and Physics Concepts

Total internal reflection (TIR) is an optical phenomenon in which light propagating within a medium of higher refractive index encounters the boundary with a medium of lower refractive index at an angle of incidence greater than the critical angle, resulting in complete reflection back into the original medium without any transmission across the interface.^[58] This occurs because the refracted ray would otherwise exceed 90 degrees, which is physically impossible, leading to an evanescent wave confined near the boundary.^[59] The critical angle \theta_c is determined by the formula

\theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right),

where n_1 > n_2 are the refractive indices of the denser and rarer media, respectively; this relation derives directly from Snell's law, n_1 \sin \theta_1 = n_2 \sin \theta_2, by setting the angle of refraction \theta_2 = 90^\circ.^[58] Snell's law itself was discovered in 1621 by Dutch mathematician Willebrord Snell through experimental measurements of light refraction, though it remained unpublished until later referenced by Christiaan Huygens in 1703.^[60] TIR underpins key applications in optics, particularly in telecommunications and medicine. In fiber optics, light signals are confined within thin glass or plastic cores by repeated TIR at the core-cladding interface, enabling low-loss transmission of data over kilometers for internet, telephony, and cable television with high bandwidth and minimal crosstalk.^[61] Similarly, in endoscopy, coherent bundles of optical fibers exploit TIR to deliver illumination deep into the body via natural orifices or small incisions, while capturing reflected images for real-time diagnostics, such as assessing gastrointestinal conditions or performing minimally invasive surgeries like arthroscopy.^[61] Total harmonic distortion (THD) quantifies the distortion in electrical waveforms, such as voltage or current signals, arising from the presence of harmonic components that are integer multiples of the fundamental frequency, deviating the signal from its ideal sinusoidal shape.^[62] THD is expressed as a percentage using the formula

\text{THD} = \sqrt{ \frac{ \sum_{h=2}^{\infty} P_h }{ P_1 } } \times 100\%,

where P_h represents the power of the h-th harmonic and P_1 is the power of the fundamental component; since power is proportional to the square of the voltage amplitude, this is equivalently \sqrt{ \sum_{h=2}^{\infty} (V_h / V_1)^2 } \times 100\%.^[62]^[63] In audio engineering, low THD values (typically below 1%) ensure high-fidelity reproduction by minimizing audible artifacts in amplifiers and speakers.^[62] In power systems, THD assesses waveform quality, where excessive distortion from nonlinear loads like variable frequency drives can lead to inefficiencies, overheating, and reduced equipment lifespan, often limited to 5% for voltage in standards like IEEE 519.^[62] The metric's standardization emerged in the 20th century with the proliferation of electronic amplifiers, evolving from early measurements in the 1930s to routine use in high-quality systems by the 1980s.^[64]

Computing and Engineering Tools

Total Commander is an Orthodox file manager software for Microsoft Windows, developed by Swiss programmer Christian Ghisler and first released on September 25, 1993, under the original name Windows Commander.^[65] The program features a dual-pane interface that displays two file directories side by side, enabling efficient file operations such as copying, moving, and deleting across panels without switching views.^[66] It supports extensive customization through plugins, including extensions for FTP client functionality, archive handling (e.g., ZIP, RAR), and integration with cloud storage services. Originally written in Delphi, the software transitioned to a 32-bit version in December 1996 with release 3.0, and it was renamed Total Commander in October 2002 (version 5.50) following a trademark dispute with Microsoft over the use of "Windows" in the title.^[67] Distributed as shareware, Total Commander offers a 30-day trial period for full functionality, after which users must purchase a license for continued commercial or extended use, though non-commercial personal use remains permissible without payment.^[68] As of August 2025, the latest version is 11.56, incorporating enhancements like Unicode support (introduced in 2009), tabbed browsing, and multi-rename tools with regular expressions.^[69] A total station is a surveying instrument that integrates a theodolite for angle measurement, an electronic distance meter (EDM) for precise distance calculation, and an onboard data collector for recording measurements, allowing surveyors to compute three-dimensional coordinates in real time.^[70] The device was pioneered in the 1970s by Hewlett-Packard, with the HP 3810A model—based on the 1970 HP 3800A EDM—representing one of the earliest commercial integrations of these components for field use.^[71] Modern total stations, such as those from Trimble and Leica, incorporate robotic controls for automated tracking and GNSS (Global Navigation Satellite System) integration, enabling hybrid positioning that combines optical measurements with satellite data for enhanced efficiency in obstructed environments.^[72] Typical accuracy specifications include angular precision of 1 arcsecond and distance measurement errors of 1 mm + 1 part per million (ppm), achieved via infrared laser pulses reflected off prisms, making them suitable for high-precision tasks.^[72] In applications, total stations are widely employed in geographic information system (GIS) mapping to generate accurate topographic data layers and in construction staking to mark precise locations for infrastructure elements like roads and buildings, reducing errors in layout and alignment.^[73] These tools rely on optical principles for targeting, similar to those in basic theodolites, but prioritize integrated data processing over standalone lens configurations.^[70]

