Infinitely More

Infinitely More

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Zeno's paradox
An ancient puzzle leads ultimately to a remarkable observation on the malleable nature of infinite sums
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Joel David Hamkins
14
The Book of Numbers
All the numbers, placed in a curious order
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Joel David Hamkins
12
Potential versus actual infinity
Potentialism and actualism offer radically different conceptions of the infinite—the dispute between them will lead us to ultrafinitism and the diverse…
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Joel David Hamkins
20
The surreal numbers
All the numbers great and small. The surreal numbers, generated in a recursive process of completion, unify the real numbers, the ordinals, and the…
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Joel David Hamkins
5
Structuralism
For mathematical insight, according to the structuralist imperative, investigate mathematical structure and consider mathematical concepts only as…
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Joel David Hamkins
2
Epistemic logic and the problem of common knowledge
With the two generals, Cheryl's birthday, hidden surprises, blue-eyed islanders, pirate treasure division, philosopher's ruling council, coordination…
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Joel David Hamkins
3
Classical propositional logic—introduction
Propositional logic as a clarification of ambiguity, truth tables, propositional worlds, logical entailment, validity, tautologies
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Joel David Hamkins
10
Infinite liars
Regrettably, this chapter consists entirely of lies—every sentence in it, including this one, is false.
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Joel David Hamkins
3
What is the essential structure of the complex numbers?
I discuss several commonly held perspectives on the complex numbers and explore how their differences engage with several aspects of structuralism in…
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Joel David Hamkins
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…
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Joel David Hamkins
2
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?
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Joel David Hamkins
8
The continuum hypothesis
Is there any infinity strictly between the infinity of the natural numbers ℕ and the infinity of the real numbers ℝ?
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Joel David Hamkins
10
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