scholarly journals Peningkatan Kemampuan Membaca Ordinal Number dengan Menggunakan Bola-Bola Hypnotist dalam 5M

2021 ◽  
Vol 5 (3) ◽  
pp. 821-842
Author(s):  
Zaimatun Zaimatun
Keyword(s):  
Ordinal Number

Tujuan penggunaan bola-bola hypnotist dalam 5M adalah untuk meningkatkan kemampuan membaca ordinal number dan keaktifan peserta didik dalam pembelajaran. Bola-bola hypnotist adalah media komunikasi dalam penerapan hypnoteaching. Sedangkan, 5M adalah pendekatan saintifik, yang melipuiti mengamati, menanya, mengumpulkan data, mengasosiasi, dan mengomunikasi. Metode penelitian ini adalah PTK model Stephen Kemmis dan Robyn Mc. Taggart yang meliputi dua siklus. Setiap siklus terdiri atas perencanaan, tindakan, observasi, dan refleksi. Hasil penelitian menunjukkan dengan bola-bola hypnotist dalam 5M kemampuan membaca ordinal number peserta didik mengalami peningkatan sebesar 38,35%. Keaktifan belajar peserta didik juga meningkat 17,24%. Bola-bola hypnotist dalam  5M sangat membantu peserta didik dalam pembelajaran.

On the Sequentiality of Ordinality and Cardinality

1981 ◽  
Vol 4 (4) ◽  
pp. 391-402 ◽  
Author(s):  
J. Kingma ◽  
W. Koops
Keyword(s):  
Primary School ◽  
Ordinal Number ◽  
Difficulty Level ◽  
School Grade ◽  
The Future ◽  
Task Variables ◽  
Number Development

Some research with Brainerd-like number tasks is reported. 266 subjects (from kindergarten and from primary school grade 1) completed 4 tasks: concrete ordinal correspondence tasks, abstract ordinal correspondence tasks, ordinal number tasks, and cardinal tasks. Results revealed no differences in difficulty level between concrete and abstract ordinal correspondence tasks. The ordinal number tasks were more difficult than the ordinal correspondence tasks. The data also suggest that the child acquires ordinality prior to cardinality. The last finding confirms the conclusion of Brainerd (1978, 1979). Nevertheless, these conclusions are rather weak because of serious differences in psychometric qualities between different kinds of tasks, because of poor operational definitions of cardinality and ordinality, and because of uncontrolled differences in task sensitivity. Only with more refined analyses of task variables will the future of a theory of number development be promising.

scholarly journals “How did the serpent of inconsistency enter Frege’s paradise?”

2019 ◽  
pp. 411-436
Author(s):  
Crispin Wright
Keyword(s):  
Cardinal Number ◽  
Ordinal Number ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Indefinite Extensibility ◽  
Basic Law ◽  
Per Se

The paper explores the alleged connection between indefinite extensibility and the classic paradoxes of Russell, Burali-Forti, and Cantor. It is argued that while indefinite extensibility is not per se a source of paradox, there is a degenerate subspecies—reflexive indefinite extensibility—which is. The result is a threefold distinction in the roles played by indefinite extensibility in generating paradoxes for the notions of ordinal number, cardinal number, and set respectively. Ordinal number, intuitively understood, is a reflexively indefinitely extensible concept. Cardinal number is not. And Set becomes so only in the setting of impredicative higher-order logic—so that Frege’s Basic Law V is guilty at worst of partnership in crime, rather than the sole offender.

scholarly journals Duration of colonial bird species egg incubation

2018 ◽  
Vol 7 (1) ◽  
pp. 58-64
Author(s):  
Yuri Gennadievich Lamekhov
Keyword(s):  
Ordinal Number ◽  
Bird Species ◽  
Early Ontogeny ◽  
Egg Laying ◽  
Early Ontogenesis ◽  
Time Interval ◽  
Egg Incubation ◽  
Colonial Bird ◽  
Incubation Duration ◽  
Colonial Settlement

