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Cardinal numeral

A cardinal numeral is a linguistic expression that denotes the quantity or exact number of entities, objects, or items, serving as a fundamental tool for counting and quantification in human languages.^[1] These numerals are basic in form and directly answer the question "how many?", distinguishing them from ordinal numerals, which indicate sequence or position (e.g., "first" or "second"). Examples in English include simple terms like one, two, and ten, as well as compounds such as twenty or one hundred.^[1] In linguistic analysis, cardinal numerals exhibit varied morphological and syntactic behaviors across languages, often blending properties of adjectives, nouns, and even verbs depending on the numeral's magnitude and context. Lower cardinals (e.g., one or two) typically function like adjectives, modifying nouns directly (as in "three books"), while higher ones (e.g., hundred or thousand) may act as nouns or heads of numeral phrases. Their usage is influenced by semantic factors such as animacy, individuation, and referentiality, and they frequently interact with plurality marking on associated nouns. Cross-linguistically, cardinal numeral systems display significant diversity, ranging from base-10 structures in Indo-European languages to base-2 or base-5 systems in some indigenous languages, reflecting cultural and cognitive patterns in numeration.^[2] The study of cardinal numerals has been central to morphology and syntax research, highlighting their non-discrete categorial status—forming a continuum from adjectival to nominal—and their role in broader numeral systems that include distributives and collectivities. This variability underscores universals in numeral semantics, such as the consistent expression of cardinality, while allowing for typological differences in form and integration with other grammatical elements.^[3]

Definition and Basics

Definition

A cardinal numeral is a word or expression in a language that denotes the exact quantity or number of entities, serving to answer the question "how many?" and functioning primarily in counting discrete items or sets.^[1] In linguistic terms, these numerals form a distinct class characterized by their basic form and role in quantification, distinguishing them from other numerical types by their focus on cardinality rather than sequence or proportion.^[1] In English, cardinal numerals appear in simple constructions such as "five apples" or "ten books," where they directly modify nouns to specify the count of countable objects.^[4] This usage highlights their semantic core: expressing the size of a set without implying order, as in "three people" to indicate a group of exactly three individuals.^[5] The scope of cardinal numerals typically encompasses values from one upward, though some languages include zero as a cardinal form for denoting absence of quantity; their primary semantic function remains the indication of cardinality, independent of positional or ordinal aspects.^[1] The term "cardinal" derives from the Latin cardinalis, meaning "principal" or "chief," underscoring the fundamental role these numerals play in basic numerical expression across languages.^[6]

Distinction from Other Numerals

Cardinal numerals primarily denote quantity or the absolute number of entities in a set, as in "three dogs," where the focus is on counting the total items without implying order. In contrast, ordinal numerals indicate position, rank, or sequence within a series, such as "third dog," which specifies the relative placement rather than mere enumeration.^[5] This semantic distinction is fundamental in linguistics, where cardinals function to quantify discrete wholes, while ordinals serve ordering functions in contexts like rankings or temporal sequences.^[7] Fractional numerals, on the other hand, express proportions or parts of a whole, differing from cardinals by incorporating division rather than whole-unit counting; for example, "two" as a cardinal counts complete items, whereas "half" or "one-third" denotes subdivisions. In linguistic typology, fractions often combine a numerator (typically cardinal) with a denominator (often ordinal-derived), highlighting their relational nature as opposed to the standalone counting role of cardinals.^[8] This separation underscores that cardinals are restricted to integers for enumeration, avoiding the partiality inherent in fractional expressions.^[9] Multiplicative numerals convey repetition or scaling, such as "four times," which implies an operation on a base quantity, unlike the fixed count of cardinals like "four." Distributive numerals, meanwhile, distribute the count across units, as in "four each," emphasizing per-item allocation rather than aggregate quantity.^[10] These types extend beyond cardinal absoluteness, introducing adverbial or relational interpretations that cardinals lack.^[11] In linguistics, cardinal numerals refer to finite, everyday counting words for natural numbers, distinct from the mathematical concept of cardinal numbers, which measure set sizes including infinite quantities like the cardinality of natural numbers, denoted \aleph_0. While both involve quantification, linguistic cardinals are semantically tied to concrete, bounded enumeration in human languages, excluding transfinite abstractions central to set theory.^[12]

