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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: WM and end segments...
Date: Mon, 22 Jul 2024 12:28:12 -0700
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On 7/21/2024 1:59 PM, FromTheRafters wrote:
> After serious thinking Chris M. Thomasson wrote :
>> For some damn reason when I hear end segments from WM I think of a 
>> tree. Take the following infinite 2-ary tree that holds the positive 
>> integers:
>> ___________________________________________
>>                    0
>>                   / \
>>                  /   \
>>                 /     \
>>                /       \
>>               1         2
>>              / \       / \
>>             /   \     /   \
>>            3     4   5     6
>>           / \   / \ / \   / \
>>        .........................
>> ___________________________________________
>>
>> this goes on and on for infinity... We all can see how this can go for 
>> infinity, right WM? Wrt trees there are only leaves in a finite view 
>> of it. However, the "infinite view" of the tree has no leafs because 
>> it never ends... Fair enough? Or too out there?
>>
>> Wrt WM, is a leaf an endsegment of an n-ary tree in your "system"? Or, 
>> I probably am missing something here. Sorry everybody. Fwiw, a finite 
>> view can be something like this:
>> ___________________________________________
>>                    0
>>                   / \
>>                  /   \
>>                 /     \
>>                /       \
>>               1         2
>>                        / \
>>                       /   \
>>                      5     6
>> ___________________________________________
>>
>> This has leaves at 1, 5 and 6, because its finite. The infinite one 
>> has no leaves. Is this a decent way to think about it? Also, if this 
>> were unit fractions, the root at zero is not a unit fraction. So, zero 
>> is not valid in that strict realm. For instance wrt the finite view 
>> above:
>>
>> ___________________________________________
>>                  (1/0)  *** NOT A UNIT FRACTION!
>>                   / \
>>                  /   \
>>                 /     \
>>                /       \
>>              (1/1)    (1/2)
>>                        / \
>>                       /   \
>>                     (1/5) (1/6)
>> ___________________________________________
>>
>>
>> Sound okay, or into kook ville! ;^o
> 
> It is kind of like that. 

Thanks. I had a "feeling" that this is what he is trying to get at, so 
to speak. So, I got a bit close. It's a bit hard to parse WM's mind... 
Dark and all... ;^)


> WM would say that each 'level' as you build it 
> step by step has twice as many leaf nodes as the previous level. More 
> and more and more. Then, when it is infinite, suddenly there are no leaf 
> nodes. What happened, he ponders.
> 
> Then you start smelling smoke...

LOL! I wonder if WM was listening to the following song while wondering 
where all of the leaves went...

https://youtu.be/6cIePqdz03A

lol. ;^)