The paper deals with one of the aspects of bird early ontogenesis biology - egg incubation duration, which was defined as the time interval between egg laying and hatching from it. The oomorphological parameters are determined taking into account the ordinal number of the laid eggs. Parameters of early ontogeny of birds are studied on the example of colonially nesting species: blackberry toadstool ( Podiceps nigricollis C.L. Brehm.) and lake gull ( Larus ridibundus L.). Within the colonial settlement of these species, the biological center and the periphery of the colony were isolated. When studying the parameters of early ontogeny of birds and oomorphological characteristics, the same number of eggs was taken into account. During field and laboratory studies it was found that the incubation of eggs lasts longer in eggs from the nests of the biological center of the colony. The first eggs are incubated longer. These features clearly manifested in the early ontogeny of the gull. The increase in the egg incubation duration occurs against the background of an increase in their mass and a decrease in the concentration of lysozyme in the protein shell of the egg. Egg incubation duration is one of the results of embryonalization as a way of evolution of ontogeny. The manifestation of the results of embryogenesis was revealed for the first eggs in the nests of the biological center of the colony. Embryonalization leads to an increase in egg incubation duration as well as to a decrease in the intensity of elimination in early ontogenesis, which affects the number of individuals breeding in the colony and, accordingly, the structure of the colonial settlement of birds.

scholarly journals Гадание по хулилам среди монголов

2021 ◽  
Vol 14 (3) ◽  
pp. 550-567
Author(s):  
Anna D. Tsendina ◽  
◽  
Keyword(s):  
Present Article ◽  
Russian Translation ◽  
Ordinal Number ◽  
Seventh Century ◽  
I Ching ◽  
Book Of Changes ◽  
The Subject

Introduction. Various collections of Mongolian xylographs and manuscripts may contain works on divination practice with eight khulils. What does the word khulil mean? Why does one use eight khulils? What are the texts devoted to the khulil divination? This article deals with the practice of khulil divination in Mongolia, while introducing a Mongolian text devoted to this form of divination. Results. The divination practice goes back to the oldest Chinese source on divination Yijing (I Ching, Book of Changes, about the seventh century BC). Divination is carried out with the help of the trigram, or the three dashes, which are the result of casting coins or of some other method. A combination of trigrams means a particular future. These three lines are called khulil in Mongolian (gua in Chinese). Divination by 8 gua, or 8 khulils, and 64 (8 × 8) or 512 (8 × 8 × 8) combinations is the most common form of divination in China. Later, each trigram was represented by a year of the 12-year animal cycle so that the ninth year was the beginning of the next cycle. Thus, each of the 8 years symbolizes a certain trigram, or khulil, according to the ordinal number of the latter. Granted the number of Mongolian manuscripts on khulil divination in various collections, this divination form was widely practiced by Mongolians. By way of introducing the literature on the subject, the present article presents the Russian translation of the initial fragment of manuscript MN 1145 originating from Ts. Damdinsuren museum in Ulaanbaatar. This is a Mongolian translation from Chinese made relatively late that has few traces of Mongolization or efforts of adaptation to nomadic realia. Besides concerns for the illnesses of relatives or issues of choosing a son-in-law or a bride, which are of a universal character, the most popular topics are questions about farming, such as: should one expect rain? what will be the harvest of grain and raw silk? Also, there are many questions related to promotion and career, e.g., passing exams for the degree of an official. The text contains numerous Sinicisms, including idioms, expressions, and names of Chinese astrological signs; there is also a reference to buying a jins, which points to the Manchu period. Notably, neither Tibetan items nor Buddhist deities are mentioned in the text.

WARFIELD INVARIANTS IN COMMUTATIVE GROUP ALGEBRAS

2008 ◽  
Vol 07 (03) ◽  
pp. 337-346 ◽  
Author(s):  
PETER V. DANCHEV
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Group Algebra ◽  
Ordinal Number ◽  
Commutative Group ◽  
Group Algebras

Let F be a field and G an Abelian group. For every prime number q and every ordinal number α we compute only in terms of F and G the Warfield q-invariants Wα, q(VF[G]) of the group VF[G] of all normed units in the group algebra F[G] under some minimal restrictions on F and G. This expands own recent results from (Extracta Mathematicae, 2005) and (Collectanea Mathematicae, 2008).

