Exactly. And since the line’s location is defined by points, where only points have exact locations AND no collection of points is a line, then a line does not have an exact location w.r.t any given amount (finite or not) of points.
Well once again you will have to show what points you think are missing from that collection.
The difference between Locality (that its minimal representation is a point) and Non-locality (that its minimal representation is a line) is not trivial, but it is profound and essential to the mathematical science, because this science is actually the linkage between these different qualities, that are used as its building blocks, whether they are interpreted by geometrical, analytical or logical aspects of this science.
Oh waiter, I ordered the Caesar salad not the word salad.
If you are again asserting that the difference between Locality and Non-locality is trivial, you, by your own trivial understanding, does not understand the profound difference between Locality and Non-locality.
It is simply a negation Doron, what ever can be defined as “local” then the negation of that definition defines what is considered “non-local”, it is about as trivial as anything can get.
Abstract concepts are exact as the nature of their abstract existence. Any definition is nothing but some use of these already existing things, and has no impact on their existence.
There is that word “existence” again, any chance of you actually giving your use of it any relevant meaning any time soon? An abstract concept is exactly its definition.
I already gave a simple example of the Empty set:
Mathematical definitions do not create the things that are defined by them, and it can easily be demonstrated by ZF axiom of the Empty set:
"There is a set such that no set is a member of it." (
http://en.wikipedia.org/wiki/Axiom_of_empty_set )
“there is” is called Existential quantification that is a statement about the existence of the considered thing, and in the case of the Empty set, one of the already existing things that are not members of the considered set, is the empty set itself.
In other words you did not understand
http://www.internationalskeptics.com/forums/showpost.php?p=5190443&postcount=6080 (your response to it in
http://www.internationalskeptics.com/forums/showpost.php?p=5190637&postcount=6081 was “<subsequent nonsense snipped>”) , which demonstrates again your inability to follow OM’s reasoning, and the understanding of a concept like Definition.
Again you simply do not understand that an abstract concept is nothing but its definition. That is why it is called, well, abstract.
The existence of a non-local atom ( known also as a non-local ur-element
http://en.wikipedia.org/wiki/Urelement ) is not based on any union of many existing elements. Therefore a non-local ur-element has a different quality, which is not the quality of the union of many elements.
Apparently by your own assertion that “different quality” is simply contradiction and self-inconsistency.
Your trivial reasoning that is based only on collections (disjoined or unioned) prevents from you to get OM’s reasoning.
You mean that contradictory and self-inconsistent “reasoning of OM"? Got that a long time ago.
Here is an example of your limited reasoning:
By your limited reasoning you are focused only on the intersection of the 3-D and the 2-D spaces (by the way, the 2-D space can be also bounded AND beyond that intersection).
More strawmen Doron? The focus on the intersection was yours as it was the central aspect of your assertions “which is the result of the penetration of the bounded 3-D space on the unbounded 2-D space.”
OM looks also at the bounded 3-D space that is defiantly belongs AND does not belong (it is beyond) to that intersection.
The same holds about the 2-D space. It belongs AND does not belong (it is beyond) to that intersection.
Again simply making your OM contradictory. If your ascription of “not belong” is “it is beyond” then the negation of ‘it is not beyond’ is your ascription of “It belongs”. Again you simply can not make up your mind what you want your reference of “belong” to mean and if “it is beyond” or not.
In other words, by your determination to define anything in terms of locations you do not get Non-locality.
What? So your whole spiel at the opening of this post…
Exactly. And since the line’s location is defined by points, where only points have exact locations AND no collection of points is a line, then a line does not have an exact location w.r.t any given amount (finite or not) of points.
was not defining things “in terms of locations”? How consistently inconsistent of you.
This gap is exactly the non-locality between any arbitrary pair of localities, and this non-locality is the very nature of this gap, that cannot be eliminated (or reduced to) by any amount of localities.
In a continuum there are no ‘gaps’ (that is what makes it a continuum), there are other “localities” “between any arbitrary pair of localities” in a continuum and specifically one locality exactly “between any arbitrary pair of localities”.
One of the results of the qualitative difference among Non-locality and Locality is the inability of a long addition of localities like 0.9+0.09+0.009+... to be exactly 1, because there is non-locality between any arbitrary pair of localities, which its notated by the “...1” part of 0.000...1 expression.
A scholar that gets things only in terms of Locality can’t get 0.000...1 expression.
Again if your are claiming that there is a “gap” in “localities” in a continuum you will have to show where you think that “gap” is, or more specifically what points are missing from that continuum.
