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Topic: Matheology § 300
Replies: 12   Last Post: Jul 22, 2013 3:19 PM

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Michael Klemm

Posts: 117
Registered: 11/13/12
Re: Matheology § 300
Posted: Jul 19, 2013 4:18 PM
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>> WM wrote:
>>> Would you think that the Binary Tree containing only all rational
>>> numbers is impossible?

>
>> A binary tree containing all finite initial path segments of the complete
>> binary tree contains, although no rational numbers,

>
> That is correct. Real numbers cannot be defined by finite initial segments
> of infinite paths (and they cannot be defined by infinite paths). Every
> real number needs a finite definition like "0.5 and only zeros following".


Path have verices and edges and real numbers have no such things.

>> a lot of other things, for example pairs of paths or paths beginnig on
>> level 13 and ending on level 17.

>
> You appear to have your own understandig of "paths". A path in the
> infinity Binary Tree is, in mathematics, an infinite path containing the
> root node. Sometimes also finite initial segments are called paths, but
> each one starts at the root node.


It is you who can not distinguish between paths with one end and paths with
two ends.

Regards
Michael




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