scholarly journals Trudności w opanowaniu odmiany liczebników w nauczaniu języka polskiego jako obcego na przykładzie studentów ukraińsko i rosyjskojęzycznych.

2021 ◽  
pp. 23-36
Author(s):  
Ольга Попова
Keyword(s):  
Comparative Method ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Causes Of Errors ◽  
Syntactic Relations

The aim of this paper is to describe the most common errors made by Ukrainian- and Russian-speaking people while learning infl ection of numerals for person and their causes. The applied comparative method permits a closer look at formal and syntactic relations as well as collocations of numerals and specifi c lexeme classes (this regards primarily agreement between cardinal numbers and masculine personal verbs, compound structures with the numeral jeden (one) and numerals showing adjectival infl ection). This study concentrates on a comparison of cardinal and ordinal numbers in Ukrainian, Russian and Polish, which allowed an analysis of the causes of errors made while learning the infl ection of numerals by Ukrainian- and Russian-speaking students.

The Natural Numbers

2018 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Natural Number ◽  
Peano Arithmetic ◽  
Number Sequence ◽  
Natural Numbers ◽  
Ordinal Numbers ◽  
Cardinal Numbers

How are the natural numbers individuated? That is, what is our most basic way of singling out a natural number for reference in language or in thought? According to Frege and many of his followers, the natural numbers are cardinal numbers, individuated by the cardinalities of the collections that they number. Another answer regards the natural numbers as ordinal numbers, individuated by their positions in the natural number sequence. Some reasons to favor the second answer are presented. This answer is therefore developed in more detail, involving a form of abstraction on numerals. Based on this answer, a justification for the axioms of Dedekind–Peano arithmetic is developed.

Type-raising operations on cardinal and ordinal numbers in Quine's “New foundations”

1973 ◽  
Vol 38 (1) ◽  
pp. 59-68 ◽  
Author(s):  
C. Ward Henson
Keyword(s):  
Set Theory ◽  
Initial Segment ◽  
Initial Section ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Basic Facts ◽  
Image Position ◽  
The Axiom Of Choice ◽  
Increasing Function ◽  
Standard Operations

In this paper we develop certain methods of proof in Quine's set theory NF which have no counterparts elsewhere. These ideas were first used by Specker [5] in his disproof of the Axiom of Choice in NF. They depend on the properties of two related operations, T(n) on cardinal numbers and U(α) on ordinal numbers, which are defined by the equationsfor each set x and well ordering R. (Here and below we use Rosser's notation [3].) The definitions insure that the formulas T(x) = y and U(x) = y are stratified when y is assigned a type one higher than x. The importance of T and U stems from the following facts: (i) each of T and U is a 1-1, order preserving operation from its domain onto a proper initial section of its domain; (ii) Tand U commute with most of the standard operations on cardinal and ordinal numbers.These basic facts are discussed in §1. In §2 we prove in NF that the exponential function 2n is not 1-1. Indeed, there exist cardinal numbers m and n which satisfyIn §3 we prove the following technical result, which has many important applications. Suppose f is an increasing function from an initial segment S of the set NO of ordinal numbers into NO and that f commutes with U.

Set Theory

2021 ◽  
pp. 25-46
Author(s):  
Adel N. Boules
Keyword(s):  
Vector Space ◽  
Set Theory ◽  
Hilbert Spaces ◽  
Ordered Sets ◽  
Proper Understanding ◽  
Partially Ordered ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
The Axiom Of Choice ◽  
Cardinal Arithmetic

The chapter is a concise, practical presentation of the basics of set theory. The topics include set equivalence, countability, partially ordered, linearly ordered, and well-ordered sets, the axiom of choice, and Zorn’s lemma, as well as cardinal numbers and cardinal arithmetic. The first two sections are essential for a proper understanding of the rest of the book. In particular, a thorough understanding of countability and Zorn’s lemma are indispensable. Parts of the section on cardinal numbers may be included, but only an intuitive understanding of cardinal numbers is sufficient to follow such topics as the discussion on the existence of a vector space of arbitrary (infinite) dimension, and the existence of inseparable Hilbert spaces. Cardinal arithmetic can be omitted since its applications later in the book are limited. Ordinal numbers have been carefully avoided.

scholarly journals Arithmatics in Serat Centhini

2021 ◽  
Vol 1 (2) ◽  
pp. 1-6
Author(s):  
Agung Prabowo
Keyword(s):  
Daily Life ◽  
Literature Study ◽  
Teaching Materials ◽  
Literary Works ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Latin Script ◽  
Made In

Serat Centhini (Suluk Tambanglaras or Suluk Tambangraras-Amongraga) is one of the greatest literary works in New Javanese literature. Its construction began in 1742 Java (1814 AD) during Sunan Pakubuwana IV. The main reference is the Jatiswara book which was made in 1711 Java or 1783 AD during Sunan Pakubuwana III. This article tracks the arithmetic information contained in Serat Centhini, including cardinal numbers, ordinal numbers, Javanese calendar, and candrasengkala. The research was carried out by using the literature study method of Serat Centhini which is translated into Indonesian and transliterated in Latin script. The results showed that Serat Centhini recorded quite a lot of mathematical information which was used in the daily life of Javanese people. The results of this study can be used as teaching materials for ethnomathematics.

