Finitism in Geometry

[Revised entry by Jean Paul Van Bendegem on May 18, 2015. Changes to: Main text, Bibliography, supplement.html] In our representations of the world, especially in physics, (mathematical) infinities
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[Revised entry by Jean Paul Van Bendegem on May 18, 2015. Changes to: Main text, Bibliography, supplement.html] In our representations of the world, especially in physics, (mathematical) infinities play a crucial role. The continuum of the real numbers, (Re), as a representation of time or of one-dimensional space is surely the best known example and, by extension, the (n)-fold cartesian product, (Re^{n}), for (n)-dimensional space. However, these same infinities also cause problems. One just has to think about Zeno's paradoxes or the present-day continuation of that discussion, namely the discussion about supertasks, to see the difficulties (see...

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News source: Stanford Encyclopedia of Philosophy

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