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In this paper a concept of infinity is described which extrapolates themeasuring properties of number rather thancounting aspects (which lead to cardinal number theory).\ud 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.\ud 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.\ud The same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.\u

Topics:
QA

Publisher: Springer Netherlands

Year: 1980

OAI identifier:
oai:wrap.warwick.ac.uk:506

Provided by:
Warwick Research Archives Portal Repository

- (1976). Foundations of Infinitesimal Calculus,
- (1980). Infinitesimals constructed algebraically and interpreted geometrically’, Mathematical Education for Teachers
- (1978). Intuition and mathematical education’,
- (1980). Looking at graphs through infinitesimal microscopes, windows and telescopes’,
- (1979). The intuition of infinity’,

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