The mathematics and philosophy of the infinite
| Platform |  | Pricing | Freemium | Publishes | Weekly |
|---|---|---|---|---|---|
| Issues | 161 | Founded | 4 years ago | Last Issue | 5 days ago |
| Active | |||||
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The Natural Field of Ordinals
Which numbers are transcendental over the ordinals? Which are irrational? Let us introduce the natural field of ordinals and consider the status of √2, √ω, e, and π, among other numbers.
Which numbers are transcendental over the ordinals?...
Fermat’s last theorem in the natural ring of ordinals
Are there any nontrivial solutions of the famous Fermat equation in the natural ring of ordinals?
Let’s have some fun by considering whether Fermat’s last theorem holds in the natural ring of ordinals. What do you think? I expect that you...
Set theory, pluralism, and the multiverse view—About Logic #13
Recently I was invited by Deniz Sarikaya and Thorsten Altenkirch to appear on their podcast About Logic to talk about logic, the philosophy of mathematics, and set theory. The episode has now been released, so please take a look—I think you...
Regrettable Failures in the Natural Ring of Ordinals
The natural ring of ordinals has unique prime factorization, but other natural features go wrong—the concept of even goes awry, greatest common divisors do not fulfill Bézout’s identity, and more.
In recent essays we have been investigatin...
The Natural Ring of Ordinals Has Prime Factorization
The natural ring of ordinals is a unique factorization domain—every number factors uniquely as a finite product of primes.
The natural ring of ordinals ⟨Ord⟩ is the mathematical system of numbers generated by the ordinals with the operatio...
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Mathematics and Philosophy of the Infinite
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