Re: Cantor Diagonal Proof

On Sun, 13 Apr 2025 19:57:14 -0400, Richard Damon wrote:

On 4/13/25 5:30 PM, Lawrence D'Oliveiro wrote:

>
Here’s another way to look at the Cantor construction.
 
It is possible to construct a list of numbers, ostensibly from ℝ, where
it is provable, by induction, that the Cantor construction cannot
produce a number not in the list. This shows that you cannot prove, a
priori, the validity of the Cantor construction.

 
Why not?

See my construction of the flipped-integer list.

But he didn't use "induction" to make his proof.

Precisely.

He used basic inspection.

How do you conduct an infinity of “basic inspections”?

That is merely an application of simple logic.

“We hold these truths to be self-evident”, is it?

But we don't need an axiom to show it works.

Yes we do. Because otherwise we can use induction to show it doesn’t.