Infinitely More

Home
The Book of Infinity
A Panorama of Logic
Infinite Games
Proof and the Art
Philosophy of Mathematics
My books
Music videos
About
Most Popular
View all
Zeno's paradox
 • Joel David Hamkins
13
The Book of Numbers
 • Joel David Hamkins
12
Potential versus actual infinity
 • Joel David Hamkins
16
Structuralism
 • Joel David Hamkins
2

The Book of Infinity

See all
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…
 • 
Joel David Hamkins
2
Infinite Liars (from the archives)
Regrettably, this essay consists entirely of lies—every sentence in it, including this one, is false.
 • 
Joel David Hamkins
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…
 • 
Joel David Hamkins
5

A Panorama of Logic

See all
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…
3
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…
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…
 • 
Joel David Hamkins

Proof and the Art

See all

Philosophy of Mathematics

See all
Infinitely More
Infinitely More
The mathematics and philosophy of the infinite
Recommendations
View all 11
Mindcreaser - Benjamin Portheault's substack
Mindcreaser - Benjamin Portheault's substack
Benjamin Portheault
Pershmail
Pershmail
Michael Pershan
M
Math and Art
Erin Carmody
The Nature-Nurture-Nietzsche Newsletter
The Nature-Nurture-Nietzsche Newsletter
Steve Stewart-Williams
A Piece of the Pi: mathematics explained
A Piece of the Pi: mathematics explained
Richard Green
JDH Links
JDH web page
JDH on Twitter
JDH on Notes
JDH on MathOverflow
JDH on YouTube
JDH on Google Scholar
JDH at MIT Press
My Books
Lectures on the Philosophy of Mathematics, MIT Press 2021
Proof and the Art of Mathematics, MIT Press 2020
Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021
A Mathematician's Year in Japan, Kindle KDP, 2015

Infinitely More

AboutArchiveRecommendationsSitemap
© 2024 Joel David Hamkins
Privacy ∙ Terms ∙ Collection notice
Start WritingGet the app
Substack is the home for great culture