==> From my perspective it appears that you have missed the context in which these statements have been made. The first part is conceding to your statements quoting above and the last part is disagreeing. From my perspective, you are now disagreeing with me conceeding your point (at least partially) At his point, I would like to use a word that metaphorically describes an Ouroboros but I do not know such a word so hopefully you'll get my meaning by description.
I cannot speak to how you arrive at your perspective, nor will I try, and I don't think I missed the context of your statements. I do think you've confused the three separate terms: canonical, canonical number, and canonical number system, believing them to be interchangeable, which they are not. The only[/i] think that I've ever claimed is out of context is the subject of "canonical number systems", and I still stand by that claim. I have not changed my position about what I agree with and what I disagree with. I knew what these terms meant and how they applied to this thread/form before this discussion started. I know what they mean now, and how they apply, and I can tell you with complete certainly, nothing has changed in either their definition nor applicability. If you see change in either one, then I suggest that you investigate the nature of the changes that you see.
==> I would like to use a word that metaphorically describes an Ouroboros but I do not know such a word so hopefully you'll get my meaning by description.
While I understand that from your perspective you see me going in circles, I can assure you that my position has not moved one iota. Therefore, if what is being observed hasn't moved, yet the observer notices movement, then it must be the observer that is moving. Just as the ancients observed the sun to be moving in a circle around the earth, we now know that it was the observers who were actually moving in a circle.
==> It just seemed to me that you were being overly precise on a subject that didn't really matter to either of us.
Yes, I do prefer to be precise, because imprecision is one factor (not the only one, but one) that leads to misunderstanding. Now with respect to it not mattering to either of us, you're being quite presumptuous to assume you have any idea of of what does or does not matter to me.
=> Getting back to the main point, and refreshing my earlier metaphor, canonical appears to be, metaphorically speaking at least, equivelent to Class or Order, where Heirarchical might be described as the Family and Dotted Decimal more specific still with Species. An ugly metaphor granted but the best I can do with the tools I have.
Class, order, and family are all part of the hierarchical biological classification scheme. Neither dotted-decimal nor canonical are.
Canonical means adherence to a given set of rules, and no where is it required that the rules be hierarchical. The rules may or may not be hierarchical. A specific multi-par number may actually be hierarchical, but not canonical because it's an exception to the underlying numbering scheme.
Dotted-decimal is an alternative representation of another number. The representation may or may not be hierarchical.
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