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Journal articles on the topic 'Ordinal numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Agustito, Denik, Krida Singgih Kuncoro, Istiqomah Istiqomah, and Agus Hendriyanto. "Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 3 (2023): 781. http://dx.doi.org/10.31764/jtam.v7i3.15039.

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The purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordinal or transfinite arithmetic, as well as the connection between infinity and theology. The study also involves constructing the objects of study, namely ordinal numbers such as finite ordinals and transfinite ordinals, and examining their arithmetic properties. The results of this research include t

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2

Jensen, Ronald. "Inner Models and Large Cardinals." Bulletin of Symbolic Logic 1, no. 4 (1995): 393–407. http://dx.doi.org/10.2307/421129.

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In this paper, we sketch the development of two important themes of modern set theory, both of which can be regarded as growing out of work of Kurt Gödel. We begin with a review of some basic concepts and conventions of set theory. §0. The ordinal numbers were Georg Cantor's deepest contribution to mathematics. After the natural numbers 0, 1, …, n, … comes the first infinite ordinal number ω, followed by ω + 1, ω + 2, …, ω + ω, … and so forth. ω is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α

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3

Samai, Mehdi. "Number Group in Machine Translation." Iranian Journal of Information Processing & Management 21, no. 1 (2005): 21–33. https://doi.org/10.5281/zenodo.14008100.

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ََThe purpose of number group representation is to construct the permissible combinations of cardinal and ordinal numbers in Persian language. In this paper 38 members of the Persian enumeration system have been placed in four multi-member and two single member groups. The said 38 members were placed into two general rule groups (Rules applying to the cardinal number groups and ordinal number groups). There are 47 rules governing cardinal numbers while there are only four rules for ordinal numbers. Ordinal numbers are also of two types. An investigation into the potentials for superposition of

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4

Hasanović, Bilal. "The etymological link between the word Al-ahad (الأحد) and Al-vahed (الواحد)". Zbornik radova Islamskog pedagoškog fakulteta u Zenici (Online), № 1 (15 грудня 2003): 182–93. http://dx.doi.org/10.51728/issn.2637-1480.2003.182.

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In this comparative language study on numbers in Semitic languages the following can be concluded: * First - cardinal and ordinal number in Semitic languages are made from different etymological bases. * Although there is a significant difference between first (cardinal and ordinal) numbers, there is a high level of overlap between other (cardinal and ordinal) numbers. We can also find the overlapping in some other, non-Semitic languages, such as: English, German and French, with some small exceptions, e.g. number two in English. * Most of Semitic languages takes the word وَحَدَ as a basis or

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Daniyarova, Evelina Yur’evna, Alexei Georgievich Myasnikov, and Vladimir Nikanorovich Remeslennikov. "Algebraic geometry over algebraic structures X: Ordinal dimension." International Journal of Algebra and Computation 28, no. 08 (2018): 1425–48. http://dx.doi.org/10.1142/s0218196718400039.

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This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

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6

Lima, Paulo Alexandre. "The Ordinal Numbers in Hesiod’s Myth of the Races." ΣΧΟΛΗ. Ancient Philosophy and the Classical Tradition 14, no. 1 (2020): 57–81. http://dx.doi.org/10.25205/1995-4328-2020-14-1-57-81.

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To understand the meaning and function of the ordinal numbers in the myth of the races it is essential to have a full grasp of how the myth is composed and its structure is supposed to be perceived by a listener or reader. There is a general silence among Hesiod scholars about the meaning and function of the ordinal numbers in the myth. A tacit agreement may be inferred from such a silence: the ordinal numbers are implicitly taken to merely express the chronological order of the races. In this article, we examine each and every one of the ordinal numbers that appear in Hesiod’s myth. We demons

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Baranova, Svetlana Vladimirovna, and Nadezda Alexandrovna Kobzeva. "COMBINATORIAL PROPERTIES OF ORDINAL NUMBERS." V mire nauchnykh otkrytiy, no. 1.1 (March 11, 2015): 737. http://dx.doi.org/10.12731/wsd-2015-1.1-25.