Ordinals by Abstraction

2020 ◽  
pp. 240-255
Author(s):  
Bob Hale
Keyword(s):  
Philosophy Of Mathematics ◽  
Ordinal Number ◽  
Abstraction Principle ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Abstraction Principles

The neo-Fregean programme in the philosophy of mathematics seeks to provide foundations for fundamental mathematical theories in abstraction principles. Ian Rumfitt (2018) proposes to introduce ordinal numbers by means of an abstraction principle, (ORD), which says, roughly, that ‘the ordinal number attaching to one well-ordered series is identical with that attaching to another if, and only if, the two series are isomorphic’. Rumfitt’s proposal poses a sharp and serious challenge to those seeking to advance the neo-Fregean programme, for Rumfitt proposes to save (ORD) from threatening paradox by avoiding dependence on an impredicative comprehension principle. However, such a principle is usually taken to be required by the neo-Fregean account of the cardinal numbers. Thus if neo-Fregean foundations for elementary arithmetic are to be saved, we must explain how we can avoid paradox for (ORD) in another way. In this chapter, the prospects for doing so are explored.

Illustrating cardial and ordinal numbers

1963 ◽  
Vol 10 (7) ◽  
pp. 448
Author(s):  
Robert C. McLean
Keyword(s):  
Ordinal Numbers ◽  
Cardinal Numbers

Puzzles are sometimes useful for illustrating differences which may be difficult for some students to understand. There is a routine often used by a well-known team of comedians which well illustrates the pitfalls of confusing ordinal and cardinal numbers. It also underlines the contribution set language can make to clarity of expression.

Letter-Labels in Greek Inscriptions

1954 ◽  
Vol 49 ◽  
pp. 1-8
Author(s):  
Marcus N. Tod
Keyword(s):  
Present Article ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
The Subject ◽  
New Evidence ◽  
Arithmetical Calculation

In a recent volume of this Annual (XLV 126 ff.) I discussed the alphabetic numeral system as employed in Attica; in the present article I examine the use of letters in Attica and elsewhere to identify different items, often similar in character and appearance, with a view of facilitating reference and simplifying inventories. For such a purpose letters have certain advantages over other symbols which might be devised; they are brief and familiar and they occur in a recognized order. They thus approach nearly to the use of ordinal numbers (contrasting sharply with acrophonic numerals, which are invariably used to represent cardinal numbers), though it cannot be said that they constitute a numeral system, any more than we could claim that we in English use an alphabetic numeral system because, e.g., a, b, c, d are used on p. 4 below to distinguish four items which might equally well have been numbered 1, 2, 3 and 4. The letters here under consideration were not, and could not be, made the instruments of arithmetical calculation, and the highest number expressed in this way in any inscription known to me is 106 (Inscr. Délos 1432 Aa ii 21; see below, p. 8).Various scholars have dealt briefly with the subject, but the accumulation of a mass of new evidence calls for a fresh treatment, especially of the part played by such letters in inventories. No technical name has, I believe, been given to letters so used, and in this article I call them ‘letter-labels’, a title which emphasizes the function they fulfil in the majority of cases where they occur.

scholarly journals A Comparative Morphological Approach to Class Maintaining Derivational Affixes in English and Kurdish

2020 ◽  
Vol 6 (4) ◽  
pp. 25
Author(s):  
Muhsin Hama Saeed Qadir ◽  
Saza Ahmed Fakhry Abdulla
Keyword(s):  
Concrete Noun ◽  
Standard English ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Grammatical Categories ◽  
New Meanings ◽  
Abstract Nouns ◽  
Morphological Approach ◽  
Concrete Nouns ◽  
Similarity And Difference

This paper is a comparative morphological study of some class maintaining derivational affixes that do not alter the grammatical categories lexemes in Standard English and Central Kurdish from the standpoints of Generative Morphology. For the comparative analysis of the two languages, some of the derivational affixes that form new meanings from the existing lexemes and retain the grammatical categories of the newly derived lexemes have been classified. The main aim of the study is to identify the points of similarity and difference of class maintaining derivational affixes in both languages. The findings indicate that in the addition of nominal affixes, English and Kurdish are similar in that ‘concrete nouns’ could remain concrete nouns, as well as could convert into abstract nouns by adding certain affixes. In English, a prefix can also be added to a concrete noun to derive a new concrete noun, whereas in Kurdish, only a prefix can be added to an abstract noun to form a concrete noun. In the addition of adjectival affixes, both languages are similar in that adjectives can derive new adjectives by attaching some prefixes and some suffixes to the existing lexemes. In English, the cardinal numbers remain cardinals when the suffixes –teen and –ty are attached to them, whereas in Kurdish the only rare case can be seen when the suffix –a is attached to the two cardinal numerals hawt/ haft ‘seven’ and hašt ‘eight’. The suffixes –th in English and -(h)am and -(h)amin  in Kurdish can be attached to the cardinal numbers to form the ordinal numbers.

Labialization and the so-called sibilant anomaly in Tigrinya

1988 ◽  
Vol 51 (3) ◽  
pp. 525-536 ◽  
Author(s):  
Rainer M. Voigt
Keyword(s):  
Ordinal Numbers ◽  
Cardinal Numbers

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.)

Multitudinous Kinds of Counting Numbers and Their Generating Functions

1970 ◽  
Vol 63 (7) ◽  
pp. 617-621
Author(s):  
Paul J. Zwier
Keyword(s):  
Generating Functions ◽  
Infinite Cardinal ◽  
Real Numbers ◽  
Arithmetic Operations ◽  
Ordinal Numbers ◽  
Cardinal Numbers ◽  
Infinite Sets ◽  
Modern Mathematics

The distinguished mathematician Herman Weyl, in attempting to characterize the “life center” of mathematics, has called mathematics “the science of the infinite.”1 If this was true in 1937, it is even more true today. Thus it is common today not only to consider such infinite sets as the set of all counting numbers, or the set of all real numbers, or the set of subsets of the reals, but to associate numbers with such infinite sets and to perform arithmetic operations with them. Early in the training of any serious student of modern mathematics the terminology of the infinite cardinal numbers and ordinal numbers and their transfinite arithmetic becomes rather standard and commonplace.

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