Grammatical Classification

Parts of Speech

In traditional grammar, cardinal numerals are often classified as a subclass of adjectives or as a distinct part of speech due to their ability to modify nouns by indicating quantity, as seen in constructions like "three books" where the numeral agrees in attributes such as case or gender in inflecting languages.^[13] In contrast, generative grammar frequently treats them as determiners, functioning similarly to articles by specifying the quantity of the noun phrase, for example, "two cats" where "two" occupies a determiner position and contributes to the definiteness or referentiality of the phrase.^[14] Cross-linguistically, cardinal numerals exhibit variability in their grammatical roles, sometimes functioning as nouns in phrases like English "the two" (referring nominally to a pair), as adverbs in expressions denoting frequency such as Latin "bis" (twice), or rarely as verbs in certain Austronesian languages like Kavalan, where a numeral can predicate quantity directly, e.g., "isa" meaning 'be one'.^[15]^[16]^[17] Theoretical debates center on whether cardinal numerals constitute a unique part of speech or a subclass of adjectives, with cross-linguistic evidence suggesting a continuum rather than discrete categories; for instance, lower numerals (e.g., one, two) often pattern adjectivally, while higher ones behave more nominally.90042-6) Within X-bar theory, numerals are analyzed as heads of quantifier phrases (QP), projecting structures like [QP two [NP books]] to account for their phrasal behavior and semantic contribution to cardinality. In English, the numeral "one" demonstrates multifunctional potential, serving as a pronoun in contexts like "one of them," which substitutes for a noun phrase and highlights the numeral's capacity to shift categories beyond strict adjectival use.^[18]

Simple vs. Complex Numerals

Cardinal numerals are categorized into simple and complex forms based on their morphological composition and derivational transparency. Simple numerals consist of monomorphemic or irregular elements that do not transparently derive from arithmetic combinations of smaller units. In English, these encompass the primary terms "one" through "ten," along with "eleven" and "twelve," which exhibit suppletive irregularity rather than systematic compounding like "ten-one" or "ten-two."^[19] Similarly, higher bases such as "hundred" and "thousand" function as simple numerals in many languages, serving as unanalyzable building blocks for larger expressions. Complex numerals, by contrast, are constructed through the combination of two or more numeral roots, typically employing arithmetic operations to express higher quantities. These formations rely on additive principles, where components sum to the total (e.g., English "twenty-three" as 20 + 3), or multiplicative principles, where a multiplier scales a base (e.g., "twenty" as two times ten, or "one hundred forty-two" as 100 + 40 + 2).^[20] Additive structures may involve explicit conjunctions, as seen in older English "two and twenty" for 22, reflecting a historical pattern of summation.^[21] Multiplicative constructions predominate in decimal systems, but irregularities arise, such as suppletive patterns in the English teens beyond eleven and twelve, where "thirteen" through "nineteen" follow a non-transparent "ten + unit" model with phonological adjustments rather than pure addition.^[19] Subtractive formations represent a rarer principle in complex numeral construction, involving the deduction of a smaller value from a larger base to yield the target number. This occurs in certain Native American languages, such as the Miluk Coos of Oregon, where juxtaposition implies subtraction: "four ten" expresses 6 (10 - 4) and "one ten" expresses 9 (10 - 1).^[22] Multiplicative irregularities further highlight deviations from standard patterns, exemplified by French "quatre-vingts" for 80, literally "four-twenties," which stems from a vigesimal (base-20) subsystem influenced by Celtic substrates rather than pure decimal multiplication.^[8] These principles and exceptions underscore the interplay between systematic arithmetic and language-specific morphological constraints in numeral formation.