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Replacement Axiom Scheme Suppose that X is a set, and ψ(y, x, w1,...,wn) is a formula of the language of set theory having the property that for all x ∈ X and ...
[26]
[PDF] Totality in applicative theories - Gerhard J ager Thomas Strahm - INF
The basis of the theory TON are the axioms of a total combinatory algebra, which are well-known to be of an enormous expressive power. p is a pairing ...
[27]
[PDF] 1. Peano's Axioms and Natural Numbers
Now proofs of all the familiar properties of addition and multiplication of integers can be carried out, by using the definitions and corresponding properties.<|separator|>
[28]
Second-order and Higher-order Logic
Aug 1, 2019 · This shows that second-order logic is not completely axiomatizable by effective means, or decidable even in the empty vocabulary. That is, ...
[29]
Hilbert's Program - Stanford Encyclopedia of Philosophy
Jul 31, 2003 · Gödel's incompleteness theorems showed that Hilbert's optimism was undue. In September 1930, Kurt Gödel announced his first incompleteness ...Missing: totality | Show results with:totality
[30]
Our History
### Summary of TotalEnergies' History
[31]
Uganda: Termination of the Agreement with Tullow
Aug 29, 2019 · Paris, August 29, 2019 – On January 9, 2017, Total and Tullow entered into a Sale and Purchase Agreement (SPA) whereby Total would acquire ...Missing: discovery | Show results with:discovery
[32]
[PDF] Strategy & Outlook 2025 - TotalEnergies
Sep 29, 2025 · The Company plans to increase energy production (oil, gas and electricity) by ~4% per year through 2030 while reducing emissions from its ...<|separator|>
[33]
Integrated Power: TotalEnergies Closes Three International ...
Apr 2, 2025 · TotalEnergies confirms the closing of its acquisitions of VSB Group, a European wind and solar developer with extensive operations in Germany, and SN Power.
[34]
TotalEnergies SE Market Cap 2011-2025 | TTE - Macrotrends
TotalEnergies SE market cap as of November 09, 2025 is $149.28B. TotalEnergies SE market cap history and chart from 2011 to 2025.
[35]
All subsidiary companies of the TotalEnergies SE group (Xetra)
TotalEnergies Renewables UK Ltd. E.F. Oil & Gas Ltd. ... Total E&P Qatar Ltd. ELF Petroleum UK Ltd. ... Prax Lindsey Oil Refinery Ltd. ... TotalEnergies Marketing ...
[36]
https://www.billboard.com/pro/bonnie-tyler-total-eclipse-of-the-heart-sales-up-500-percent/
[37]
Total Songs, Albums, Reviews, Bio & More | All... - AllMusic
Active. 1990s - 2020s ; Formed. 1994 in Plainfield, NJ ; Genre. R&B ; Styles. Contemporary R&B ; Group Members. JaKima Raynor, Keisha Spivey, Pam Long.
[38]
‎Total - Apple Music
Total were one of the first acts signed to Diddy's Bad Boy Records in 1993 alongside The Notorious B.I.G. and Craig Mack. • In 1994, Total made their first ...
[39]
https://www.rugbyworld.com/rugby-positions/no-8s/jim-telfer-67120
[40]
Total - Album by Total - Apple Music
15 Songs, 52 minutes ℗ 1996 Bad Boy Records. Marketed by Rhino Entertainment Company, a Warner Music Group Company.<|control11|><|separator|>
[41]
Total Opens Up About Their Hiatus | [site:name] | Essence
Oct 26, 2020 · Total Gets Real About Their Hiatus From The Spotlight, The Bad Boy Reunion Tour & What's Next. One of R&B's favorite girl groups gives ...
[42]
Total - MusicBrainz
Oct 13, 2024 · American R&B group, Type: Group, Founded: 1994 in Newark, Dissolved: 2000, Area: United States.
[43]
The Top 10 Best Songs by R&B Group Total - YouKnowIGotSoul.com
Jul 16, 2020 · We now take a look at the discography of Bad Boy Records R&B group Total. It might be hard to imagine that the group has enough content to ...
[44]
Bonnie Tyler Hit No. 1 in 1983, and a Risque Video Helped - Billboard
Oct 1, 2015 · BONNIE TYLER'S WAGNERIAN POWER ballad “Total Eclipse of the Heart” hit No. 1 on the Billboard Hot 100 on Oct. 1, 1983, giving the ...
[45]
'Total Eclipse of the Heart' Sales Rise More Than 500% - Billboard
Aug 21, 2017 · “Eclipse” became Tyler's only No. 1 hit on the Billboard Hot 100 chart, spending four weeks atop the tally in 1983. The single's success was ...
[46]
Shogun: Total War - IGN
Rating 8.5/10 · Review by IGN StaffJun 22, 2000 · Shogun: Total War really is the best of both worlds. It combines a real-time tactical combat system with a turn-based strategic game.