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8

Keddie, P. "Ordinal Operations on Surreal Numbers." Bulletin of the London Mathematical Society 26, no. 6 (1994): 531–38. http://dx.doi.org/10.1112/blms/26.6.531.

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9

Bagemihl, Frederick, and F. Bagemihl. "ORDINAL NUMBERS IN ARITHMETIC PROGRESSION." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 38, no. 1 (1992): 525–28. http://dx.doi.org/10.1002/malq.19920380148.

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10

Macaulay, Monica. "Participial Ordinal Numbers in Menominee." Anthropological Linguistics 62, no. 4 (2020): 337–63. http://dx.doi.org/10.1353/anl.2020.0015.

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11

Abrusci, V. Michele, Jean-Yves Girard, and Jacques van de Wiele. "Some uses of dilators in combinatorial problems. II." Journal of Symbolic Logic 55, no. 1 (1990): 32–40. http://dx.doi.org/10.2307/2274952.

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AbstractWe study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with “+ 1” instead of “−1”). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator F the point where the increasing F-sequence terminates.We apply these results to inverse Goodstein sequences, i.e. increasing

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12

Shirley, Lawrence. "Nominals: Numbers As Names." Teaching Children Mathematics 2, no. 4 (1995): 242–45. http://dx.doi.org/10.5951/tcm.2.4.0242.

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13

Kemoto, Nobuyuki, Haruto Ohta, and Ken-ichi Tamano. "Products of spaces of ordinal numbers." Topology and its Applications 45, no. 3 (1992): 245–60. http://dx.doi.org/10.1016/0166-8641(92)90007-m.

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14

Altman, Harry J. "Intermediate arithmetic operations on ordinal numbers." Mathematical Logic Quarterly 63, no. 3-4 (2017): 228–42. http://dx.doi.org/10.1002/malq.201600006.

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15

Yue, Qi. "Two-Sided Matching with Ordinal Numbers and Costs." Applied Mechanics and Materials 587-589 (July 2014): 2299–302. http://dx.doi.org/10.4028/www.scientific.net/amm.587-589.2299.

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A novel decision method for solving the two-sided matching problem is proposed in this paper, in which the preferences provided by agents are in the format of ordinal numbers and the preference provided by intermediary is in the format of costs. The concept of two-sided matching is firstly introduced, and the two-sided matching problem with ordinal numbers and costs is discribed. Then the related concepts on costs are given. Considering the ordinal number of each agent and the cost of intermediary, a multi-objective optimization model is set up. The method of weighted sums based on membership

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16

Avigad, Jeremy, and Richard Sommer. "A Model-Theoretic Approach to Ordinal Analysis." Bulletin of Symbolic Logic 3, no. 1 (1997): 17–52. http://dx.doi.org/10.2307/421195.

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AbstractWe describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.

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Simpson, Stephen G. "Ordinal numbers and the Hilbert basis theorem." Journal of Symbolic Logic 53, no. 3 (1988): 961–74. http://dx.doi.org/10.2307/2274585.

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In [5] and [21] we studied countable algebra in the context of “reverse mathematics”. We considered set existence axioms formulated in the language of second order arithmetic. We showed that many well-known theorems about countable fields, countable rings, countable abelian groups, etc. are equivalent to the respective set existence axioms which are needed to prove them.One classical algebraic theorem which we did not consider in [5] and [21] is the Hilbert basis theorem. Let K be a field. For any natural number m, let K[x1,…,xm] be the ring of polynomials over K in m commuting indeterminates

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Hirata, Yoshito, Masanori Shiro, and José M. Amigó. "Surrogate Data Preserving All the Properties of Ordinal Patterns up to a Certain Length." Entropy 21, no. 7 (2019): 713. http://dx.doi.org/10.3390/e21070713.

