Re: Cantor Diagonal Proof

On Thu, 2025-04-10 at 17:23 -0700, Keith Thompson wrote:

wij <wyniijj5@gmail.com> writes:
[...]

"lim(x->c) f(x)=L" means the limit of f approaching c is L, not f(c)=L 'eventually'.
f at c is not defined (handled) in limit.

 
Correct.
 

lim 0.333...=1/3    ... The *limit* is 1/3, not 0.333....=1/3
0.3+0.33+0.333+...  ... The sequence converges to 1/3
Σ(n=1,∞) 3/10^n     ... The sum converges to 1/3 (or you can use lim)

 
The limit as the number of 3s increases without bound *is exactly what
we mean* by the notation "0.333...".  Once you understand that, it's
obvious that 0.333... is exactly equal to 1/3, and that 0.333... is a
rational number.

You agree "f at c is not defined (handled) in limit", yet, on the other hand
ASSERTING 0.333... is 'exactly' 1/3 from limit? Are you nut?

As usual, you need to prove what you say. Or you are just showing yourself
another olcott, just blink belief, nothing else.