Odd
''Odd'' may refer to:- An [[odd number]], an integer not divisible by two
- An [[odd function]], a function that satisfies ''f''(''−x'') = −''f''(''x'')
- [[Odds]], the ratio of the probability of an event happening to it not happening, used in gambling
- An [[odd lot]], in finance, a stock trade of fewer than 100 shares
- [[Odd (given name)|Odd]], a given name, including people with that name
- [[Odd, West Virginia]], an unincorporated community
- [[Odd (crater)]], a crater on Mars
- [[Odd (meteorite)]], a meteorite found in Norway
- [[USS Odd|USS ''Odd'']], a United States Navy patrol vessel
- [[Odd (whaler)|''Odd'' (whaler)]], a 19th-century whaling ship
- [[Odd (software)]], a software framework
- [[Odd (typeface)]], a typeface
- [[Odd (cycling team)]], a Norwegian cycling team
Mathematics
Odd number
An odd number is an integer that cannot be divided evenly by 2, leaving a remainder of 1; formally, it can be expressed as $2k + 1 where k is any integer, yielding the sequence \dots, -3, -1, 1, 3, 5, \dots.[1] This definition distinguishes odd numbers from even numbers, which are multiples of 2, and forms the basis of parity in integer arithmetic.[2] Key properties of odd numbers include the fact that the sum of two odd numbers is even, as (2k + 1) + (2m + 1) = 2(k + m + 1) for integers k and m.[3] Similarly, the product of two odd numbers is odd, since (2k + 1)(2m + 1) = 4km + 2k + 2m + 1 = 2(2km + k + m) + 1.[4] Odd numbers also alternate with even numbers in the natural sequence of integers, as each consecutive integer shifts parity due to addition or subtraction by 1.[5] The concept of odd and even numbers traces back to ancient Greek mathematics, where Euclid defined an odd number in his Elements (Book VII, Definition 7) as one "which is not divisible into two equal parts, or that which differs by a unit from an even number."[6] Earlier Pythagoreans around the 6th century BCE associated odd numbers with the limited and male, contrasting them with the unlimited even, integrating parity into philosophical and numerical explorations.[7] Euclid employed parity in various proofs, including those related to the infinitude of primes in Book IX. In applications, odd numbers in computing correspond to binary representations with a least significant bit of 1, indicating odd parity for error detection or bit manipulation.[8] Everyday uses include urban house numbering systems in many cities, such as in the United States, where odd numbers typically designate one side of a street (e.g., north or east) and even numbers the opposite, facilitating navigation—a practice established in the 19th century.[9] Representative examples include 1, the first positive odd number, and 9, which equals the sum of the first three odd numbers: $1 + 3 + 5 = 9.[10]Odd function
In mathematics, an odd function is defined as a function f for which f(-x) = -f(x) holds for every x in its domain.[11] This condition implies that the graph of an odd function exhibits point symmetry with respect to the origin, meaning that rotating the graph 180 degrees around the origin leaves it unchanged.[11] Equivalently, the defining relation can be expressed as f(-x) + f(x) = 0, which directly follows from the symmetry property.[12] A key property of odd functions arises in integration: if f is integrable, the definite integral over any symmetric interval [-a, a] around zero equals zero, as the areas on either side of the origin cancel due to the antisymmetry.[12] Common examples include the trigonometric functions sine and tangent, which satisfy the odd condition, whereas cosine is even since \cos(-x) = \cos(x).[13] Polynomial examples are functions like f(x) = x^3 and f(x) = x, where odd powers of x preserve the symmetry.[14] Odd functions play a significant role in Fourier analysis, where an odd periodic function decomposes exclusively into a sine series, as the cosine terms vanish due to orthogonality over symmetric intervals.[15] In physics, they model antisymmetric phenomena, such as certain vector fields or displacements that reverse direction under coordinate inversion, aiding in the analysis of systems with inherent odd symmetry.[16]Probability and finance
Odds
In probability theory, odds express the ratio of the probability of an event occurring to the probability of it not occurring. The odds in favor of an event with probability p are given by \frac{p}{1 - p}, while the odds against are \frac{1 - p}{p}.[17] These ratios provide an alternative measure to probability, often used to quantify relative likelihoods in uncertain scenarios. To convert between odds and probability, the formula p = \frac{\text{odds}}{1 + \text{odds}} applies for odds in favor; for example, odds of 3:1 correspond to a probability of p = \frac{3}{4} = 0.75.[17] In betting contexts, fixed odds refer to predetermined payouts that remain constant after the wager is placed, shielding bettors from market fluctuations.[18] Fair odds, by contrast, represent ratios in unbiased games where the expected value is zero, aligning exactly with the true underlying probabilities without any house advantage.[19] The concept of odds originated in 16th-century gambling analysis, notably through Gerolamo Cardano's calculations of ratios for dice games in his unpublished manuscript Liber de Ludo Aleae.