Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
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: Tue, 8 Oct 2024 14:25:04 -0700
Organization: A noiseless patient Spider
Lines: 116
Message-ID: <ve47vh$2apvn$2@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <vdua6f$18vqi$2@dont-email.me>
 <05a3027798506434bf2f30b527e0f57d300e76c3@i2pn2.org>
 <ve0570$1kqpu$2@dont-email.me>
 <6f188d193341a3862f4c788a44dff3dfb27fb6bd@i2pn2.org>
 <81f6f0271a53803c0bf79be304ce2484e33aecda@i2pn2.org>
 <ve0hip$1eu7$1@news.muc.de>
 <7403c9bb7e2d0ac17197c219c6a04eace8fef108@i2pn2.org>
 <ve2upc$ggk$1@news.muc.de>
 <1c738ed4cd31385d0360dcd1821327b803fa5047@i2pn2.org>
 <ve3b2q$2iid$1@news.muc.de>
 <3ec9e38c968a5433962dce9270a23815e5e797bc@i2pn2.org>
 <ve3dtk$2iid$2@news.muc.de>
 <8ca8a17f8002dc960b4f339ec7274222aa079cd2@i2pn2.org>
 <ve4406$29nbq$11@dont-email.me>
 <c3fe33064190ea60e3e52b87ee1a3c5b17fc8b7b@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 08 Oct 2024 23:25:06 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="d938895af8a55dcdf6009a32333c8ef4";
	logging-data="2451447"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/vvaVntc4wESHKIKdCEObIDbB0u4YG/tw="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:vGLWawKiTzaYmuX4JSd/v6fj0IE=
Content-Language: en-US
In-Reply-To: <c3fe33064190ea60e3e52b87ee1a3c5b17fc8b7b@i2pn2.org>
Bytes: 6891

On 10/8/2024 2:21 PM, Richard Damon wrote:
> On 10/8/24 4:17 PM, Chris M. Thomasson wrote:
>> On 10/8/2024 7:10 AM, Richard Damon wrote:
>>> On 10/8/24 10:00 AM, Alan Mackenzie wrote:
>>>> Richard Damon <richard@damon-family.org> wrote:
>>>>> On 10/8/24 9:11 AM, Alan Mackenzie wrote:
>>>>>> Richard Damon <richard@damon-family.org> wrote:
>>>>>>> On 10/8/24 5:42 AM, Alan Mackenzie wrote:
>>>>>>>> Richard Damon <richard@damon-family.org> 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".
>>>>
>>>>>>>> OK, maybe you're right, there.  The semantics are a bit ambiguous.
>>>>>>>> Joes is not a native English speaker.  Apologies to Joes.
>>>>
>>>>>>>>>> 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).
>>>>
>>>>>>>> Whoa!  There're rather a lot of argument steps missing there.  Just
>>>>>>>> because WM asserts the existence of both actual infinity and a 
>>>>>>>> first
>>>>>>>> strictly positive unit fraction doesn't mean the one implies the 
>>>>>>>> other.
>>>>
>>>>
>>>>>>> It does in his logic, which is all that matters to him.
>>>>
>>>>>> Were we talking about WM's "logic", just there?  I don't think I was.
>>>>
>>>>> But my quote came from his logic.
>>>>
>>>> Ah, OK.
>>>>
>>>>>>> Yes, it is a wrong conclusion, but that error is based on his 
>>>>>>> initial
>>>>>>> assumption that something could be used that isn't available as a
>>>>>>> understandable entity to us finite beings.
>>>>
>>>>>> I think infinity is understandable.  I think I understand it.  My
>>>>>> position is that the distinction between "potential infinity" and 
>>>>>> "actual
>>>>>> infinity" is bogus.  It makes no difference in mathematics, which is
>>>>>> probably why the terms have vanished from mathematical discourse.
>>>>
>>>>> The difference is that in his "actual infinity" the generation process
>>>>> is complete and nothing can change.
>>>>
>>>> In a sense, the "actual infinity" _is_ the generation process, which is
>>>> fixed and complete.
>>>
>>> But only after that infinite process has completed. Finite beings 
>>> can't actually SEE that result.[...]
>>
>> When does an infinite process finally complete? If it does, well, it 
>> was NOT infinite in any way shape, or form... Right?
> 
> The infinite process completes in the infinite, thus beyond what we can 
> perceive, but only dimly imagine.
> 
> That is why we can't have actual infinity, we can't get to the infinite 
> to see it done.

since a step-by-step process for the naturals aka:

1, 1+1, 1+1+1, ...

Will never end, well... That does not mean there is a largest natural. 
WM is strange on this aspect. See, this right here is pondering on the 
infinite from a finite being... ;^)