How to pronounce “diagonalization” in English

That's why this is called Cantor's Diagonalization Proof and it shows there must be more real numbers between zero and one than there are natural numbers extending out

is using in an abstract way the idea of diagonalization.

And this diagonalization

Russell's paradox and the halting problem and the recursion theorem, and so many other principles are using diagonalization at their core.

It's a kind of distilling the abstract diagonalization idea