Visualizing paradoxical sets (Q483351)
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scientific article; zbMATH DE number 6380988
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Visualizing paradoxical sets |
scientific article; zbMATH DE number 6380988 |
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Visualizing paradoxical sets (English)
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17 December 2014
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This paper shows how several counterintuitive ideas of set theory, such as the Banach-Tarski paradox and the existence of a certain type of Sierpiński set, can be given concrete interpretations in the hyperbolic plane. The authors use the upper-half plane model of hyperbolic geometry and the Poincaré disk model. The article ends with a conjecture which states that there is no discrete weak Sierpiński set in \(\mathbb R^3\).
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Banach-Tarski paradox
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Sierpiński set
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Hausdorff paradox
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paradoxical set
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