EDIT:
The Man you are using a reasoning that has no ability to deal with things that save their ids with respect to each other under co-existence.
Again Dorn these are just “ids” that you ascribe, so can save them as much as you want.
As a result you are unable to understand the non-local id of a thing that exists at more than one location, and the local id of a thing that exists at no more than one location, under their co-existence.
Nope, I got no problem with “a thing that exists at more than one location, and” some other “thing that exists at no more than one location”. Its your “non-local/local” “id”s with all the nonsense baggage you try to just ascribe with them that gets you into trouble.
You simply use the word "order" even if there is no order, so even if one follows your reasoning, the next element of a given collection is not necessarily determined by any particular order exactly as the cardinality of some infinite set is not impacted by the order of its members (cardinality is not ordinality and vice versa).
The “cardinality of some infinite set, or any set, is not impacted by the order of its members”, I certainly won’t argue otherwise but “the next element of a given collection” is an aspect of ordering. You do understand what an ordinal number is, don’t you? Hint; look to the root of the word ‘ordinal’ if you are still missing it.
By understanding the arbitrariness of the next member of some infinite set and the fact that multiplicity is the result of the co-existence of the local with the non-local, we have the needed logical basis to conclude that any given amount of local elements can't completely cover a non-local element under the co-existence, and any given amount of non-local elements can completely reducible into local elements.
Once again your stated ‘conclusion’ simply doesn’t follow from your purported “logical basis” .
The non-transformation of the local and the non-local into each other under their co-existence, guarantees the existence of multiplicity in the first place, and prevents the existence of the final non-local or local element in any given infinite collection (or in other words, the completeness of any given infinite collection, where the permanent existence of the next non-local or local elements, is an inherent property of its existence).
You are still thinking (apparently deliberately) of lists instead of sets. All the members of a set don’t need a “final non-local or local element“ to be all the members of that set.
As for non-locality and locality, let's demonstrate again their ids under co-existence by using the minimal needed elements, which are points and line-segments:
OK, I doubt this will go well for you though, but let’s just see how it pans out.
A line segment X is located at endpoint A AND at endpoint B.
So far so good, at least two points define a line segment.
Let endpoint B be a limit of X, such that X is at B AND at any arbitrary closer point C to B, which is located along X AND it is between endpoint A and endpoint B.
You’re still doing fine, at least in a continuous space there is always another point between any two. Heck, you might actually be learning something here, Doron. Congratulations.
No matter how close is C to B, C is not B only if X is irreducible to B OR C.
“irreducible”? “X” isn’t “C”, “B” or “A”. Those are points while your “X” was a line segment by your own, well, “id”s. Similarly your “A”, “B” and “C” are still just points that you have defined as being different so your ‘irreducibility’ has nothing to do with one not being the other, you have defined them such that they can’t be each other. You might be. starting to lose your own “id”s here, but again let's just see.
No point along X, whether it is endpoint A endpoint B or arbitrary point C, is at more than one location along X.
A point is only one location, so again no argument there.
The co-existence of line segment X, endpoint A, endpoint B and arbitrary point C (C is taken as a placeholder of any point between endpoint A and endpoint B, along X) under a one framework, guarantees the existence of the Real line.
Of course line segments and points ‘co-exist’, in fact it is a requirement that they do such. Remember at least two points define a line segment and the number of co-ordinates needed to identify a particular point in some space defines the dimensions of that space (again please look up the root of the word ‘ordinate’). You have surprised me, Doron ,you might actually be learning some basic geometry. Again congratulations. Other than that, what was your point?
, isn't it epix?