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We propose a method for generating surrogate data that preserves all the properties of ordinal patterns up to a certain length, such as the numbers of allowed/forbidden ordinal patterns and transition likelihoods from ordinal patterns into others. The null hypothesis is that the details of the underlying dynamics do not matter beyond the refinements of ordinal patterns finer than a predefined length. The proposed surrogate data help construct a test of determinism that is free from the common linearity assumption for a null-hypothesis.

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19

Marx, Melvin H. "Elementary Counting of Cardinal and Ordinal Numbers by Persons with Mental Retardation." Perceptual and Motor Skills 68, no. 3_suppl (1989): 1176–78. http://dx.doi.org/10.2466/pms.1989.68.3c.1176.

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Cardinal and ordinal counting skills were assessed in 37 mentally retarded adult workers and 42 school children with mental retardation. The major results were the very poor performance of the younger children (essentially at chance beyond the numbers 1 and 2) and the overall marked inferiority in ordinal compared with cardinal counting.

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20

Maseleno, Andino, Miftachul Huda, Mazdi Marzuki, Fauziah Che Leh, Azmil Hashim, and Mohd Hairy Ibrahim. "Translating Islamic identity into numbers." Linguistics and Culture Review 5, S1 (2021): 139–59. http://dx.doi.org/10.21744/lingcure.v5ns1.1030.

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This research aims to define various Islamic based identity profile to different individuals by identifying the various degrees of Islamic based identity profile. A scale of measurement in ordinal scale has been used to determine an Islamic based identity profile. The scale is subdivided into three main subsections, namely very rarely, average level and very frequently. By using the scale of measurement on an ordinal scale, it assists in developing a numerical hypothesis that is then used to determine an individual's Islamic based identity profile using the Dempster-Shafer theory of evidence.

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21

Yulianti, Yulianti. "Penerapan Metode Role Playing untuk meningkatkan kemampuan berbicara Bahasa Inggris Pada materi Date, Day, Time, Ordinal Numbers, and Preposition of Time pada siswa kelas VII 1 MTsN 3 Rokan Hulu Semester Ganjil Tahun Pelajaran 2019/2020." JURNAL JENDELA PENDIDIKAN 2, no. 02 (2022): 190–99. http://dx.doi.org/10.57008/jjp.v2i02.162.

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Tujuan penelitian ini adalah meningkatkan kemampuan berbicara Bahasa inggris siswa pada materi Date, Day, Time, Ordinal Numbers, and Preposition of Time melalui penerapan metode Role Playing. Penelitian ini adalah jenis Penelitian Tindakan kelas yang dilaksanakan dalam dua siklus dan masing-masing siklus dilaksanakan selama tiga kali pertemuan. Subjek dalam penelitian ini adalah siswa kelas VII 1 Semester Ganjil Tahun Pelajaran 2019/2020. Berdasarkan hasil penelitian diperoleh kesimpulan, yaitu: (1) Pelaksanaan pembelajaran dengan menerapkan metode Role Playing dapat meningkatkan kemampuan ber

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22

Gentner, Dedre, and Nina Simms. "Language and analogy in conceptual change." Behavioral and Brain Sciences 34, no. 3 (2011): 128–29. http://dx.doi.org/10.1017/s0140525x10002736.

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AbstractCarey proposes that the acquisition of the natural numbers relies on the interaction between language and analogical processes: specifically, on an analogical mapping from ordinal linguistic structure to ordinal conceptual structure. We suggest that this analogy in fact requires several steps. Further, we propose that additional analogical processes enter into the acquisition of number.

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23

Chermidov, Sergey Ivanovich. "PRIME NUMBER LAW. DEPENDENCE OF PRIME NUMBERS ON THEIR ORDINAL NUMBERS AND GOLDBACH – EULER BINARY PROBLEM USING COMPUTER." Vestnik of Astrakhan State Technical University. Series: Management, computer science and informatics 2020, no. 4 (2020): 80–100. http://dx.doi.org/10.24143/2072-9502-2020-4-80-100.

