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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Mon, 30 Dec 2024 22:41:22 +0100
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On 30.12.2024 17:11, Richard Damon wrote:
> On 12/30/24 3:50 AM, WM wrote:
>> On 30.12.2024 01:39, Richard Damon wrote:
>>> On 12/29/24 12:53 PM, WM wrote:
>>>> On 29.12.2024 13:34, Richard Damon wrote:
>>>>> On 12/29/24 6:01 AM, WM wrote:
>>>>
>>>>>>
>>>>>> All definable numbers (FISONs) stay below 1 %. Every union of 
>>>>>> "below 1 %" stays below 1 %.
>>>>>
>>>>> Since 0 is Less than 1, you are sort of correct, but that fact 
>>>>> doesn't prove your claim.
>>>>>
>>>>> The problem is that when you get to *ALL* 
>>>>
>>>> I get to all FISONs below a certain threshold, namely a threshold 
>>>> between which and ω there exist ℵ₀ natnumbers.
>>>>
>>> Which isn't "All FISONs"
>>
>> Do you personally know FISONs larger than those? Please let me know them.

> Sure, if your threshold is n,

My threshold is not a fixed number but a potentially infinite set which 
never grows to more than 1 % of ℕ. Proof: Every FISON that is multiplied 
by 100 remains a FISON that can be multiplied by 100 without changing 
this property.

Regards, WM