[20] It was formalized within probability theory in the 17th century, with Jacob Bernoulli's Ars Conjectandi (published posthumously in 1713) establishing key principles for evaluating such ratios in repeated trials.[21] Odds find applications in Bayesian statistics, where posterior odds update prior beliefs by multiplying prior odds by the likelihood ratio of observed data, enabling iterative refinement of hypotheses.[22] In horse racing, quoted odds imply probabilities of outcomes, derived as the reciprocal of the odds plus one (adjusted for the bookmaker's margin), guiding bettors on perceived chances.[23] For instance, a fair coin flip yields odds of 1:1, corresponding to p = 0.5, while for a standard six-sided die, the odds against rolling a specific face are 5:1, reflecting p = \frac{1}{6}.[17]Odd lot
An odd lot refers to a stock trade involving a number of shares that is not a multiple of the standard trading unit, typically fewer than 100 shares on major exchanges like the New York Stock Exchange (NYSE).[24] This contrasts with a round lot, which consists of 100 shares or multiples thereof, representing the conventional unit for efficient market execution.[25] Odd lots commonly arise from corporate actions such as stock splits, dividend reinvestment plans, or partial share purchases by individual investors.[24] For instance, an investor purchasing 75 shares of a stock executes an odd lot order, whereas acquiring 100 shares qualifies as a round lot.[24] The practice of odd lot trading originated in the 19th century amid the development of early stock exchanges, including the NYSE, where it provided an efficient mechanism for commission brokers to process small orders from retail investors without interfering with the primary auction in round lots.[26] Historically, odd lots were managed separately by specialized odd lot dealers on the NYSE, who executed these trades at a small differential—often a fraction of a point—above or below the prevailing round lot price to account for handling costs.[27] This separation persisted until the U.S. securities markets transitioned to decimal pricing in 2001, mandated by the Securities and Exchange Commission (SEC), which reduced minimum price increments to one cent and diminished the economic distinction between odd and round lots by enabling finer-grained pricing.[28] Following decimalization, odd lot executions became more integrated into standard trading systems, though they remain distinguishable for reporting and liquidity assessment purposes.[29] Odd lot trading carries specific implications for investors, particularly retail participants who dominate these orders due to smaller capital allocations.[24] Per-share transaction costs are generally higher for odd lots, as fixed commissions and fees are spread over fewer shares, and executions can be slower owing to limited priority in order books compared to round lots.[24] Additionally, odd lots often receive less favorable price improvement in off-exchange venues, with studies indicating up to 10% lower improvements relative to round lots in certain high-volume scenarios.[30] In limit orders, the inclusion of an odd lot component can influence the average fill price, as partial executions may occur at varying quotes within the order's parameters.[31] Regulatory frameworks further differentiate odd lots to ensure fair market practices. Under SEC Regulation NMS, odd lot orders are excluded from national best bid and offer (NBBO) computations and certain trade reporting metrics, though brokers are required to evaluate them for best execution obligations.[30] This exclusion can limit visibility and liquidity for odd lots in public quotes. For operational efficiency, many brokers aggregate or round up odd lot orders to the nearest round lot before routing, minimizing handling discrepancies while complying with execution standards.[32] Recent SEC updates, such as those in the 2024 Market Data Infrastructure Rule, aim to enhance transparency by mandating dissemination of odd lot quotes, addressing longstanding disparities in smaller trades.[33]Arts and entertainment
Odd in music
In music, "Odd" has been used as a title for notable albums and as a stage name for artists embracing unconventional styles within their genres. The album Odd is the fourth Korean studio album by the South Korean boy band SHINee, released on May 18, 2015, by SM Entertainment.[34] This 11-track project blends K-pop with experimental electronic and house influences, marking a departure from the group's earlier dance-pop sound toward more avant-garde production. Key tracks include the lead single "View," a deep house-infused uptempo song co-written by band member Jonghyun, as well as "Odd Eye" and "Love Sick," which explore themes of love and perception through layered vocals and synth-driven beats.[35] The full tracklist comprises: "Odd Eye," "Love Sick," "View," "Romance," "Trigger," "Farewell My Love," "An Ode to You," "Alive," "Woof Woof," "So Wonderful," and "Married to the Music." Odd debuted at number one on the Gaon Album Chart in South Korea, selling over 165,000 copies in its first month, and topped the Billboard World Albums chart, demonstrating SHINee's global appeal.