[47]
Rinus Michels and the Total Football rebellion
Jan 28, 2016 · As manager at Ajax, Michels used Total Football to capture four Eredivisie titles (1966, 1967, 1968, 1970), three KNVB Cups (1967, 1970, 1971), ...
[48]
Rugby's Greatest: Jim Telfer of Scotland and the Lions
Mar 17, 2020 · Jim Telfer is a legend of Scottish rugby on two fronts. As a belligerent back-row, his courage, work-rate and rucking skills made him an automatic choice for ...
[49]
Stephen Jones: My 200 most influential figures - The Times
Dec 3, 2010 · 82: Jim Telfer Is ... But The Needle, as he was known, is best-known as an inspired, and revolutionary coach whose devotion to “total rugby ...Missing: tactic | Show results with:tactic
[50]
The Role of Data Analytics in Modern Football Strategy
Aug 23, 2024 · In this post, we will discuss how data analytics has changed football forever. The Evolution of Data Analytics in Football. Football has come ...Missing: Rugby adaptations 2020
[51]
How Analytics and AI Are Changing the Way UK Rugby Teams Play
Feb 5, 2025 · Advanced machine learning systems are revolutionizing tactical analysis in rugby. Teams now are able to process vast amounts of match footage to ...
[52]
Stephane Ratel outlines exciting future plans during annual Total 24 ...
Jul 26, 2019 · Few events can claim the same depth of history as the Total 24 Hours of Spa. First staged in 1924, it began on the tree-lined country roads ...
[53]
The TotalEnergies 24 Hours of Spa in 24 facts
Jul 31, 2021 · This year's TotalEnergies 24 Hours of Spa will feature the biggest Silver Cup grid since the class was introduced in 2018. A field of 17 cars will chase class ...
[54]
Everything you need to know about the 2022 TotalEnergies 24 ...
Jul 27, 2022 · One of Spa's unique features is that its class structure is based solely on driver grading. So, while there will be five categories on-track ...Missing: history | Show results with:history
[55]
CrowdStrike Takes Over 24H Spa Title Sponsorship from 2023
The cybersecurity company takes over from energy giant TotalEnergies, which previously held title sponsorship of the event since 2007 when it ...<|separator|>
[56]
Revised 67-Car Entry List For Spa 24 Published - dailysportscar.com
Jun 21, 2024 · Revised 67-Car Entry List For Spa 24 Published | One class change, one withdrawal, one new car and TBA driver slots filled.Missing: record | Show results with:record
[57]
Record-breaking field ready to chase glory at 77th CrowdStrike 24 ...
Jun 19, 2025 · • Record entry list features 10 manufacturers and a wealth of driving talent. ENTRY LIST: CROWDSTRIKE 24 HOURS OF SPA. A 75-car field will ...
[58]
Spa 24 Hours rules tweaked to combat "lottery effect" - Motorsport.com
Jan 14, 2020 · The key revision in rules governing the mandatory technical stop at Spa, which was introduced to allow for a free change of brakes, is that cars ...
[59]
[PDF] CrowdStrike 24 Hours of Spa - Supplementary Regulations
Jun 25, 2024 · During the race, the green and red lights at the exit of the Pit Lane will be used only to stop cars when the. Safety Car is deployed. The ...
[60]
100th Anniversary 24 Hours of Spa Practice and Qualifying Updates
Jun 26, 2024 · ... safety upgrades. Now, the 7km track retains its iconic character, pushing drivers and machines to the limit with its sweeping corners and ...
[61]
TotalEnergies 24 Hours of Spa Entry List 2022 | Belgium | 28
2022 TotalEnergies 24 Hours of Spa ; 19, Emil Frey Racing, Lamborghini Huracan GT3 Evo ; 21, AF Corse, Ferrari 488 GT3 ; 25, Audi Sport Team Sainteloc, Audi R8 LMS ...
[62]
Main Race TotalEnergies 24 Hours of Spa 2022 Results
Main Race TotalEnergies 24 Hours of Spa 2022 Results ; 35, 563, Silver Cup, Karol Basz, Michele Beretta, Benjamin Hites, Yuki Nemoto, VSR ; 36, 28, Silver Cup ...Missing: examples | Show results with:examples
[63]
TotalEnergies to introduce a 100% renewable fuel at the 24 Hours of ...
Aug 20, 2021 · Since 2018, TotalEnergies is the partner and official fuel supplier of the Automobile Club de l'Ouest (A.C.O.), creator and organizer of the 24 ...Missing: Quartz | Show results with:Quartz
[64]
Total Official fuel supplier to endurance for five years | 24h-lemans ...