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The article considers the methods of defining and finding the distribution of composite numbers CN, prime numbers PN, twins of prime numbers Tw and twins of composite numbers TwCN that do not have divisors 2 and 3 in the set of natural numbers - ℕ based on a set of numbers like Θ = {6∙κ ± 1, κ ∈ ℕ}, which is a semigroup in relation to multiplication. There has been proposed a method of obtaining primes by using their ordinal numbers in the set of primes and vice versa, as well as a new algorithm for searching and distributing primes based on  a closedness of the elements of the set Θ. It

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Kaczmarek, Mirosława, and Piotr Tarka. "Analiza porównawcza metod pomiaru postaw respondentów." Wiadomości Statystyczne. The Polish Statistician 2013, no. 8 (2013): 37–47. http://dx.doi.org/10.59139/ws.2013.08.3.

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The article deals with the issue of obtaining high-accuracy measurement of the attitudes of respondents using ordinal scales with different numbers of degrees. Two methods of research — ordinal scales 5- and 7-stage were considered. The key issue was to decide which of these methods can provide a higher level of accuracy in the results. For this purpose, the data collected in a survey of students were compared. The analysis of both types of scales with different numbers of response options included attitudes of the respondents to their value system. The authors indicated the usefulness of the

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Chan, Jenny Yun-Chen, and Michèle M. M. Mazzocco. "New measures of number line estimation performance reveal children’s ordinal understanding of numbers." Journal of Experimental Child Psychology 245 (September 2024): 105965. http://dx.doi.org/10.1016/j.jecp.2024.105965.

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26

BROUWER, ROELOF K. "FUZZY CLUSTERING OF FEATURE VECTORS WITH SOME ORDINAL VALUED ATTRIBUTES USING GRADIENT DESCENT FOR LEARNING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 02 (2008): 195–218. http://dx.doi.org/10.1142/s0218488508005133.

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There are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale. Not so well established are methods to be applied when the feature values are ordinal or nominal. In that case there is no one best method it seems. This paper discusses a method where unknown numeric variables are assigned to the ordinal values. Part of minimizing an objective function for the clustering is to find numeric values for these variables. Thus real numbers of interval scale and even ratio scale for that matter are assigned to the origi

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Voigt, Rainer M. "Labialization and the so-called sibilant anomaly in Tigrinya." Bulletin of the School of Oriental and African Studies 51, no. 3 (1988): 525–36. http://dx.doi.org/10.1017/s0041977x00116519.

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In Tigrinya, the cardinal numbers from 5 to 9 show a hushing sibilant instead of the hissing sibilant which is found in the corresponding ordinal numbers, i.e., 5th to 9th, and the multiples of ten, i.e., 50 to 90. We cite the forms as given by W. Leslau (1941: 127 ff.)

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Jäger, Gerhard, та Thomas Strahm. "Some theories with positive induction of ordinal strength φω0". Journal of Symbolic Logic 61, № 3 (1996): 818–42. http://dx.doi.org/10.2307/2275787.

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AbstractThis paper deals with: (i) the theory which results from by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω0.

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Amersi, Shamsah, and David A. Grimes. "THE CASE AGAINST USING ORDINAL NUMBERS FOR GESTATIONAL AGE." Obstetrics & Gynecology 91, no. 4 (1998): 623–25. http://dx.doi.org/10.1097/00006250-199804000-00028.

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Amersi, S. "The case against using ordinal numbers for gestational age." Obstetrics & Gynecology 91, no. 4 (1998): 623–25. http://dx.doi.org/10.1016/s0029-7844(98)00033-7.

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Hudcovičová, Marianna, and Ingrid Cíbiková. "ENGLISH AND SLOVAK CONCEPT SYSTEMS OF WHOLE NUMBERS." KNOWLEDGE - International Journal 54, no. 3 (2022): 563–68. http://dx.doi.org/10.35120/kij5403563h.

