Unveiling Infinity: Cantor's Bold Challenge and Infinite Hotel Paradox
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Resources & Recommendations
Books
- "Mathematical Adventures" - This book by Asuka contains a good illustration of Cantor's method for arranging fractions.
Videos & Documentaries
- 60 Second Adventures in Thought (Open University, UK) - A mini-series of videos that includes a discussion of Hilbert's infinite hotel, illustrating properties of countable infinity.
People Mentioned
- Kronecker - A mathematician who opposed Cantor's work and prevented him from returning to the University of Berlin.
- David Hilbert - An influential mathematician born in Königsberg and died in Göttingen, known for his work, including Hilbert's infinite hotel thought experiment, and as an advocate for Cantor's work.
- Paul Cohen - An American mathematician who contributed to the understanding of the continuum hypothesis.
- Pythagoras - Referenced in the context of representing numbers as a ratio of two numbers (fractions).
Concepts & Theories
- Königsberg Bridge Problem - A famous problem in mathematics, mentioned in relation to David Hilbert's birthplace.
- Hilbert's Infinite Hotel - A thought experiment used to illustrate the properties of countable infinity, particularly how an infinite hotel can always accommodate more guests even when full.
- L'Hopital's Rule - A rule in calculus mentioned in the context of dealing with infinity.
Organizations & Institutions
- University of Berlin - The university where Cantor studied and wished to work.
- University of Halle - The university where Cantor spent his career.
- Open University (UK) - Produces the "60 Second Adventures in Thought" video series.
Websites & Online Resources
- infinitelyirrational.com - The podcast's official website for more math and research behind the stories.