Syntactic and Morphological Properties

Syntactic Functions

Cardinal numerals primarily function as determiners within noun phrases, specifying the quantity of the noun they modify. In English, they typically occupy a pre-nominal position, as in "three cats," where the numeral directly precedes the noun to form a quantified noun phrase. This determiner role often renders them incompatible with indefinite articles in certain constructions, such as the ungrammatical "*a three cats," though they can co-occur with definite articles like "the three cats" to denote a specific set. Beyond their attributive use, cardinal numerals can serve nominal functions, acting as the head of a noun phrase in predicative or subject positions, for example, "Three is enough" or "I need five." They also appear in partitive constructions, expressing a subset of a larger group, as in "three of the books," where the numeral quantifies elements from a definite noun phrase. Syntactic constraints govern the integration of cardinal numerals with nouns, particularly regarding number agreement. In English, "one" typically pairs with a singular noun ("one cat"), while higher cardinals require plural forms ("two cats"), reflecting the numeral's influence on the noun's morphological realization. Positioning varies cross-linguistically; while pre-nominal in English, cardinals are post-nominal in some languages, such as Egyptian Arabic for the numerals "one" and "two," as in "walad wāḥid" (one boy).^[23] Cardinal numerals interact distinctly with other quantifiers, distinguishing precise counts from indefinite approximations; for instance, "five students" contrasts with "many students" in terms of specificity and scope.^[14] In interrogative contexts, questions like "How many?" specifically elicit a cardinal numeral response, highlighting their role in quantifying exact amounts within the sentence's semantic structure.

Agreement and Case

In many languages, cardinal numerals trigger number agreement with the nouns they modify, where numerals greater than one typically require plural forms of the noun, while "one" pairs with a singular noun. For instance, in English, the phrase "one dog" uses the singular noun form, whereas "two dogs" employs the plural, reflecting the distributive semantics of counting multiple entities. This pattern is widespread but varies; in Russian, numerals two through four (dva, tri, četyre) govern the genitive singular of the noun, as in "dva sobaki" (two dogs), treating the counted items as a partial set rather than a full plural, while five and above take the genitive plural.^[24] Gender agreement between cardinal numerals and nouns is prominent in Indo-European languages with grammatical gender systems. In French, the numeral "one" (un/une) inflects to match the gender of the noun, as in "un chat" (a cat, masculine) versus "une chatte" (a female cat, feminine), but higher numerals like "deux" (two) do not inflect for gender and remain invariant regardless of the noun's gender. This selective agreement highlights how lower numerals often behave more adjectivally, aligning closely with the noun's phi-features (gender and number), while higher ones function more distributively without such inflection. Cardinal numerals in some languages inflect for case themselves or impose specific case markings on associated nouns. In Latin, certain cardinals like "duo" (two) decline for case to agree with the noun, appearing as "duo" in the nominative (e.g., duo canes, two dogs) but "duobus" in the ablative (e.g., duobus canibus, with two dogs).^[25] Similarly, in Finnish, numerals other than "one" (yksi) require the noun to appear in the partitive case, indicating an indefinite or partial quantity, as in "kaksi kissaa" (two cats, partitive), which conveys distributivity and unbounded reference in numeral-noun constructions.^[26] In classifier languages like Mandarin Chinese, cardinal numerals do not directly agree with nouns in gender, number, or case but instead integrate with measure words (classifiers) to form agreement-like structures that specify the noun's countability. For example, "sān gè rén" (three CL people) uses the classifier "gè" to mediate between the numeral "sān" (three) and the noun "rén" (people), enabling precise enumeration without inflectional agreement on the noun itself.^[27] This system ensures grammaticality by categorizing nouns via classifiers, contrasting with inflectional agreement in languages like those of the Indo-European family.