[36] It also ranked number one on various domestic sales charts like Hanteo and Synnara during its release week.[37] Another prominent figure is Oddisee, an American hip-hop artist and producer born Amir Mohamed el Khalifa on February 24, 1985, in Washington, D.C.[38] Known for his conscious rap style that fuses jazz, soul, and boom-bap elements, Oddisee gained recognition through mixtapes like Odd Spring (2010), which was praised for its introspective lyrics and self-produced beats. His discography includes full-length albums such as Traveling Man (2010) on Mello Music Group, featuring collaborations with artists like Phonte of Little Brother, and later works like The Beauty in All (2012), which highlight his eclectic production and themes of personal growth.[39] Oddisee's stage name underscores his "odd" or distinctive approach to hip-hop, often incorporating live instrumentation and narrative-driven flows that set him apart in the underground scene. He has collaborated with producers like DJ Jazzy Jeff and rappers such as Homeboy Sandman, contributing to projects that blend hip-hop with broader musical influences. These examples illustrate how "odd" in music titles and artist names often signifies innovation and departure from norms, with SHINee's Odd pushing K-pop boundaries through genre fusion and Oddisee's work carving a niche in conscious hip-hop via experimental beats and storytelling. Both have influenced their respective scenes by prioritizing artistic risk over commercial conformity, fostering appreciation for unconventional expression.[34][40]Odd in film and television
Odd is a 2013 Egyptian short film directed by Karim El-Shenawy that examines social tensions and the concept of otherness through a comedic lens. The 15-minute drama follows a man's challenging journey home amid everyday obstacles, highlighting silenced minority struggles without overt sectarian focus, starring Khaled Nabawy and Khaled Bahgat. It premiered at BAFTA in January 2013 and toured international film festivals.[41][42][43] In 2013, American filmmaker Stephen Sommers directed Odd Thomas, a supernatural comedy-horror feature based on Dean Koontz's novel, starring Anton Yelchin as a short-order cook who sees the dead and uncovers a plot for mass murder through bizarre supernatural encounters. The 92-minute film blends quirky humor with thriller elements and received mixed reception, earning a 37% approval rating on Rotten Tomatoes for its inventive visuals despite pacing issues.[44][45] Norway's 2016 animated short Odd is an Egg, directed by Kristin Ulseth, offers a surreal 11-minute tale of isolation and self-acceptance, centering on a boy named Odd who fears crushing his egg-shaped head until romance with the confident Gunn transforms his life. The experimental piece screened at Cannes' Short Film Corner and won Best Animated Short at the 2017 Tribeca Film Festival.[46][47] The Norwegian broadcaster NRK aired the children's TV series Odd Squad from 2014 onward, a Canadian-American production featuring young agents combating "oddness"—supernatural disruptions—with logic and teamwork, featuring multiple episodes across its seasons, including a fourth season of 12 episodes released in 2024. The educational show, emphasizing diversity through its ensemble of quirky characters, promotes acceptance of differences and problem-solving skills.[48] These works are noted for their quirky storytelling that ties into themes of eccentricity and unusual experiences, while Odd Squad has been particularly praised for fostering inclusivity and educational value in children's programming.[44]Odd in other media
"Odd" serves as the central character in the webcomic The Odd 1s Out, created by James Rallison and launched in 2012 when he was 16 years old.[49] Depicted as an anthropomorphic stick figure, Odd embodies the creator's own quirky and awkward life experiences through humorous, relatable narratives that highlight everyday eccentricities and social mishaps.[50] The webcomic originated on platforms like Tumblr, evolving into a broader digital presence that resonates with audiences by capturing the essence of feeling like an outsider in relatable scenarios.[49] The series expanded into animated content on YouTube, where Rallison's storytime animations featuring Odd have amassed over 20.6 million subscribers as of November 2025.[51] These animations maintain the webcomic's style, using simple line art and voiceover narration to explore themes of awkward humor and personal anecdotes, such as childhood memories and social faux pas, fostering a sense of shared strangeness among viewers.[52] Further media adaptations include the 2018 book The Odd 1s Out: How to Be Cool and Other Things I Definitely Learned from Growing Up, a New York Times bestseller that compiles comic strips and new stories centered on Odd's adventures.[53] This publication, illustrated with the character's signature minimalist design, extends the narrative into print, emphasizing self-deprecating wit and lessons from adolescence. The franchise's influence lies in popularizing awkward, introspective humor within online communities, where Odd symbolizes the relatable oddity of human experiences in digital storytelling.[54]Ships