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Terminology documents the knowledge of various subject fields. The paper describes the structure ofknowledge and models the conceptual systems of ordinal numbers in English and Slovak language. In the theory ofterminology, the designation can be expressed by a term, a symbol, and an appellation. Worth noticing is the factthat in the case of mathematical sciences, in algebra, both two types of designations are used, i.e., by a term andpredominantly by a symbol. Mathematical science is precise and systemic. That is the reason why designation by thesymbol is largely used in practice. An additiona

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Melaku, Zelalem, and Samuel Gondere. "Determiner Morphology of Ale." Journal of Linguistics, Literature, and Language Teaching (JLLLT) 3, no. 1 (2023): 53–59. http://dx.doi.org/10.37249/jlllt.v3i1.688.

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This study was focused on describing the determiner of the Ale language. Therefore, the study followed a descriptive research design and language consultants were selected using purposeful sampling. Then, the linguistic data was collected using interviews, focus group discussions and elicitation. The collected data were analyzed using qualitative methods. The findings show that the demonstrative determiner in Ale is used to show something is near to the speaker/ listener, expressed by husi 'This' for singular and hisi 'These' for plural. Oppositely, to describe some things far from the speaker

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Grabowski, Adam. "Polygonal Numbers." Formalized Mathematics 21, no. 2 (2013): 103–13. http://dx.doi.org/10.2478/forma-2013-0012.

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Summary In the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = Δ+Δ+Δ”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar language evolved and attributes with arguments were implemented, we decided to extend these lines and we characterized polygonal numbers. We formalized centered polygonal numbers, the connection between

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Gutjahr, Tim, and Karsten Keller. "Generalized Ordinal Patterns and the KS-Entropy." Entropy 23, no. 8 (2021): 1097. http://dx.doi.org/10.3390/e23081097.

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Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based on the probability distributions of such patterns is equal to Kolmogorov–Sinai entropy in simple one-dimensional systems. The general reason for this is that, roughly speaking, the system of ordinal patterns obtained for a real-valued “measuring arrangement” has high potential for separating orbits. St

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Snyder, Eric, Stewart Shapiro, and Richard Samuels. "Cardinals, Ordinals, and the Prospects for a Fregean Foundation." Royal Institute of Philosophy Supplement 82 (July 2018): 77–107. http://dx.doi.org/10.1017/s1358246118000176.

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AbstractThere are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. This paper addresses two related issues. First, we review some of

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Aylar Çankaya, Ebru, Esengül Yıldız, and Cemre Cengiz. "EXAMINING INTEGERS-BASED MATH GAME CREATED BY A FOURTH GRADE STUDENT." Problems of Education in the 21st Century 80, no. 6 (2022): 750–64. http://dx.doi.org/10.33225/pec/22.80.750.

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An integer-based mathematical game was the main subject of the study. The aim of this study was to analyse the mathematical content of the game which was developed by a fourth-grade student called Esin, and to examine the intuitive learning that develops through this game. The game was based on the addition of the positive or negative numbers won in each round. The integer is regarded as an abstract topic and is taught in secondary school. It is also regarded as a topic that students have difficulty in learning. However, in the case examined by this research, a fourth grader created an integer

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Izadikhah, Mohammad, Razieh Roostaee, and Ali Emrouznejad. "Fuzzy Data Envelopment Analysis with Ordinal and Interval Data." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 03 (2021): 385–410. http://dx.doi.org/10.1142/s0218488521500173.

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In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficienci

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Xiang, Jianxin. "The concept of infinity and the development of set theory solutions." Theoretical and Natural Science 14, no. 1 (2023): 96–101. http://dx.doi.org/10.54254/2753-8818/14/20240891.

