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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: Mon, 7 Oct 2024 17:35:50 -0700
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On 10/7/2024 3:58 PM, Richard Damon wrote:
> On 10/7/24 7:44 AM, Alan Mackenzie wrote:
>> Richard Damon <richard@damon-family.org> wrote:
>>> On 10/7/24 7:13 AM, joes wrote:
>>>> Am Mon, 07 Oct 2024 10:13:21 +0200 schrieb WM:
>>>>> On 06.10.2024 17:55, joes wrote:
>>>>>> Am Sun, 06 Oct 2024 17:26:07 +0200 schrieb WM:
>>>>>>> On 06.10.2024 16:52, Alan Mackenzie wrote:
>>>>>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>
>>>>>>>> This idea of time may be what misleads the mathematically less 
>>>>>>>> adept
>>>>>>>> into believing that 0.999... < 1.
>>>>>>> That is true even in actual infinity.
>>>>>>> We can add 9 to 0.999...999 to obtain 9.999...999. But multiplying
>>>>>>> 0.999...999 by 10 or, what is the same, shifting the digits 9 by one
>>>>>>> step to the left-hand side, does not increase their number but 
>>>>>>> leaves
>>>>>>> it constant: 9.99...9990.
>>>>>>> 10*0.999...999 = 9.99...9990 = 9 + 0.99...9990 < 9 + 0.999...999 ==>
>>>>>>> 9*0.999...999 < 9 as it should be.
>>>>>> In actual infinity, there is no last 9 (that would not be infinite).
>>>>> Actual means all, but not more. This implies a last before ω. The
>>>>> infinity means an end cannot be determined. It is produced by the dark
>>>>> numbers.
>>>> Actually infinite means infinite, which doesn’t change when you add or
>>>> subtract a finite number.
>>
>>
>>> Actual infinity doesn't exist for us finite beings.
>>
>> English language tip: The "Actually" in that sentence was not attached to
>> the word "infinite", it meant something like "This is really true:".
> 
> But all his reference to the word "Actually" are part of his trying to 
> define the term "Actual Infinity".
> 
>>
>> Anyhow, what do you mean when you say that "actual infinity doesn't
>> exist"?  I think we established over the weekend that for a mathematical
>> entity not to exist, it must cause a contradiction.  Or something like
>> that.
>>
>> So what contradiction would the existence of actual infinity cause?
>>
> 
> It implies that there exists a first positive real, rational number or 
> unit fraction for one (at least the way WM uses it).

A first unit fraction would be 1/1? :^) However this is in the very 
_strict_ realm of unit fractions. WM seems to like to mix and match 
realms. Not sure why he thinks there is a smallest unit fraction... 
Anyway, shit happens.