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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 17 Nov 2024 00:40:44 +0100
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Am 16.11.2024 um 23:22 schrieb Moebius:
> Am 16.11.2024 um 23:16 schrieb Chris M. Thomasson:
>> On 11/16/2024 2:11 PM, Moebius wrote:
>>> Am 16.11.2024 um 22:48 schrieb Chris M. Thomasson:
>>>> On 11/16/2024 1:29 PM, FromTheRafters wrote:
>>>>> Chris M. Thomasson pretended:
>>>>>>
>>>>>> (infinity - infinity) = undefined
>>>>>>
>>>>>> ?
>>>>>
>>>>> https://en.wikipedia.org/wiki/ 
>>>>> L%27H%C3%B4pital%27s_rule#Other_indeterminate_forms
>>>
>>> Or this one: https://en.wikipedia.org/wiki/Indeterminate_form
>>>
>>> "oo - oo" is an "indeterminate form".
>>>
>>
>> I must be missing something: [...]
>>
>> [1] = a gallon of water out of an infinite pool
>> [2] = another gallon of water out of an infinite pool
>> [3] = on and on... taken to infinity...
>>
>> The pool would always have infinite water for this process?
> 
> Assume that the H2O molecules in the pool are "numerated" by 1, 2, 
> 3, ... (i.e. that ALL H2O molecules in the pool are "numerated" by 
> natural numbers).
> 
> Taking out the "infinite amount of H2O molecules" numerated by 1, 2, 
> 3, ... would lead to an EMPTY pool.

Hint: If the first gallon of water consists of the H2O molecules 
numbered by 1, ..., n_1, the second gallon of water consists of the H2O 
molecules numbered by (n_1)+1, ..., n_2 (with n_2 > (n_1)+1), and so on, 
the "outcome" would be an empty pool. (Hint: try to name the number 
attached to an H2O molecule which "remains" in the pool.)

> On the other hand, taking out the "infinite amount of H2O molecules" 
> numerated by 2, 4, 6, ... would not drain the pool. 😛 It would still be 
> filled (sort of) with infinitely many H20 molecules. 😛
> 
> Be aware if the infinite, man!
> 
> .
> .
> .
>