Typology and Cross-Linguistic Variation

Numeral Bases

Cardinal numeral systems are structured around a numerical base, or radix, which serves as the foundational unit for counting beyond the initial simple numerals (typically 1 through 9). The base determines how higher numbers are formed through multiplication, addition, and sometimes exponentiation, enabling systematic compounding to express quantities efficiently. While bases can vary across languages, they reflect both cognitive and cultural patterns in human numeration.^[28] The decimal system, or base-10, is by far the most widespread, attested in approximately 125 languages worldwide and dominant in global communication due to historical and colonial influences. In decimal systems, numbers beyond 10 are typically constructed by multiplying a coefficient by powers of 10 and adding a remainder, as seen in English where "ten" represents the base, "hundred" denotes 10², and compounds like "twenty-one" (2×10 + 1) follow this pattern. This structure allows for straightforward grouping and scalability in arithmetic operations.^[28]^[29] Vigesimal systems, based on 20, are less common but prominent in certain regions, appearing in pure form in about 20 languages and as hybrids with decimal in 22 others. These systems use 20 as the primary unit for multiplication, often leading to expressions like "four twenties" for 80 in French ("quatre-vingts"), a remnant of Celtic vigesimal influence on Gaulish substrates. In Mesoamerican languages such as Nahuatl, 20 functions as a sub-base, with numbers formed via multiplication by 20 (e.g., 400 as 20×20) before shifting to higher powers, reflecting a hierarchical structure adapted for larger counts.^[28]^[30] Other bases include quinary (base-5), which occurs in mixed systems among about 24% of Austronesian languages, where numbers above 5 are built additively from multiples of 5 (e.g., 6 as 5+1), often combined with decimal for higher ranges. Vigesimal-quinary hybrids blend these, using 5 as a sub-base within 20 (e.g., 100 as 5×20). Binary bases (base-2) are exceedingly rare in spoken languages, typically limited to specialized or derived systems rather than core cardinal numeration. These variations influence compounding: decimal favors additive transparency (e.g., "twenty-one"), while vigesimal may yield more opaque forms like "one after four twenties" equivalents, affecting ease of calculation and learning.^[28]^[31] Cultural factors often underpin base selection, with decimal linked to finger-counting (10 digits) and vigesimal extending to fingers plus toes (20 total), as evident in Mesoamerican traditions where body-part tallying shaped early systems. Historical trade and migration further propagated bases, such as vigesimal patterns in West Africa and hybrids in Europe from pre-Indo-European substrates. These bases not only organize numerals but also encode societal practices in linguistic structure.^[30]^[29]^[28]

Formation Patterns

Cardinal numerals are formed through a variety of morphological and syntactic strategies across languages, often combining basic lexical roots with operations like addition and multiplication to express higher values. These patterns build upon numeral bases but introduce complexities through irregularities and external influences. While most languages employ systematic constructions for numbers beyond a small set of primitives, variations arise from historical, cognitive, and contact factors.^[9]^[32] Additive patterns involve juxtaposing or combining smaller numeral units to denote sums, particularly in systems with limited bases or restricted ranges. For instance, some languages express 34 as "three four," directly adding the units without a higher multiplier. This method is common in binary-based systems, where numbers like 3 are formed as "two one" and 4 as "two two." Additive constructions extend to higher values in certain cases but are often supplemented by other operations for efficiency.^[32] Multiplicative patterns scale numerals by repeating a base unit a specified number of times, typically yielding tens, hundreds, or higher powers. A widespread example is "two ten" for 20, where the multiplier precedes the base. These formations combine with addition for non-round numbers, such as 54 as "five ten four" in decimal systems. Multiplication dominates in base-10 languages but appears with vigesimal (base-20) or other bases cross-linguistically.^[9]^[32] Subtractive patterns, though rarer, express numbers by deducting from a higher unit, such as 19 as "twenty minus one" in some systems. These often mark the operation explicitly and combine with addition, as in 82 as "(one hundred minus twenty) plus two." Suppletive forms disrupt regular patterns, replacing expected compounds with irregular roots, like "eleven" instead of "one ten" or "forty" diverging from "four ten." Such suppletions frequently affect lower complex numerals and stem from historical phonological shifts.^[32]^[20] Many languages with limited native numeral systems resort to borrowings from dominant contact languages or invent ad hoc terms. Indigenous languages in the Americas and Australia often adopt higher numerals from Spanish, Portuguese, or Arabic due to colonial influence, while retaining native forms for 1–4. For example, the Hup language borrows a Portuguese-based system for numbers beyond 20 alongside indigenous body-part tallies. In isolates like Pirahã, the system is severely restricted to approximations of 1 and 2, with no stable words for higher exact quantities, effectively using "one-two-many" for larger sets; this reflects an invented minimalism rather than borrowing.^[33]^[34] Asymmetries in formation are prominent in the 10–19 range ("teens"), where numerals often deviate from patterns used for 20 and above, exhibiting suppletive or inverted structures due to the cognitive salience of the first decade post-base. This irregularity appears in diverse languages, with 11 and 12 frequently unique, while 13–19 blend units and tens non-transparently. Such patterns highlight how frequency and perceptual grouping influence morphological evolution over regular arithmetic logic.^[20]^[32]

