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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: Sat, 2 Nov 2024 13:19:22 -0700
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On 11/2/2024 10:44 AM, WM wrote:
> On 02.11.2024 14:54, FromTheRafters wrote:
>> WM was thinking very hard :
> 
>>> That means, there is always another element. Potential infinity.
>>
>> Sets don't change. Forget about amplifying 'not finite' with such as 
>> 'actual' and potential' -- infinite simply means not finite and 
>> 'actual/potential' is a distinction without a difference. A useless 
>> concept outside of math philosophy.
> 
> You are wrong because you cannot comprehend the difference between 
> elapsing time and points of an interval.

Huh? Elapsing time? WTF! Here... How long does it take you to read this:

All of the natural numbers

vs

all of them

vs

N

The others are dark? ;^o


>>
>>>> the set of denominators have no largest element to 'start' with.
>>>
>>> If all unit fractions are existing, then a smallest unit fraction is 
>>> existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions 
>>> must be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals 
>>> of uncountably many points must be between 0 and x₀. That cannot 
>>> happen at x₀ = 0.
>>>
>>> Is that too hard to understand?
>>
>> Apparently, for you.
> 
> Chuckle.
> 
> Regards, WM
>