Re: Cantor Diagonal Proof

On Fri, 2025-04-11 at 12:04 +0000, Mr Flibble wrote:

On Fri, 11 Apr 2025 19:52:20 +0800, wij wrote:
 

On Fri, 2025-04-11 at 04:21 -0700, Keith Thompson wrote:

wij <wyniijj5@gmail.com> writes:

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.

 
Keep the insults to yourself.  Last warning.

 
I still think 'nut' is a common word, at least a terse word for people
saying one thing and doing the other (or a liar more appropriate?)
 

My assertion is simply about what the "..." notation means.
 
Do you agree that the limit of 0.3, 0.33, 0.333, as the number of 3s
increases without bound, is exactly 1/3?  (You said so above.)

 
Increases without bound -> yes is exactly 1/3 -> no such logic
 

What exactly do you think the notation "0.333..." means?  I and many
others use that notation to mean the limit, which you agree is exactly
1/3.

 
Is this a lie? I have always consistently claiming "repeating decimals
are irrational".

 
The decimals only repeat in certain bases: 

Agree

it is wrong to think that any
part of mathematics relies on a specific base such as base 10.

Did I claimed what you said "any part of mathematics relies on a specific base"?

 
/Flibble