The notion of infinite measuring number and its relevance in the intuition of infinity
Tall, David. (1980) The notion of infinite measuring number and its relevance in the intuition of infinity. Educational Studies in Mathematics, Vol.11 (No.3). pp. 271-284. ISSN 0013-1954
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Official URL: http://dx.doi.org/10.1007/BF00697740
In this paper a concept of infinity is described which extrapolates themeasuring properties of number rather thancounting aspects (which lead to cardinal number theory).
Infinite measuring numbers are part of a coherent number system extending the real numbers, including both infinitely large and infinitely small quantities. A suitable extension is the superreal number system described here; an alternative extension is the hyperreal number field used in non-standard analysis which is also mentioned.
Various theorems are proved in careful detail to illustrate that certain properties of infinity which might be considered false in a cardinal sense are true in a measuring sense. Thus cardinal infinity is now only one of a choice of possible extensions of the number concept to the infinite case. It is therefore inappropriate to judge the correctness of intuitions of infinity within a cardinal framework alone, especially those intuitions which relate to measurement rather than one-one correspondence.
The same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Social Sciences > Institute of Education ( -2013)|
|Library of Congress Subject Headings (LCSH):||Infinity, Mathematics|
|Journal or Publication Title:||Educational Studies in Mathematics|
|Page Range:||pp. 271-284|
|Access rights to Published version:||Open Access|
 Fischbein, E.: 1978, ‘Intuition and mathematical education’, Osnabrücker Schriften
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