I have the greatest admiration for the theorems and proofs of transfinite set theory, what we've called Cantor's transfinite set theory.

I taught it for years, wrote restatements for my students, and wrote a piece viewing it in the perspective of historical thinking about the infinite.
http://nrs.harvard.edu/urn-3:HUL.InstRepos:3715468

Now I've learned that #Cantor deliberately suppressed the role of #Dedekind in some of his work, particularly the proof that the set of real numbers is larger than the sets of natural and rational numbers. This was the first glimpse of the infinite hierarchy of infinite cardinalities.
https://www.quantamagazine.org/the-man-who-stole-infinity-20260225/

Cantor had the first germ of the proof, so props for that. But Dedekind helped him clarify it and Cantor published the clarified version without credit to Dedekind. I respect the math as much as ever but am now dealing with a serious case of flawed-hero syndrome.

First, make amends. Kudos to Dedekind. Second, give thanks. Kudos to the sleuths who turned up the empirical evidence of Cantor's #plagiarism -- Emmy Noether, Ivor Grattan-Guinness, José Ferreirós, and (decisively) Demian Goos.

Also thanks to Joseph Howlett for the Quanta article summarizing the evidence -- and in passing for calling Leopold #Kronecker an ideologue. Exactly!

#Infinity #Mathematics #SetTheory

If I'm really committed to the fact that there is no such thing as actual infinity - and I am: https://www.wisdomneverdies.com/blog/no-infinity -
then there are no actual irrational numbers. By Kronecker's Theorem then, all apparently chaotic behavior is ultimately periodic. An interesting corollary 🙂

#infinity #math #philosophy #Cavendish #Cantor #Locke #Aristotle #Knuth #chaos #Kronecker #Diophantine

The real vectorization vec(⋅) stacks the input columns into a vector. The Kronecker product ⊗ is related by vec(ABC) = (Cᵀ ⊗ B) vec(B).

We can similarly define a complex version vecc(⋅) = [vec(Re(⋅)); vec(Im(⋅))], with a corresponding #Kronecker product kroncc(⋅,⋅) such that vecc(ABC) = kroncc(Cᵀ, B) vecc(B).

Does anyone know of any literature that discusses the relevant properties of vecc and kroncc? They naturally appear when computing #Jacobians of functions of complex matrices.

'EiGLasso for Scalable Sparse Kronecker-Sum Inverse Covariance Estimation', by Jun Ho Yoon, Seyoung Kim.

http://jmlr.org/papers/v23/21-0511.html

#kronecker #sparse #gaussian