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- Title
On the Brink of Paradox: by Augustín Rayo MIT PRESS, 2019, 302 PP., US$ 45.00, ISBN: 978-0-262-03941-3 REVIEWED BY ANDREW J. SIMOSON.
- Authors
Simoson, Andrew
- Abstract
Thus HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">S</mi></math> ht is a theorem. Paradoxes abound here, for many bounded subsets of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="double-struck">R</mi></math> ht cannot be measured reasonably unless we allow the usually untenable premise that the sum of the parts may exceed the whole. From each equivalence class, select a member HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht by the axiom of choice, and let I B i be the set of all numbers HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo>+</mo><mfrac><mi>p</mi><mi>q</mi></mfrac></mrow></math> ht for all odd integers I p i and I q i . Next, refine this statement to the following self-referential statement HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">S</mi></math> ht : I I am a statement that has no proof. i We show that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">S</mi></math> ht is a true statement.
- Subjects
PARADOX; MATHEMATICAL proofs; ZENO'S paradoxes; TURING machines
- Publication
Mathematical Intelligencer, 2022, Vol 44, Issue 3, p296
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-021-10139-w