Examples from Major Language Families

In the Indo-European language family, cardinal numerals exhibit varied bases and morphological features across branches. English employs a decimal system where compounds like twenty-one (for 21) combine a multiple of ten (twenty) with a unit numeral (one), following a high-low order in the tens place. French shows traces of vigesimal influence in its higher teens and tens, as seen in soixante-dix (literally 'sixty-ten' for 70, derived from 3 × 20 + 10), a remnant of Celtic substratum effects on the Romance numeral system.^[35] In Sanskrit, an ancient Indo-Aryan language, cardinal numerals from one to four inflect for gender to agree with the nouns they modify, such as ekaḥ (masculine singular 'one'), ekā (feminine singular 'one'), and ekam (neuter singular 'one'), while higher numerals remain uninflected.^[36] Sino-Tibetan languages, exemplified by Mandarin Chinese, integrate cardinal numerals with obligatory classifiers to specify noun types, as in liǎng gè rén ('two CL people' for two people), where gè is a general classifier for countable nouns.^[37] Additionally, numerals exhibit tonal variations through sandhi rules; for instance, yī ('one') shifts from its neutral tone to a rising second tone before another tone, and liǎng ('two') changes from a falling-rising third tone to a rising second tone in compounds like liǎng gè to facilitate prosodic flow.^[38] Austronesian languages display base-10 structures in many cases, with additive compounding for teens, as in Māori where tekau mā rua means 'ten and two' for 12, using mā as a conjunction between the decade and unit.^[39] Some Austronesian languages, particularly in eastern Indonesia and Papua New Guinea, incorporate body-part terms in higher counting, such as using words for fingers, hands, arms, and legs to extend beyond 20 in a quinary-vigesimal hybrid, reflecting cultural practices tied to physical enumeration. In the Niger-Congo family, Yoruba (a Yoruboid language) favors additive and multiplicative compounds without strict noun class agreement like in Bantu branches, but with tonal harmony; for example, ẹgbẹ̀rún méjì ('thousand two') denotes 2000 through simple juxtaposition of the base numeral ẹgbẹ̀rún (1000) and méjì (2).^[40] This contrasts with more morphologically complex systems in other Niger-Congo languages, where numerals may align with noun prefixes for gender or animacy. Uto-Aztecan languages like Nahuatl employ a vigesimal base, multiplying units by 20; caxtolli represents 20 (from caxtol 'one twenty'), while macuīlcaxtolli (5 × 20 = 100) illustrates the system's integration with the Aztec calendar, where 20-day periods (trecenas) structure time reckoning. Some languages feature limited numeral systems, highlighting cross-linguistic diversity in precision. The Amazonian Tupi-Guarani language Mundurukú has exact terms only up to five (pug 'one', xep xep 'two', ebap 'three', ebap moipu 'four', pukati 'five'), with approximations like ebap pug ('many ones' for six or more) beyond that, relying on an innate approximate number sense rather than recursive counting.^[41] This stands in contrast to the precise, expansive systems in the aforementioned families, underscoring how numeral inventories correlate with cognitive and cultural demands for quantification.