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The concept of infinity is intricately connected to and comprehended via the framework of cardinal and ordinal numbers. Cardinal and ordinal numbers are fundamental mathematical ideas within the field of set theory. The cardinal number is used to denote the quantity of items inside a given set while ordinal defines basic algorithms. This article demonstrates how the discipline of set theory may be used as a tool to investigate the nature of infinity, or at the very least give some insights into the subject. The idea of infinity may be better understood by looking at it through the lens of set

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Alvarez-Samaniego, Borys, and Andres Merino. "Some properties related to the Cantor-Bendixson derivative on a Polish space." New Zealand Journal of Mathematics 50 (February 4, 2021): 207–18. http://dx.doi.org/10.53733/82.

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We show a necessary and sufficient condition for any ordinal number to be a Polish space. We also prove that for each countable Polish space, there exists a countable ordinal number that is an upper bound for the first component of the Cantor-Bendixson characteristic of every compact countable subset of the aforementioned space. In addition, for any uncountable Polish space, for every countable ordinal number and for each nonzero natural number, we show the existence of a compact countable subset of this space such that its Cantor-Bendixson characteristic equals the previous pair of numbers. F

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Bierzeņš, Aņss Ataols. "NUMERALS’ USAGE PROBLEMS IN LATGALIAN LANGUAGE." Via Latgalica, no. 4 (December 31, 2012): 33. http://dx.doi.org/10.17770/latg2012.4.1693.

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<p>In the article is told about some actual problems with numerals which came up in Latgalian language after intensification of its’ usage in 90ties:</p><p>1) to use or not to use a dot after ordinal numbers;</p><p>2) to use an ordinal indicator „№“ or „Nr.“;</p><p>3) how to decline the noun „gods“ ‘year’;</p><p>4) how to write calendar dates.</p><p>The author analyses a variety of sources: old Latgalian written texts – newspapers and calendars, spontanous dialectal speech, as well as solutions of these problems in other languag

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Escardó, Martín H. "Infinite sets that Satisfy the Principle of Omniscience in any Variety of Constructive Mathematics." Journal of Symbolic Logic 78, no. 3 (2013): 764–84. http://dx.doi.org/10.2178/jsl.7803040.

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AbstractWe show that there are plenty of infinite sets that satisfy the omniscience principle, in a minimalistic setting for constructive mathematics that is compatible with classical mathematics. A first example of an omniscient set is the one-point compactification of the natural numbers, also known as the generic convergent sequence. We relate this to Grilliot's and Ishihara's Tricks. We generalize this example to many infinite subsets of the Cantor space. These subsets turn out to be ordinals in a constructive sense, with respect to the lexicographic order, satisfying both a well-foundedne

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Rousseau, George. "The theorem of the means for cardinal and ordinal numbers." Mathematical Logic Quarterly 39, no. 1 (1993): 279–86. http://dx.doi.org/10.1002/malq.19930390133.

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WEBER, ZACH. "TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY." Review of Symbolic Logic 3, no. 1 (2010): 71–92. http://dx.doi.org/10.1017/s1755020309990281.

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This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the exist

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Ehrlich, Philip. "The Absolute Arithmetic Continuum and the Unification Of all Numbers Great and Small." Bulletin of Symbolic Logic 18, no. 1 (2012): 1–45. http://dx.doi.org/10.2178/bsl/1327328438.

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AbstractIn his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including −ω, ω/2, 1/ω, and ω − π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG (von Neumann–Bernays–Gödel set theory with global choice), it may be said to contain “All Numbers Great and Small.” In this respect, No bears

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Wang, Qiangqiang, Tingting Nie, Weixia Zhang, and Wendian Shi. "The Mechanism of the Ordinal Position Effect: Stability Across Sense Modalities and the Hands Crossed Context." i-Perception 10, no. 2 (2019): 204166951984107. http://dx.doi.org/10.1177/2041669519841071.