Odd (whaler)
Odd I was a Norwegian steam-powered whaling catcher ship launched in July 1912 by Porsgrunds Mekaniske Værksted in Porsgrunn, Norway, as yard number 68. Originally named Dominion II, she measured 31.7 meters (104 feet) in length, with a beam of 6.12 meters and depth of 3.56 meters, displacing 156 gross register tons. Powered by a triple-expansion steam engine of 58 nominal horsepower, she was designed for high-speed pursuit and harpoon whaling, typically carrying a crew of around 20 to 30, though expedition voyages could involve larger complements up to 50 including scientists and support staff.[55] Under initial ownership by A/S Dominion Whaling Ltd. of Sandefjord, managed by T. Dannevig & Co., the vessel operated in southern ocean whaling grounds from 1912 onward. Renamed Odd I in 1921 following acquisition by A/S Odd (managed by Chr. Christensen jr. A/S) and later transferred to Bryde & Dahls Hvalfangerselskap A/S in 1925, she continued pelagic operations in Antarctic waters through the 1920s and 1930s. These voyages supported factory ships processing blue and fin whales, with Odd I serving as a catcher in fleets targeting the rich krill-fed populations off South Georgia and the South Shetland Islands. In 1932, ownership shifted to Thorland Ltd. (A/S Thor Dahl) in London, maintaining her role in commercial expeditions until shifting to other uses later in the decade.[55] The ship's significance extended beyond commercial hunting, contributing to Norway's preeminence in the global whaling industry, where Norwegians developed explosive harpoons and steam catchers that revolutionized pelagic operations and accounted for over half of worldwide whale oil production by the 1930s. Odd I participated in the first of Lars Christensen's nine Antarctic expeditions from 1926 to 1927, led by Captain Eyvind Tofte with Antarctic veteran Anton Amundsen aboard; departing Sandefjord in November 1926, she surveyed from South Georgia westward to Peter I Island, discovering Cape Ingrid on Peter I Island and Cecil Cave while gathering oceanographic and biological data. This voyage exemplified Norway's blend of economic and exploratory interests, aiding territorial claims like the 1939 annexation of Queen Maud Land. Amid growing international concerns over overharvesting—evidenced by the 1931 Geneva Convention's failed quotas and declining whale stocks—Odd I's operations tapered by the late 1930s, reflecting the industry's shift toward regulation.[56] Documented extensively in expedition logs, photographs, and reports from Christensen's voyages, Odd I symbolizes the zenith of Norwegian pelagic whaling in the interwar period, when fleets like those from Sandefjord processed tens of thousands of whales annually before post-World War II restrictions curtailed the trade. During World War II, she served as the German auxiliary Orkan with pennant numbers V 5103, V 5104, and V 5102; she was damaged in a British air raid off Lister, Norway, on 7 January 1942, but was repaired. She was lengthened to 40 meters and repowered with a diesel engine in 1947, transitioning to fishing as a purse seiner. Renamed Annstein in 1963, she was deleted from the Norwegian Ship Register on 15 March 1971.[55])Names
Odd (given name)
Odd is a masculine given name of Old Norse origin, derived from the word oddr, meaning "point of a sword" or "edge of a blade."[57] This etymology reflects the martial connotations common in Viking Age nomenclature, where names often evoked strength and weaponry. The name has been in use since the Viking Age (approximately 793–1066 CE) and remains primarily associated with Norway, though it appears sporadically in other Scandinavian countries.[58] In contemporary Norway, Odd ranks as the 11th most common male given name as of 2023, borne by approximately 20,000 individuals, underscoring its enduring place in Norwegian culture.[59] The name's popularity in Norway peaked during the early to mid-20th century, frequently appearing in the top 10 boys' names from 1918 to 1953, with its highest rankings in the 1920s and 1930s—reaching first place in 1923 and 1924.[59] This surge aligned with a broader revival of traditional Norse names amid national romanticism movements. Variants include Oddvar, combining oddr with varðr (meaning "guard" or "ward"), which similarly peaked in usage during the same era.[60] Today, while less frequently given to newborns—not appearing in the top 50 boys' names as of 2024—Odd retains cultural familiarity in Norway, where its English homonym meaning "strange" creates an ironic contrast for non-Norwegian speakers.[59][61] Notable bearers include Odd Nerdrum (born April 8, 1944), a prominent Norwegian figurative painter known for his classical style and critiques of modernism, whose works are held in museums worldwide.[62] Another is Odd Einar Dørum (born October 12, 1943), a longtime Norwegian politician who served four terms in the Storting (parliament) and held ministerial positions in transport and justice under Prime Minister Kjell Magne Bondevik.[63] These figures exemplify the name's association with creative and public leadership in modern Norway. In Norse literature, the name features prominently in the Ǫrvar-Odds saga (Saga of Arrow-Odd), a 13th-century fornaldarsaga depicting the hero Ǫrvar-Oddr as a long-lived warrior prophesied to live 300 years before dying from a snakebite in the skull of his horse Faxi, embodying themes of fate, adventure, and heroism that highlight the name's deep roots in Scandinavian heritage. This legendary tale, preserved in medieval manuscripts, underscores Odd's role in preserving Viking Age storytelling traditions.[64]Places and science
