Riffs on the infinite ping-pong ball conundrum

• Autores: Ami Mamolo, Tristram Bogart
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 42, Nº. 5, 2011, págs. 615-623
• Idioma: inglés
• DOI: 10.1080/0020739x.2011.562317
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• Resumen

  • This article presents a novel re-conceptualisation to a well-known problem - The Ping-Pong Ball Conundrum. We introduce a variant of this super-task by considering it through the lens of 'measuring infinity' - a conceptualisation of infinity that extrapolates measuring properties of numbers, rather than cardinal properties. This approach is consistent with a nonstandard analysis approach to infinite numbers, and gives credence to the intuitive (but otherwise normatively incorrect) resolution. We explore the mathematical motivation and consequences of this variant, as well as offer further 'riffs' on the infinite ball problem for consideration.