Wyniki wyszukiwania - Biblioteka Nauki

1

Różne reprezentacje liczb rzeczywistych

100%

Pieronkiewicz B.

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2017

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tom 9

49-83

PL

This article is devoted to the different representations of real numbers. In particular, the following types are distinguished and discussed: (1)representations based on theorems referring to the axiomatic characterization of the field of real numbers, (2) genetic representations – related to the construction of real numbers, (3) visual representations – mainly related to the geometrical way of presenting numbers. The paper addresses different representations of real numbers from a higher standpoint as well as from a classroom perspective.

2

Some Remarks of Different Aggregation Modes Applications Within the Framework of Intuitionistic Fuzzy Weights

75%

Tikhonenko-Kędziak A. , Kurkowski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2016

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tom Vol. 21

145--159

EN

In the classical intuitionistic fuzzy sets theory it is known, that the use of all aggregation modes is not always possible, because of the lack of definition of raising intuitionistic fuzzy values to the intuitionistic fuzzy power. The main aim of this work is to introduct an operation of raising of intuitionistic fuzzy values to an intuitionistic fuzzy power,which does not require conversion to intuitionistic fuzzy values. Additionally, we will present a heuristic method of raising an intuitionistic fuzzy values to the intuitionistic fuzzy power and consideration about its properties.

3

On objective and subjective difficulties in understanding the notions of the least upper bound and the greatest lower bound

75%

Jędrzejewski J.

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tom Vol. 12

245-248

EN

The notion of the least upper bound (the greatest lower bound) of a subset of real numbers is discussed from different points of view and some difficulties of this notion are presented.

4

Remarks on connectivity and I-connectivity

75%

Jędrzejewski J. , Kowalczyk S.

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tom Vol. 12

49-54

5

Some remarks on definition of the absolute value of a real number

75%

Major J. , Powązka Z.

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tom Vol. 12

283-288

EN

The article presents a didactic proposition of introducing the definition of the absolute value of a real number.

6

Cantor on Infinitesimals. Historical and Modern Perspective

75%

Błaszczyk P. , Fila M.

Bulletin of the Section of Logic

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2020

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tom 49

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nr 2

EN

In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false.

7

Cantorův diagonální důkaz

63%

Vlasáková M.

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tom 45

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nr 2

153-193

EN

Cantor’s diagonal proof is significant both because the central method of proof used in it has been subsequently applied in a number of other proofs, and because it is considered to confirm the existence of infinite sets whose size fundamentally and by an order of magnitude exceeds the size of the “classical” infinite set represented by all natural numbers, while their size can theoretically exceed every conceivable limit. Although Cantor’s proof is generally accepted by the scientific community, some experts are somewhat reserved about it. The aim of this paper is to present Cantor’s proof in an accessible way, while pointing out its (hidden) assumptions and possible problematic points, and pointing out that some of its underlying assumptions are not indisputable mathematical truths, but rather postulated propositions that may or may not be accepted.

CS

Cantorův diagonální důkaz je významný jednak proto, že jím použitá ústřední dokazovací metoda byla následně aplikována i v řadě dalších důkazů, jednak z toho důvodu, že je považován za potvrzující existenci nekonečných množin, které svojí velikostí zásadně a řádově přesahují velikost „klasického“ nekonečného souboru představovaného všemi přirozenými čísly, přičemž tato jejich velikost může teoreticky překročit kaž dou myslitelnou mez. Ač bývá Cantorův důkaz obecně vědeckou komunitou přijímán, někteří odborníci k němu přistupují poněkud rezervovaně. Cílem tohoto pojednání je představit Cantorův důkaz přístupným způsobem a zároveň poukázat na jeho (skryté) předpoklady a možná problematická místa a upozornit na fakt, že některé z jeho výchozích předpokladů nejsou nějaké nezpochybnitelné matematické pravdy, ale spíše postulované teze, které mohou, ale nemusejí být přijaty.

8

Transient analysis in 1st order electrical circuits in violation of commutation laws

51%

Kukharchuk V. V. , Pavlov S. V. , Katsyv S. S. , Koval A. M. , Holodiuk V. S. , Lysyi M. V. , Kotyra A. , Mamyrbaev O. , Kalabayeva A.

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tom R. 97, nr 9

26--29

EN

The paper considers the usage of non-standard analysis mathematical apparatus to solve some non-trivial problems of electrical engineering theory. The axiomatics of non-standard analysis makes it possible to simplify the transient analysis in the 1st order electrical circuits in violation of the commutation laws. Examples of solving such problems are given.

PL

W artykule rozważono zastosowanie aparatu matematycznego analizy niestandardowej do rozwiązywania niektórych nietrywialnych zadań z teorii elektrotechniki. Aksjomatyka analizy niestandardowej pozwala na uproszczenie analizy stanów nieustalonych w obwodach elektrycznych I rzędu z naruszeniem praw komutacji. Podane są przykłady rozwiązywania takich przypadków.