Only one pair of integers satisfy the equation m^n = n^m

Re:Only one pair of integers satisfy the equation m^n = n^m by actuallyalys on Thursday April 20, 2023 @03:45PM (#35645264)

This back-and-forth makes me wonder, is it possible to write proofs about proofs? e.g., you cannot prove this result without logarithms or there must exist a proof that involves prime factors?

I suppose at least some proofs vaguely like that are possible because Gödel's incompleteness theorem is one, although I suspect that that same theorem puts some constraints on these "metaproofs."

[ Parent | on HN ]

Re:Only one pair of integers satisfy the equation m^n = n^m by pdpi on Friday April 21, 2023 @09:04AM (#35653099)

Well, Proof Theory is a branch of maths in its own right, and Category Theory also has a definite "meta-proof-y" feel to it.

[ Parent | on HN ]

Re:Only one pair of integers satisfy the equation m^n = n^m by westurner on Friday April 21, 2023 @10:51AM (#35654628)

Axiomatic system > Axiomatic method https://en.wikipedia.org/wiki/Axiomatic_system#Axiomatic_met...

Inference https://en.wikipedia.org/wiki/Inference ; inductive, deductive, abductive

Propositional calculus > Proofs in propositional calculus: https://en.wikipedia.org/wiki/Propositional_calculus

Quantum logic: https://en.wikipedia.org/wiki/Quantum_logic

https://twitter.com/westurner/status/1609495237738496000 :

Is quantum logic the correct logic for propositional logic?

What are quantum "expectation values"; and how is that Axiomatic wave operator system different from standard propositional calculus?

[ Parent | on HN ]

Re:Only one pair of integers satisfy the equation m^n = n^m by dvt on Saturday April 22, 2023 @02:12PM (#35669397)

> is it possible to write proofs about proofs

Yep, I took several metamathematics classes at UCLA! Mostly on proof theory, but also analyzing metamathematical results (like Godel's theorems, Henkin construction, and so on).

[ Parent | on HN ]