Products of some special compact spaces and restricted forms of AC

2010 ◽  
Vol 75 (3) ◽  
pp. 996-1006 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis
Keyword(s):  
Set Theory ◽  
Closed Subset ◽  
Choice Function ◽  
Ordinal Number ◽  
Axiom Of Choice ◽  
Finite Support ◽  
Compact Spaces ◽  
The Axiom Of Choice ◽  
Infinite Set

AbstractWe establish the following results:1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent:(a) The Tychonoff product of ∣α∣ many non-empty finite discrete subsets of I is compact.(b) The union of ∣α∣ many non-empty finite subsets of I is well orderable.2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1]Iwhich consists offunctions with finite support is compact, is not provable in ZF set theory.3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF0 (i.e., ZF minus the Axiom of Regularity).4. The statement: For every set I, every ℵ0-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ0many non-empty finite discrete subsets of I is compact, is not provable in ZF0.

A Measure Theoretical Version of the Aleksandrov Theorem

2008 ◽  
Vol 15 (1) ◽  
pp. 53-61
Author(s):  
Majid Gazor
Keyword(s):  
Borel Measure ◽  
Measure Theory ◽  
Ordinal Number ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Closed Sets

Abstract In this paper a theorem analogous to the Aleksandrov theorem is presented in terms of measure theory. Furthermore, we introduce the condensation rank of Hausdorff spaces and prove that any ordinal number is associated with the condensation rank of an appropriate locally compact totally imperfect space. This space is equipped with a probability Borel measure which is outer regular, vanishes at singletons, and is also inner regular in the sense of closed sets.

scholarly journals Ordinal numbers and the Hilbert basis theorem

1988 ◽  
Vol 53 (3) ◽  
pp. 961-974 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Ordinal Number ◽  
Second Order ◽  
Weak Base ◽  
Apparent Lack ◽  
Hilbert Basis ◽  
Second Order Arithmetic ◽  
Basis Theorem ◽  
Logical Strength ◽  
Ring Of Polynomials ◽  
Order Arithmetic

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 x1,…,xm. The Hilbert basis theorem asserts that for all K and m, every ideal in the ring K[x1,…,xm] is finitely generated. This theorem is of fundamental importance for invariant theory and for algebraic geometry. There is also a generalization, the Robson basis theorem [11], which makes a similar but more restrictive assertion about the ring K〈x1,…,xm〉 of polynomials over K in mnoncommuting indeterminates.In this paper we study a certain formal version of the Hilbert basis theorem within the language of second order arithmetic. Our main result is that, for any or all countable fields K, our version of the Hilbert basis theorem is equivalent to the assertion that the ordinal number ωω is well ordered. (The equivalence is provable in the weak base theory RCA0.) Thus the ordinal number ωω is a measure of the “intrinsic logical strength” of the Hilbert basis theorem. Such a measure is of interest in reference to the historic controversy surrounding the Hilbert basis theorem's apparent lack of constructive or computational content.

Flat sets

1994 ◽  
Vol 59 (3) ◽  
pp. 1012-1021
Author(s):  
Arthur D. Grainger
Keyword(s):  
Set Theory ◽  
Ordinal Number ◽  
Transfer Principle ◽  
Nonstandard Model ◽  
Infinite Set

AbstractLet X be a set, and let be the superstructure of X, where X0 = X and is the power set of X) for n ∈ ω. The set X is called a flat set if and only if for each x ∈ X, and x ∩ ŷ = ø for x, y ∈ X such that x ≠ y. where is the superstructure of y. In this article, it is shown that there exists a bijection of any nonempty set onto a flat set. Also, if is an ultrapower of (generated by any infinite set I and any nonprincipal ultrafilter on I), it is shown that is a nonstandard model of X: i.e., the Transfer Principle holds for and , if X is a flat set. Indeed, it is obvious that is not a nonstandard model of X when X is an infinite ordinal number. The construction of flat sets only requires the ZF axioms of set theory. Therefore, the assumption that X is a set of individuals (i.e., x ≠ ϕ and a ∈ x does not hold for x ∈ X and for any element a) is not needed for to be a nonstandard model of X.

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