Odd, West Virginia
Odd is an unincorporated community located in Raleigh County, in the southern part of West Virginia, United States. Situated along Tommy Creek in a remote valley near the town of Beckley, the county seat, it lies within the Appalachian region approximately 75 miles southeast of Charleston, the state capital. The community is served by ZIP code 25902 and falls under the jurisdiction of the Raleigh County school district. As of 2023, the ZIP code area has an estimated population of 326 residents, reflecting its small, rural character with a median age of 69 and a focus on older demographics.[65] The area surrounding Odd was settled in the late 19th century amid the expansion of bituminous coal mining in Raleigh County, which began in the 1890s as railroads like the Chesapeake & Ohio facilitated extraction from the region's rich seams. Early development centered on coal operations, with communities forming to support mining activities, including an abandoned United Coal mine along Odd Road that once employed many locals. The post office, a key community landmark, was established in 1937 and named "Odd," reportedly chosen for its unusual nature during a local meeting.[66] Once a quintessential mining town tied to the coal industry that dominated southern West Virginia's economy, Odd has transitioned to a primarily residential community following the broader decline of Appalachian coal production since the mid-20th century. This shift has been influenced by environmental regulations, mechanization, and market changes, leading to population stagnation and economic challenges typical of former mining areas. Today, the local economy benefits modestly from tourism drawn to the nearby New River Gorge National Park and Preserve, which attracts visitors for outdoor activities like hiking, rafting, and bridge tours, providing indirect opportunities for residents in proximity to Beckley. The community maintains a post office but lacks larger amenities, underscoring its quiet, rural lifestyle amid the ongoing impacts of regional industrial transformation.[67] In recent years, Odd has gained some media attention due to documentaries and online videos about local families, contributing to niche tourism interest as of 2025.[68]Technology and sports
Odd (software)
Odd is an open-source software development kit (SDK) designed for building decentralized web applications that incorporate user-controlled identity and content-addressed storage without relying on centralized backends. It facilitates tracking changes in data stored on IPFS-like systems by leveraging content hashes to detect additions, deletions, and modifications efficiently. This approach ensures data integrity and enables seamless decentralized data management, particularly for applications requiring privacy and offline functionality.[69] Developed in 2018 by Fission, a team within the Protocol Labs ecosystem, Odd is implemented in TypeScript and integrates directly with IPFS and IPLD (InterPlanetary Linked Data) to support Merkle DAG structures for optimized storage and retrieval. Fission's contributors, including those with backgrounds in Protocol Labs projects, focused on creating tools that empower developers to build humane, user-sovereign software. The SDK supports versioning mechanisms that avoid full rescans by comparing hash-based representations of data states, making it suitable for dynamic, distributed environments.[70][71] Key features include a POSIX-style file system interface via WNFS (Web Native File System), which uses content addressing to handle encrypted private data and public sharing, along with authorization through UCAN capabilities for secure access control. Developers can implement diff-like operations to compare directory states or versions, identifying changes through hash differences in the underlying Merkle DAGs, thus promoting efficiency in decentralized applications. Odd is widely used in projects for local-first computing and edge-based data handling, such as web apps that store user data off-chain while maintaining verifiability.[72][73] For usage, developers integrate the SDK into JavaScript or TypeScript projects, initializing user accounts with Web Crypto APIs or blockchain wallets, then performing operations like file uploads or comparisons via API calls. For example, theodd [diff](/page/Diff) equivalent can be achieved by querying version hashes to compute changes between directory snapshots, supporting efficient Merkle DAG traversals without rescanning entire datasets. This makes Odd a foundational tool for decentralized storage workflows.[69]