Historical Development

In Indo-European Languages

The cardinal numerals of Proto-Indo-European (PIE), the reconstructed ancestor of the Indo-European language family, exhibit a decimal base that likely solidified early in the proto-language's development, with numbers from 1 to 10 serving as the foundational units for higher counting. Reconstructed forms include *óynos for "one" (masculine), *dwóh₁ for "two," *tréyes for "three," *kʷétwores for "four," *pénkʷe for "five," *s(w)éḱs for "six," *séptm̥ for "seven," *oḱtṓw for "eight," *h₁néwn̥ for "nine," and *déḱm̥(t) for "ten."^[42] These numerals were originally inflected like adjectives, particularly the first four, agreeing in case, number, and gender with the nouns they modified, reflecting the highly synthetic morphology of PIE.^[43] As Indo-European languages diverged from PIE around 4500–2500 BCE, the numeral systems retained the decimal structure but developed irregularities, especially in the teens (11–19), which often show suppletive or composite forms hinting at pre-decimal influences such as dual or body-part counting (e.g., fingers and thumbs). For instance, the form for 11 typically combined "ten" and "one" (*déḱa h₁oi-nos), but variations emerged across branches, with some preserving older patterns before standardizing to unit + "ten."^[44] This evolution underscores a shift from potentially mixed bases in early PIE to a predominantly decimal system, as evidenced by consistent *dekṃ-derived terms for multiples of ten in daughter languages. Branch-specific innovations highlight the diversity within Indo-European numeral systems. In Germanic languages, such as English and German, the teens from 13 to 19 invert the order to "unit + ten" (e.g., English thirteen from Old English þrīotīne, meaning "three-ten"), while 11 and 12 retain special forms (eleven from "one-left," twelve from "two-left"), possibly reflecting a pre-decimal duodecimal influence in Proto-Germanic.^[44] Romance languages, descending from Latin's decimal system, show vigesimal remnants in French (e.g., quatre-vingts for 80, literally "four-twenties"), attributed to Celtic substrate influence from Gaulish, a vigesimal system. Slavic languages maintain robust inflectional agreement for low numerals, with gender distinctions like Russian dva (masculine) and dve (feminine/neuter) for "two," and case/gender harmony for 1–4, preserving more of PIE's adjectival properties than analytic branches.^[45] In modern Indo-European languages, the adoption of Arabic numerals since the Middle Ages has standardized written forms across branches, decoupling them from spoken irregularities and promoting uniformity in global contexts like science and commerce. However, oral traditions retain historical vestiges, such as Welsh un ar hugain ("one on twenty" for 21), echoing Celtic vigesimal patterns. A widespread trend has been the loss of inflection, from PIE's declined forms to invariant numerals in languages like English (e.g., "one" unmodified regardless of gender or case), driven by analytic shifts in syntax and contact with non-inflecting substrates.^[44]^[43]

In Other Language Families

In the Sino-Tibetan language family, cardinal numerals trace their origins to the ancient Chinese oracle bone script of the Shang dynasty (circa 14th century BCE), where a decimal system was already in use for recording numbers on tortoise shells and animal bones, employing additive and multiplicative principles to denote quantities up to tens of thousands.^[46] Over time, this evolved in Sinitic branches like Chinese to incorporate numeral classifiers, a grammatical feature that pairs numbers with measure words for countable nouns, reflecting a shift toward more analytic structures in East Asian linguistics.^[47] In Tibeto-Burman languages such as Tibetan, the system retained a base-10 foundation with multiplicative compounding, where higher numbers like thirty are formed as "three tens" (sum bcu), preserving ancient patterns of base multiplication seen in proto-forms across the family.^[48] Within the Afro-Asiatic family, Semitic languages like Arabic developed a decimal numeral system rooted in triconsonantal stems, exemplified by the word thalāthah ("three"), derived from the root θ-l-θ, which underlies related terms for multiplicity and has cognates in other Semitic branches such as Hebrew šālôš.^[49] This root-based morphology allowed for consistent derivation of numerals, evolving from Proto-Semitic reconstructions around 3000 BCE. In Berber languages of North Africa, primarily decimal systems predominate, but traces of vigesimal (base-20) elements appear in certain dialects, such as the Amiln tribe's use of Arabic-influenced terms for twenty (iSerin), likely introduced through trans-Saharan trade routes connecting Berber speakers with sub-Saharan vigesimal traditions.^[50] The Austronesian family exhibits numerals that spread alongside human migrations from Taiwan around 4000–3000 BCE, with Proto-Austronesian forms like isa ("one") and duSa ("two") reconstructed from comparative evidence across Formosan and Malayo-Polynesian languages, facilitating counting in early seafaring societies.^[51] These basic terms diffused widely, but in remote Polynesian outliers like some Micronesian and Melanesian varieties, higher numerals beyond ten were limited or absent before European contact, relying instead on descriptive phrases or body-part terms due to isolated island ecologies that reduced the need for large-scale enumeration.^[52] Among Amerindian language families, Uto-Aztecan languages such as Nahuatl (spoken by the Aztecs) historically employed a vigesimal system derived from body-counting practices, where twenty represented a full set of fingers and toes, evolving from proto-forms around 2000 BCE in Mesoamerica to support complex calendrical and mercantile calculations.^[53] In contrast, Algic family members like Algonquian languages (e.g., Ojibwe) featured additive numeral systems, compounding smaller units sequentially—such as "three tens and five" for thirty-five— a pattern disrupted by European contact from the 16th century onward, which introduced borrowings for higher numbers and decimal standardization in trade contexts.^[54] Colonial contacts profoundly shaped numeral evolution in several families; for instance, in Quechuan languages of the Andes, Spanish influence from the 16th century led to the adoption of terms like mil ("thousand") and millón ("million") for higher quantities, supplanting native decimal extensions and aligning with European decimal norms in administrative records.^[55] Language isolates like Yuchi in North America demonstrate independent numeral inventions, maintaining a distinct decimal system without evident external borrowing until recent centuries, highlighting localized developments amid broader continental shifts. In sign languages, particularly rural variants emerging in isolated communities since at least the 18th century, numerals originated from gestural representations of fingers and hands, gradually lexicalizing into arbitrary signs influenced by surrounding spoken languages while preserving visual-motoric counting traditions.^[56]