Nov 27, 2017 · The Automobile Club de l'Ouest and Total have recently signed a partnership agreement, a founding act of long term and sustained collaboration ...Missing: Quartz history
[65]
Nissan Partnership | Total Lubrifiants - TotalEnergies Lubricants
History was made at the 24 Hours of Le Mans 2014, when the Nissan ZEOD RC* completed a full all-electric lap of the legendary 13.6-kilometer circuit during ...
[66]
[PDF] All 24 Hours of Le Mans Race Cars to Use 100% Renewable Fuel ...
As the hydrogen partner to ACO and the “H24 Racing” team, TotalEnergies will also deploy this year a mobile hydrogen filling station at Le Mans to supply the “ ...
[67]
“In 2025, a hydrogen-powered car may well challenge the other ...
Sep 21, 2021 · The future hydrogen-electric prototype class to be introduced at the 2025 24 Hours of Le Mans, paving the way for zero-emission endurance racing.
[68]
https://www.ghisler.com/order.htm
[69]
Total Internal Reflection - RP Photonics
Total internal reflection is the phenomenon that light incident on the boundary between two transparent media is fully reflected under certain conditions.Missing: formula | Show results with:formula
[70]
Willebrord Snell (1580 - Biography - MacTutor History of Mathematics
... Snell. Although he discovered the law of refraction now known as "Snell's law" in 1621, a basis of modern geometric optics, he did not publish it and only ...
[71]
Total Internal Reflection – ISP209: The Mystery of the Physical World
Fiber optics involves the transmission of light down fibers of plastic or glass, applying the principle of total internal reflection. Endoscopes are used to ...
[72]
Understanding, Calculating, and Measuring Total Harmonic ...
Feb 20, 2017 · Total harmonic distortion (THD) is a measurement that tells you how much of the distortion of a voltage or current is due to harmonics in the signal.
[73]
Total Harmonic Distortion and Effects in Electrical Power Systems
The summation of all harmonics in a system is known as total harmonic distortion (THD). ... The formula above shows the calculation for THD on a voltage signal.
[74]
Harmonic Distortion - an overview | ScienceDirect Topics
In the half century between 1935 and 1985, typical percentage total harmonic distortion (%THD) of high quality amplifiers working in the top 30% (0 to 10dB ...
[75]
History of Total Commander - TotalcmdWiki - ghisler.ch
Dec 14, 2009 · The history of Total Commander starts on the 25th of September 1993 when Christian Ghisler released a 16-bit application for Windows 3.1x named Windows ...
[76]
Total Commander - home
Total Commander, Version 11.56, is a Shareware file manager for Windows® 95/98/ME/NT/2000/XP/Vista/7/8/8.1/10/11, and Windows® 3.1. · Two file windows side by ...Download · What's new · Order · USB installerMissing: development | Show results with:development
[77]
Name change - Total Commander
The new name "Total Commander" was chosen together with a trademark attorney. "Total Commander" was also registered as a trademark.Missing: development 1993<|separator|>
[78]
Order - Total Commander
Ordering Total Commander for Windows (the mobile versions are free). Total Commander for Windows is a Shareware (demo version) program.
[79]
What's new - Total Commander
August 19, 2025: Total Commander 11.56 is now available for download. This is mainly a bugfix release to fix a vulnerability in the included unrar.dll library.The newsletter · Download 11.55 beta · Name change · Update instructionsMissing: manager Christian development
[80]
Leica Total Stations
### Summary of Total Stations from Leica Geosystems
[81]
1970s Hewlett-Packard HP 3810A Total Station - Nicolàs de Hilster
It was based on their HP 3800A Distance Meter which was introduced in April 1970. Most likely the concentric lens of the EDM influenced Wild-Heerbrugg in ...
[82]
Trimble Total Stations - Geospatial
Powered by industry-leading technologies, surveyors around the world trust our high-performance total station solutions for maximum productivity.
[83]
Total Station And Its Applications In Surveying - GIS Resources
Total station and its application involve measuring slant distances, horizontal & vertical angles, and elevations in topographic & geodetic works.