Counting systems and the First Hilbert problem

被引：30

作者：

Sergeyev, Yaroslav D. ^{[1
,2
]}

机构：

[1] Univ Calabria, I-87036 Arcavacata Di Rende, CS, Italy

[2] NI Lobatchevsky State Univ, Nizhnii Novgorod, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 3-4期

关键词：

The First Hilbert problem; Numeral systems; Piraha counting system; Relativity of mathematical languages; Infinite numbers;

D O I：

10.1016/j.na.2009.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different accuracies. The traditional and the new approaches are compared and discussed. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1701 / 1708

页数：8

共 17 条

[1]

[Anonymous], 2003, ARITHMETIC INFINITY

[2]

[Anonymous], 1956, AM SOCIOL REV

[3]

[Anonymous], 1992, GRAMMATICAL CATEGORI

[4]

CANTOR G, 1955, CONTRIBUTIONS FDN TH

[5]

Cohen P. J., 1966, SET THEORY CONTINUUM

[6]

Gdel K., 1931, Monatshefte fr Mathematik, V38, P173, DOI DOI 10.1007/BF01700692

[7]

Godel Kurt, 1940, Annals of Mathematics Studies, V3

[8] Numerical cognition without words: Evidence from Amazonia [J].

Gordon, P .

SCIENCE, 2004, 306 (5695) :496-499

[9]

Gumperz J., 1996, Rethinking linguistic relativity

[10]

Hilbert D., 1902, Bull. Am. Math. Soc, V8, P437, DOI [10.1090/S0002-9904-1902-00923-3, DOI 10.1090/S0002-9904-1902-00923-3]

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