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Tiling problems
A selection from Proof and the Art of Mathematics
Sep 4
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Joel David Hamkins
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Tiling problems
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August 2024
We can predict the future
Is there a reliable strategy to predict the current and immediate future values of an arbitrary unknown function on the reals?
Aug 28
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Joel David Hamkins
13
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We can predict the future
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The guessing-box puzzle
Which number is in your box? Using the axiom of choice, we shall find a strategy for the guessing-box puzzle, predicting the contents of various…
Aug 21
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Joel David Hamkins
6
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The guessing-box puzzle
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The chocolate bar problem
A brief excerpt from Proof and the Art of Mathematics
Aug 13
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Joel David Hamkins
9
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The chocolate bar problem
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More pointed at than pointing
A selection from Proof and the Art of Mathematics
Aug 7
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Joel David Hamkins
8
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More pointed at than pointing
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3
July 2024
Infinitary Hat Puzzles and the Aftermath
What color is your hat? The hat puzzle genre of logic puzzle grows from easy finite cases to absurd spectacular settings with infinitely many people in…
Jul 30
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Joel David Hamkins
8
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Infinitary Hat Puzzles and the Aftermath
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The Axiom of Choice
Can we choose an element from each set in a family of nonempty sets? Does every set have a well order? Is the axiom of choice arrogant overreach or does…
Jul 21
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Joel David Hamkins
12
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The Axiom of Choice
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Least upper bound principle and continuous induction
The least-upper-bound principle The subject of real analysis can be founded upon the least-upper-bound principle, a version of Dedekind completeness…
Jul 13
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Joel David Hamkins
13
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Least upper bound principle and continuous induction
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Quantifier elimination — Presburger arithmetic
The elementary theory of addition in the natural numbers admits a certain logical triviality—every assertion is equivalent to a simple combination of…
Jul 6
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Quantifier elimination — Presburger arithmetic
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3
June 2024
Quantifier elimination — theory of successor
Every assertion about the structure ⟨ℕ,S,0⟩ of the natural-number successor is trivial, being equivalent to a quantifier-free assertion in this…
Jun 29
9
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Quantifier elimination — theory of successor
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Continuity, instantaneous change, infinitesimals
How we faced the ghosts of departed quantities
Jun 22
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Joel David Hamkins
9
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Continuity, instantaneous change, infinitesimals
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Quantifier elimination — dense linear orders
In certain special theories, every assertion is equivalent to a trivial combination of atomic facts. Proving this for a given theory typically both…
Jun 15
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Joel David Hamkins
7
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Quantifier elimination — dense linear orders
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