Temat: real numbers - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Różne reprezentacje liczb rzeczywistych
The different representations of real numbers
Autorzy:: Pieronkiewicz, Barbara
Tematy:: real numbers
number representations
transparent representation; Pokaż więcej
Wydawca:: Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Powiązania:: https://bibliotekanauki.pl/articles/1791028.pdf Link otwiera się w nowym oknie
Opis:: 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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Cantor on Infinitesimals. Historical and Modern Perspective
Autorzy:: Błaszczyk, Piotr
Fila, Marlena
Tematy:: infinitesimals
infinite numbers
real numbers
hyperreals
ordinal numbers
Conway numbers; Pokaż więcej
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Powiązania:: https://bibliotekanauki.pl/articles/750052.pdf Link otwiera się w nowym oknie
Opis:: 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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Galileo’s paradox and numerosities
Autorzy:: Błaszczyk, Piotr
Tematy:: non-standard real numbers
numerosities
cardinal numbers
Galileo's paradox; Pokaż więcej
Wydawca:: Copernicus Center Press
Powiązania:: https://bibliotekanauki.pl/articles/1943055.pdf Link otwiera się w nowym oknie
Opis:: Galileo's paradox of infinity involves comparing the set of natural numbers, N, and the set of squares, {n2 : n ∈ N}. Galileo (1638) sets up a one-to-one correspondence between these sets; on this basis, the number of the elements of N is considered to be equal to the number of the elements of {n2 : n ∈ N}. It also characterizes the set of squares as smaller than the set of natural numbers, since ``there are many more numbers than squares". As a result, it concludes that infinities cannot be compared in terms of greater--lesser and the law of trichotomy does not apply to them. Cantor's cardinal numbers provide a measure for sets. Cantor (1897) gives a definition of the relation greater–lesser between cardinal numbers and establishes the law of trichotomy for these numbers. Yet, when Cantor's theory is applied to subsets of N, it gives that any set can be either finite or of the power ℵ0. Thus, although the set of squares is the subset of N, they are of the same cardinality. Benci, Di Nasso (2019) introduces specific numbers to measure sets called numerosities. With numerosities, the following claim is true: numerosity of A < numerosity of B, whenever A ⊈ B. In this paper, we present a simplified version of the theory of numerosities that applies to subsets of N. This theory complies with Galileo's presupposition that when A ⊈ B, then the number of elements in A is smaller than the number of elements in B. Specifically, we show that as the numerosity of N is the number α, the numerosity of the set of squares is the integer part of the number √α, that is ⌊√α⌋, and the inequality ⌊√α⌋ < α holds.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Some Remarks of Different Aggregation Modes Applications Within the Framework of Intuitionistic Fuzzy Weights
Autorzy:: Tikhonenko-Kędziak, A.
Kurkowski, M.
Tematy:: zbiór rozmyty
liczba rzeczywista
MCDM
fuzzy set
real numbers; Pokaż więcej
Wydawca:: Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Powiązania:: https://bibliotekanauki.pl/articles/121800.pdf Link otwiera się w nowym oknie
Opis:: 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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Three algebraic number systems based on the q-addition with applications
Autorzy:: Ernst, Thomas
Tematy:: q-real numbers
q-rational numbers
q-integers
q-trigonometric functions
biring
semiring; Pokaż więcej
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Powiązania:: https://bibliotekanauki.pl/articles/2078940.pdf Link otwiera się w nowym oknie
Opis:: In the spirit of our earlier articles on $q-\omega$ special functions, the purpose of this article is to present many new $q$-number systems, which are based on the $q$-addition, which was introduced in our previous articles and books. First, we repeat the concept biring, in order to prepare for the introduction of the $q$-integers, which extend the $q$-natural numbers from our previous book. We formally introduce a $q$-logarithm for the $q$-exponential function for later use. In order to find $q$-analogues of the corresponding formulas for the generating functions and $q$-trigonometric functions, we also introduce $q$-rational numbers. Then the so-called $q$-real numbers $\mathbb{R}_{\oplus_{q}}$, with a norm, a $q$-deformed real line, and with three inequalities, are defined. The purpose of the more general $q$-real numbers $\mathbb{R}_{q}$ is to allow the other $q$-addition too. The closely related JHC $q$-real numbers $\mathbb{R}_{\boxplus_{q}}$ have applications to several $q$-Euler integrals. This brings us to a vector version of the $q$-binomial theorem from a previous paper, which is associated with a special case of the $q$-Lauricella function. New $q$-trigonometric function formulas are given to show the application of this umbral calculus. Then, some equalities between $q$-trigonometric zeros and extreme values are proved. Finally, formulas and graphs for $q$-hyperbolic functions are shown.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Some properties of openly ϱ-continuous functions
Autorzy:: Nowakowska, K.
Tematy:: funkcja rzeczywista
zestaw liczb rzeczywistych
funkcja ciągła
actual function
set of real numbers
continuous function; Pokaż więcej
Wydawca:: Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Powiązania:: https://bibliotekanauki.pl/articles/121872.pdf Link otwiera się w nowym oknie
Opis:: In the paper we present definition and some properties of openly ϱ-upper continuous functions. Connections with ϱ-upper continuous and porouscontinuous functions are studied.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: FUZZY NUMBERS IN VALUATION OF REAL INVESTMENT PROFITABILITY
Autorzy:: Górski, Arkadiusz
Tematy:: real investment profitability
fuzzy numbers
Certainty Equivalent; Pokaż więcej
Wydawca:: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie
Powiązania:: https://bibliotekanauki.pl/articles/599566.pdf Link otwiera się w nowym oknie
Opis:: In response to the weakness of traditional efficiency assessment methods taking risk into account, the modification of the Certainty Equivalent method is proposed in this paper. The possibility of connecting solutions from different fields provides for the elaboration of a more effective tool to illustrate and indicate the accurate level of risk in the investment efficiency calculus, which is the matter under consideration in the paper. The authors propose to use the modified method of a Certainty Equivalent that is based on fuzzy numbers. The aim of the method is to make decisions that are less incorrect. The work should be treated as an introduction to proposed further research on the subject.
Dostawca treści:: Biblioteka Nauki

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