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Subject: Re: There is a first/smallest integer (in =?UTF-8?Q?M=C3=BCckenland=29?=
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Date: Wed, 17 Jul 24 18:07:31 +0000
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 17/07/2024 à 20:02, Moebius a écrit :
> Am 17.07.2024 um 19:49 schrieb WM:
>> Le 17/07/2024 à 19:13, FromTheRafters a écrit :
>>> WM presented the following explanation :
>>>> Le 17/07/2024 à 15:42, FromTheRafters a écrit :
>>>>> Moebius presented the following explanation :
> 
>>>>>> WM> All unit fractions are separated. Therefore there is a first one
>>>>>>
>>>>>> Moebius> All integers are separated. Therefore there is a first one 
>>>>>> [?]
>>>>>>
>>>>>> WM> This is true but difficult to understand.
>>>>>
>>>>> Perhaps, with professional counseling,
>>>>
>>>> you could explain how NUF(x) can increase from 0 to many more in one 
>>>> point although all unit fractions are separated by finite distances?
>>>
>>> Sure, it jumps because of your stepwise function.
>> 
>> Of course it jumps, but what is the maximum size of a jump?
> 
> The jump "at" 0 is THE ONLY jump here,

No, ℵo finite intervals do not fit between [0, 1] and (0, 1]. 

> Hint: img(NUF) = {0, aleph_0}.

It is highly deplorable how acquired "knowledge" can paralyse the brain.

Regards, WM