Infinity
There are Different Kinds of Infinities
From Brilliance to Madness
Cantor
Philosophy
Beginner’s Guide to Mathematical Constructivism
The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’
Set Theory
When Cantor Taught us to Count
My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. — Georg Cantor
Set Theory
Refuting the Refutation of Cantor
On August 2. 2020 Cantor’s Paradise published Bruno Campello’s brief critique of Cantor’s approach in transfinite mathematics. The author…
Analysis
Cantor’s Diagonal Argument
“Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén…
Analysis
Cantor Pairing Function
Represent an ordered pair of integers with a single integer.
Set Theory
Proving Cantor’s Theorem
“No one will drive us from the paradise which Cantor created for us” — David Hilbert
Number Theory
Proving The Existence of Transcendental Numbers
… and how to compare the infinite?
Mathematics
The Nature of Infinity — and Beyond
An introduction to Georg Cantor’s transfinite paradise