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[PDF] Partitive Case in Finnish Numeral-Noun Constructions
1 With yksi, the noun bears the same case as the numeral (1a). With kaksi, the noun must bear partitive (PAR) case (1b). In this contribution, I propose a ...
[27]
[PDF] The syntax of classifiers in Mandarin Chinese - Li Julie Jiang 蒋鲤
Mandarin classifiers are words between a numeral and a noun, counting frequency or duration. Nominal classifiers have two structures, and verbal classifiers ...
[28]
Chapter Numeral Bases - WALS Online
In all numeral systems with a base of 20 or greater, and in several with a smaller base, numbers less than the base are constructed using smaller bases. For ...
[29]
The Mayan Numeral System | Mathematics for the Liberal Arts
Our own base-ten system probably arose from the fact that we have 10 fingers (including thumbs) on two hands. This is a natural development. However, other ...<|control11|><|separator|>
[30]
Numbers | Nahua Glyphs - UO Blogs - University of Oregon
The Nahua numbering system was vigesimal, in other words it had a base of twenty (deriving originally from the fingers and toes combined).
[31]
https://www.jbe-platform.com/content/journals/10.1075/dia.22005.bar
[32]
[PDF] Toward a typology of numeral systems - Macrolinguistics
Most numeral systems across the world are characterized by the use of both addition and multiplication, making use of an arithmetic base, which is multiplied ...<|separator|>
[33]
The history of number words in the world's languages—what have ...
Mar 22, 2021 · In some languages spoken in New Guinea, decimal number systems used for higher numbers were eventually replaced by quinary or body-counting ...
[34]
Number as a cognitive technology: Evidence from Pirahã language ...
We show that the Pirahã have no linguistic method whatsoever for expressing exact quantity, not even “one.”
[35]
Transcoding of French numbers for first- and second-language ...
In contrast to some languages, such as English, the number words for the decade values from 70 to 90 in French are partially based on a vigesimal (i.e., base-20) ...Number Words And The Arabic... · Results · Discussion
[36]
Comparative Analysis of Cardinal Numerals of Russian and Sanskrit ...
Sep 23, 2023 · In contrast, Sanskrit employs root numerals and declensional suffixes, adapting numerals for gender, number and case agreement. Gender and case ...
[37]
oa Structure of numerals and classifiers in Chinese - John Benjamins
Jan 12, 2017 · Structure of numerals and classifiers in Chinese. Historical and typological perspectives and cross-linguistic implications.
[38]
[PDF] Suppletion of numerals 'one' and 'two' in Mandarin Chinese
First, there is no tone sandhi process like (11b) anywhere else in the language, where a syllable changes to the fourth tone when followed by a non-fourth tone.<|separator|>
[39]
[PDF] http://researchcommons.waikato.ac.nz/ Research Commons at the ...
Like English, Māori makes a distinction between cardinal and ordinal numerals. Moreover, Māori ordinal numerals are morphologically marked by the prefix tua-.
[40]
[PDF] The Linguistic Analysis of the Structure of the Yoruba Numerals
The purpose of this paper is to examine the traditional system of counting in Yoruba (a New Benue Congo language spoken in the South. Western Nigeria). The ...
[41]
[PDF] Exact and Approximate Arithmetic in an Amazonian Indigene Group
Aug 19, 2004 · Here, we studied numerical cognition in native speakers of MundurukU, a language that has number words only for the numbers 1 through 5 (24, 25) ...
