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ERIC Number: EJ925083
Record Type: Journal
Publication Date: 2005-Aug
Pages: 19
Abstractor: As Provided
Reference Count: 41
ISBN: N/A
ISSN: ISSN-0926-7220
Bolzano's Approach to the Paradoxes of Infinity: Implications for Teaching
Waldegg, Guillermina
Science & Education, v14 n6 p559-577 Aug 2005
In this paper we analyze excerpts of "Paradoxes of the Infinite", the posthumous work of Bernard Bolzano (1781-1848), in order to show that Georg Cantor's (1845-1918) approach to the problem of defining actual mathematical infinity is not the most natural. In fact, Bolzano's approach to the paradoxes of infinity is more intuitive, while remaining internally coherent. Bolzano's approach, however, had limitations. We discuss implications for teaching, which include a better understanding of the responses of students to situations involving actual mathematical infinity, for it is possible to draw a kind of parallel between these responses and Bolzano's reasoning.
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A