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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Sun, 22 Sep 2024 07:02:26 -0400
Organization: Peripheral Visions
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Chris M. Thomasson submitted this idea :
> On 9/21/2024 4:25 PM, Richard Damon wrote:
>> On 9/21/24 9:57 AM, WM wrote:
>>> On 21.09.2024 01:06, Richard Damon wrote:
>>>> On 9/20/24 2:33 PM, WM wrote:
>>>
>>>>> How can 10 points exist in linear order without a first one?
>>>
>>>> Who says they can't.
>>>
>>> In order to count to 10, you have to start at 1.
>>>>
>>>> Its just when they become infinite that there might be ends that don't 
>>>> exist.
>>>
>>> In order to count a countable set, you have to start at 1.
>>>
>>> Regards, WM
>>>
>> 
>> Right, so the countable numbers have ONE end that can be used to count 
>> from.
>
> What about the signed integers? Well, we can always start from origin, at 0. 
> ;^)

You could think of them as a sequence of ordered pairs of naturals.

((0,0),(1,0),(1,1),(2,0),(2,1),...)

First of the pair is the magnitude and the second of the pair is the 
sign where one equals negation. The sequence is one-ended and perhaps 
now more obviously countable.

(0,1,-1,2,-2,3,-3,...)