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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 24 Nov 2024 15:29:03 -0800
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On 11/24/2024 9:22 AM, Richard Damon wrote:
> On 11/24/24 7:26 AM, WM wrote:
>> On 24.11.2024 13:12, Richard Damon wrote:
>>> On 11/24/24 5:31 AM, WM wrote:
>>>> On 24.11.2024 03:22, Richard Damon wrote:
>>>>> On 11/23/24 4:11 PM, WM wrote:
>>>>
>>>>>>>> Cover the unit intervals of prime numbers by red hats. Then 
>>>>>>>> shift the red hats so that all unit intervals of the positive 
>>>>>>>> real axis get red hats.
>>>>>>>>
>>>>>>> And you can, as
>>>>>>> the red hat on the number 2, can be moved to the number 1
>>>>>>> the red hat on the number 3, can be moved to the number 2
>>>>>>> the red hat on the number 5, can be moved to the number 3
>>>>>>
>>>>>> A very naive recipe.
>>>>>
>>>>> But it works.
>>>>
>>>> It fails in every step to cover the interval (0, n] with hats taken 
>>>> from this interval.
>>>
>>> But that isn't the requirement.
>>>
>>> The requirement it to map from ALL Prime Natural Numbers to ALL 
>>> Natural Numbers
>>>
>>>>
>>>>>> Yes, for every n that belongs to a tiny initial segment.
>>>>>
>>>>> No, for EVERY n.
>>>>>
>>>>> Show one that it doesn't work for!
>>>>
>>>> The complete covering fails in every interval (0, n] with hats taken 
>>>> from this interval.
>>>
>>> Which isn't the interval in question.
>>>
>>> Your funny-mental fallacy is that you think an infinite set can be 
>>> thought of as just some finite set allowed to keep growning until it 
>>> reaches infinity,
>>>
>>> That is just the wrong model.
>>>
>>>>>>
>>>>>>> so all the numbers get covered.
>>>>>>
>>>>>> No.
>>>>>
>>>>> WHich one doesn't.
>>>>
>>>> Almost all. The reason is simple mathematics. For every interval (0, 
>>>> n] the relative covering is 1/10, independent of how the hats are 
>>>> shifted. This cannot be remedied in the infinite limit because 
>>>> outside of all finite intervals (0, n] there are no further hats 
>>>> available.
>>>
>>> But finite sets aren't infinite sets, and don't act the same as them.
>>>
>> All finite sets are the infinite set.
>>>>
>>> You can not just use finite mathematics on infinite sets.
>>
>> But I can use the analytical limit of the constant sequence.
>>
>> Regards, WM
>>
> 
> Nope, since the finite sets are not the same as the infinite set, the 
> property you are looking at just doesn't exist in the infinite set.
> 
> Limit theory only works if the limit actually exists
> 
> You can get things that APPEAR to reach a limit, but actually don't.

Let me guess... WM thinks there is a limit wrt the natural numbers? lol!


> 
> You are just confirming that yoiu mind HAS benn exploded by the 
> contradictions of using finite logic on infinite sets, and that has left 
> the great big "dark hole" in your logic, that doesn't actually exist.