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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Mon, 15 Jul 2024 19:10:42 -0700
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On 7/15/2024 7:06 PM, Chris M. Thomasson wrote:
> On 7/15/2024 7:02 PM, Chris M. Thomasson wrote:
>> On 7/15/2024 6:57 PM, Moebius wrote:
>>> Am 16.07.2024 um 03:49 schrieb Chris M. Thomasson:
>>>> On 7/15/2024 6:47 PM, Moebius wrote:
>>>>> Am 16.07.2024 um 03:32 schrieb Chris M. Thomasson:
>>>>>
>>>>>> going left to right, so to speak, [...]
>>>>>>
>>>>>> 1/1, 1/2, 1/3, 1/4, ...
>>>>>
>>>>> Nope, here you are going "from right to left" (on the real line).
>>>>>
>>>>> You see, 1/1 is larger than, say, 1/2, hence on "the real line" 1/1 
>>>>> is RIGHT from 1/2. No?
>>>>>
>>>>> Hint:
>>>>>
>>>>> ... | ... | ... | ... (real line)
>>>>>
>>>>>      0    1/2   1/1 (=1)
>>>>>
>>>>>> Huh? WM is backwards?
>>>>>
>>>>> Actually, not. :-)
>>>>>
>>>> Actually, my real line is, say
>>>>
>>>> ...-1...0...+1...
>>>
>>>
>>> Seems poor. :-P
>>>
>>> Let's fill in some unit fractions (at least 1/2). :-)
>>>
>>> ...| ... | ... | ... | ...       (real line)
>>>    -1     0    1/2   1/1 (=1)
>>>
>>>> So, left to right with origin at zero [...] the natural numbers, 
>>>> starting at zero the origin of the real line:
>>>>
>>>> 0, 1, 2, 3, 4, ...
>>>
>>> Right. But ALL unit fractions are between 0 and 1 (incl.). :-)
>>>
>>>> 0 is at origin point on my real line, the x axis so to speak. It has 
>>>> an origin at 0. Fair enough?
>>>
>>> Sure. Why do you ask? :-P
>>>
>>>> Left of zero, or origin if you will, is negative, right of zero is 
>>>> positive...
>>>
>>> Yeah.
>>>
>>> And between 0 and 1 (=1/1) there are the unit fractions 1/2, 1/3, ...:
>>>
>>> 0 < ... < 1/3 < 1/2 < 1/1 .
>>>
>>> See? :-P
>>>
>>>
>>>
>>>
>>
>> I see that you increased the granularity from natural numbers into the 
>> unit fractions...
>>
>> Wrt enumeration unit fractions I like to go from 1/1, to 1/2, to 1/3, 
>> ect... Is that wrong? There is no way to go the other way because then 
>> we have to think of a a smallest unit fraction, WM world, right?
> 
> What about a special real line with unit fraction granularity, and signs?
> 
> (-) ... <-(1/2)<-(1/1)<-(0)->+(1/1)->+(1/2)-> ... (+)
> 
> Ahh, this is backwards? Shit!

I say this because this is using say, +(1/1) for the first number on the 
position real axis. Going from zero seems to want to make some people 
ponder on a so-called "smallest" unit fraction. Right next to zero so to 
speak... Strange!

Going 0, ..., +(1/1)

Is a normalized interval with say:

(0)->+(1/2)->+(1/1)

1/2 is in there! Now what about 1/4? lol. They get infinitely smaller 
therefore there is no smallest unit fraction? However there is a largest 
at 1/1? Fair enough? Or hyper crap! ;^o