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The ordinal position effect posits that items positioned earlier in an ordinal sequence are responded to faster with the left key than the right key, and items positioned later in an ordinal sequence are responded to faster with the right key than the left key. Although the mechanism of the ordinal position effect has been investigated in many studies, it is unclear whether the ordinal position effect can extend to the auditory modality and the hands crossed context. Therefore, the present study employed days as the order information to investigate this question. Days were visually or acoustic

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TURBIĆ-HADŽAGIĆ, Amira. "DECLENSION OF CARDINAL NUMBERSIN THE LEGAL TEXTS OF BOSNIA AND HUMFROM THE 12TH TO 15TH CENTURY." Lingua Montenegrina 4, no. 2 (2009): 147–56. https://doi.org/10.46584/lm.v4i2.107.

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Cardinal numbers in the legal texts of Bosnia and Hum from the 12thto 15th century have been analysed in this article, i. e. the graphic recording of cardinal numbers and their faculty to decline are to be shown. In the literature that considers the medieval legal texts written on parchment or paper� numbers were not analysed until now, with the exception of Slavko Vukomanović’s article “The Lexicon and the Grammatical Meaning in the Charter of Ban Kulin”, where he only recounts the presence of two cardinal numbers and one ordinal number in the same charter as one of the segments in the statis

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Thomas, M. A. "Mathematization, Not Measurement: A Critique of Stevens’ Scales of Measurement." Journal of Methods and Measurement in the Social Sciences 10, no. 2 (2020): 76–94. http://dx.doi.org/10.2458/v10i2.23785.

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In the early 1900s, physics was the archetypical science and measurement was equated with mathematization to real numbers. To enable the use of mathematics to draw empirical conclusions about psychological data, which was often ordinal, Stevens redefined measurement as “the assignment of numerals to objects and events according to a rule.” He defined four scales of measurement (nominal, ordinal, interval, and ratio) and set out criteria for the permissible statistical tests to be used with each. Stevens' scales of measurement are still widely used in data analysis in the social sciences. They

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Wang, Na, Yinzhen Li, Cunjie Dai, and Francesco Zammori. "Decision-Making Approach of Two-Sided Matching of Supply and Demand of Logistics Service Based on the Uncertain Preference Ordinal." Mathematical Problems in Engineering 2020 (September 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/5480842.

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Aiming at the problem of matching logistics service supply and demand, this paper proposes a two-sided matching decision model of logistics service supply and demand based on the uncertain preference ordinal. In this model, the uncertain preference ordinal information is first expressed by the interval numbers of the logistics service supply and demand, and it is converted into the satisfaction degree of supply and demand matching uncertainty expressed by the interval number. Then, a multiobjective optimal matching model is constructed based on the largest overall satisfaction of the logistics

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Faliszewski, Piotr, Jitka Mertlová, Pierre Nunn, Stanisław Szufa, and Tomasz Wąs. "Distances Between Top-Truncated Elections of Different Sizes." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 13 (2025): 13823–30. https://doi.org/10.1609/aaai.v39i13.33511.

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The map of elections framework is a methodology for visualizing and analyzing election datasets. So far, the framework was restricted to elections that have equal numbers of candidates, equal numbers of voters, and where all the (ordinal) votes rank all the candidates. We extend it to the case of elections of different sizes, where the votes can be top-truncated. We use our results to present a visualization of a large fragment of the Preflib database.

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Yusupova, Maksuda Umidjonovna. "THE LINGUISTIC NATURE OF NUMBERS: STRUCTURE AND MEANING." Multidisciplinary Journal of Science and Technology 5, no. 4 (2025): 1078–80. https://doi.org/10.5281/zenodo.15319638.

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This article explores the linguistic nature of numbers, emphasizing their structural and semantic roles in language. It highlights how numbers, rooted in cultural and spiritual values, manifest in proverbs and everyday speech across different nations. The study discusses historical developments in number formation, particularly within Turkic languages, and addresses the grammatical, morphological, and syntactic features distinguishing numerals from other parts of speech. Different types of numerals—cardinal, ordinal, and collective—are analyzed in terms of their linguistic function

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