Sizes of Countable Sets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00375328" target="_blank" >RIV/68407700:21240/24:00375328 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1093/philmat/nkad021" target="_blank" >https://doi.org/10.1093/philmat/nkad021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/philmat/nkad021" target="_blank" >10.1093/philmat/nkad021</a>

Result language

angličtina

Original language name

Sizes of Countable Sets

Original language description

The paper introduces the notion of size of countable sets, which preserves the Part-Whole Principle. The sizes of the natural and the rational numbers, their subsets, unions, and Cartesian products are algorithmically enumerable as sequences of natural numbers. The method is similar to that of Numerosity Theory, but in comparison it is motivated by Bolzano’s concept of infinite series, it is constructive because it does not use ultrafilters, and set sizes are uniquely determined. The results mostly agree, but some differ, such as the size of rational numbers. However, set sizes are only partially, not linearly, ordered. Quid pro quo.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Philosophia Mathematica

ISSN

0031-8019

e-ISSN

1744-6406

Volume of the periodical

32

Issue of the periodical within the volume

1

Country of publishing house

GB - UNITED KINGDOM

Number of pages

33

Pages from-to

82-114

UT code for WoS article

001124109900001

EID of the result in the Scopus database

2-s2.0-85185782581