Diagonal Argument : Cantor, Turing, Tarski and Lawvere
Channel: Mathematical Coincidence
Date: 2021-12-06

Diagonal Argument with 3 theorems from Cantor, Turing and Tarski. I show how these theorems use the diagonal arguments to prove them, then i show how they are related to Lawvere theorem and how it can change your point of view about them.

The paper on Lawvere theorem and self referential paradoxes from Noson S. Yanofsky : https://arxiv.org/pdf/math/0305282.pdf

Update : There is a mistake at 5:50 on the turing proof : the "reverse diagonal program" definition should be {1 if d(i)=0, Undefined if d(i)=1} which means it should stop if the program loop and loop (undefined) if the program stop.

#mathematics #math #maths #turing  #cantor #proof #diagonal #self #theorem #theorems #category #paradox #surjective 

Music : https://soundcloud.com/user-938398110/ambiance-diagonal?utm_source=clipboard&utm_medium=text&utm_campaign=social_sharing