[42]
The Oxford Introduction to Proto-Indo-European and ... - Google Books
Aug 24, 2006 · J. P. Mallory and Douglas Adams show how over the last two centuries scholars have reconstructed it from its descendant languages, the surviving ...
[43]
[PDF] The Oxford Introduction to Proto-Indo-European and ... - smerdaleos
... Mallory and D. Q. Adams 2006. The moral rights of the authors have been ... book in any other binding or cover and you must impose the same condition on ...
[44]
typology and diachrony of higher numerals in Indo-European
Apr 25, 2016 · This article contains a comprehensive typological account of how languages in the Indo-European language family code numerals beyond 10 (10–99, ...
[45]
The Development of Slavic Numeral Agreement - veche.net
Slavic numeral agreement varied due to the loss of dual, with 'one' always adjectival. 'Five-ten' were genitive, but now often align with lower numerals, and ' ...
[46]
Chinese numerals - MacTutor History of Mathematics
The number system which was used to express this numerical information was based on the decimal system and was both additive and multiplicative in nature.
[47]
(PDF) Structure of numerals and classifiers in Chinese - ResearchGate
Jun 15, 2025 · This paper reviews evidence for the [Num C/M] constituency from modern Chinese and then provides evidence from historical and typological ...
[48]
(PDF) Number-Building in Tibeto-Burman Languages - ResearchGate
May 28, 2018 · Likewise, in a complex numeral with a multiplicative composition, the base may follow the multiplier as in [ n×base ], e.g., san-bai 'three ...
[49]
Origin of ?Semitic? Languages - Adel S. Bishtawi - Google Books
Bishtawi The unity of what is traditionally called Semitic languages may be traced in the roots, in the inflections, and in the general features of the syntax.
[50]
[PDF] Blažek, Václav Berber numerals In - Masarykova univerzita
Klingenheben 1926-27: 44 found traces of the vigesimal system in the dialect of the tribe of Amiln (region of Sus) based on the Arabic borrowing. iSerin "20": ?Missing: trade | Show results with:trade
[51]
[PDF] austronesian numerals¹
Before the migration to. Formosa began, the AN society thus seems to have had so little need of numbers that count- ing on only one hand was sufficient. The ...
[52]
Innovative Numerals in Malayo-Polynesian Languages outside of ...
RECONSTRUCTIBLE AUSTRONESIAN NUMERALS. Proto-Austronesian Proto-Oceanic. 1 *esa/isa *ta-sa/(sa)-kai. 2. *duSa *rua. 3. *telu. *tolu. 4 *Sepat *pat(i). 5. *lima ...
[53]
Mathematics of the Aztecs/Mexica - Mexicolore
The Aztecs wrote numbers in a base 20 (vigesimal) system. In our familiar decimal system, when counting we group individual things in groups of ten, then in ...Missing: Uto- body-
[54]
[PDF] The West-to-East Cline in Algonquian Dialectology
An examination of the dialectal relationships of the Algonquian languages sheds light on the linguistic history, and by implication the non-linguistic history, ...
[55]
Quechua oral numeration and its writing in quipus - Inalco
We consider that this evolution is probably due to the Spanish influence, which moves from the simple numeral mil (one thousand) to the following one millón ...
[56]
[PDF] The Time Depth and Typology of Rural Sign Languages - MPG.PuRe
Dec 18, 2018 · This special issue of Sign Language Studies is focused on recent developments in the study of rural sign languages, which have.