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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Tue, 17 Dec 2024 07:34:16 -0500
Organization: i2pn2 (i2pn.org)
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On 12/17/24 5:25 AM, WM wrote:
> On 17.12.2024 00:55, Richard Damon wrote:
>> On 12/16/24 3:55 AM, WM wrote:
>>> On 15.12.2024 22:14, Richard Damon wrote:
>>>> On 12/15/24 2:29 PM, WM wrote:
>>>
>>>>> Next is a geometric property, in particular since the average 
>>>>> distance of intervals is infinitely larger than their sizes.
>>>
>>>> Not sure where you get that the "average" distance of intervals is 
>>>> infinitely larger than ther sizes.
>>>
>>> The accumulated size of all intervals is less than 3 over the 
>>> infinite length. Hence there is at least one location with a ratio oo 
>>> between distance to the interval and length of the interval. Start 
>>> there with the cursor. It will hit one next interval. Crash.
>>
>> Since none of the gaps are infinte, and none of the intervals are of 0 
>> size, there is no "infinite" ratio of any gap to any interval.
> 
> There is no upper bound for the ratio between distance and size of 
> intervals. This excludes the density of intervals. This excludes 
> covering of all rationals by intervals. This excludes a bijection 
> between natural numbers and rational numbers.
> 
> Regards, WM
> 

Nope, just shows you don't know what you are talking about and are using 
a broken logic.

Remember, I showed that your logic says that 0 == 1, so you are just 
admitting you don't care about truth.