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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 7 Nov 2024 13:18:56 -0800
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On 11/6/2024 6:27 PM, Richard Damon wrote:
> On 11/6/24 10:15 AM, WM wrote:
>> On 06.11.2024 12:46, Richard Damon wrote:
>>> On 11/5/24 11:45 AM, WM wrote:
>>>> On 05.11.2024 04:08, Richard Damon wrote:
>>>>> On 11/4/24 12:11 PM, WM wrote:
>>>>>> On 04.11.2024 13:14, Richard Damon wrote:
>>>>>>> On 11/4/24 6:07 AM, WM wrote:
>>>>>>
>>>>>>>> By induction you can prove the sum n(n+1)/2 for every initial 
>>>>>>>> segment 1+2+3+...+n. But not for all natural numbers.
>>>>>>
>>>>>>> But all Natural Numbers can be defined.
>>>>>>
>>>>>> All defined numbers can be summed. Not all natural numbers can be 
>>>>>> summed.
>>>>>
>>>>> Why not?
>>>>
>>>> because most cannot be defined.
>>>
>>> But they ARE defined.
>>
>> Then sum all of them.
>>
>> Regards, WM
> 
> They will sum to Aleph_0, since there is a countable infinite number of 
> them.

The will sum, but they will never sum to a so-called largest natural 
number... Right?



> 
> Note, Addition on Natural Numbers is closed for FINITE sums (the sum of 
> a finite number of numbers), not necessarily for infinite series of them.