d) Addition operation among finitely many shorter __ objects that are marked by . along 0_____1, can be added up to value 1, since the complement of any finitely many accurate values of shorter __ , is itself a shorter ___ object with an accurate value.[/OUOTE]
Anywhere or anytime you stop the process, you have a finite number of boundaries and regions. Say you've divided up the original Region One:
0______1 into smaller areas or lots, you can add those back up to the original area.
There is a finite length between the boundaries of Toddler Todd's playpen and the front door. The couch is halfway between the playpen and the door, so Toddler Todd, who has escaped the playpen could be said to have two regions to traverse, but those add up to the original exact one, and Baby Todd makes a finite number of steps and pushes open the screen door and is out! (Except of course his older sister grabs him.)
This is what happens IRL, but now for some more of the verbal_symbolic/visual_spatial of the AND:
e) Addition operation among infinitely many shorter __ objects that are marked by . along 0_____1, can't be added up to value 1, since the complement of any infinitely many accurate values of shorter __ , is itself a shorter ___ object without an accurate value (it is an endlessly more and more shorter __ object that its accurate value (that can be used in order to reach value 1) is undefined, exactly because (by (1)) ______ existence is not defined as a collection of shorter or shortest objects.
Enter the hypothetical that we just keep on doing the process activity that generates numbers indefinitely. This indefinitely points to a notion of a potential infinity. You posit that the activity process does not stop. This is the notion of Infinity: first as the boundless line and then as the never stopping in the Marking.
Baby Todd sets out on an impossible journey (Or should I say "Stewie" for Kid Eagar and make this a Family Guy episode?) He must cross from his playpen to the front door counting the halves as he goes, First he must get half way, and then half of that, a quarter way. Well doing this abstract process, he'll never reach the front door. Of course this is not IRL, because a potential Infinity of adding up shorter and shorter fragments is just a mental exercise and not what physically happens in a finite world. But we are in the process of generating numbers which come from not only the visual_spatial, but the verbal_symbolic in a dynamic AND.
Case (d) is called finitely weaker than the non-composed existence of _______ , and by this case shorter objects __ can be added up to some accurate value that has been given to some _____ object.
Case (e) is called infinitely weaker than the non-composed existence of _______ , and by this case shorter objects __ can't be added up to some accurate value that has been given to _____ object.
Our original Non-Complexity ______________ is unbounded and not composed of any smaller pieces. (Again, it's not the mathematical line composed of points.) Markers, boundaries create fragments. If you stop at a finite number of fragments you can add them up to your
bounded region, but you can't add them up to the unbounded ground _________.
Positing that you continue the process of chasing the potential infinity, you just keep generating more albeit shorter fragments that never even add up to the length of your original bounded region 0_______1.
Case (e) is defined as potential infinity (infinity that is based on the notion of collections, with respect to actual infinity (infinity that is based on the non-composed existence of, at least, ____ (1-dim object).
By verbal_symbolic-only reasoning, potential infinity, is "a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and each individual result is finite and is achieved in a finite number of steps."
By visual_spatial AND verbal_symbolic reasoning potential infinity is a collection of infinitely many objects that can't define the existence of, at least, _____ (as given by The Axiom Of Non-Complexity), where (e) is the result of this inability.
Potential Infinity is thus a "non-terminating process" that entails ever more and more without ceasing objects in a collection that cannot be completed.
"Actual Infinity" is boundless and non-composed. It's the seamless ground. All is One in respect to it, but it isn't even one. As Doron applies it to metaphysics, it's the neutral substance that is neither material nor mental. It is neither this nor that.
Classical Mathematics, is a framework that tries to define actual infinity in terms of sets (which are a particular case of the notion of collection).
My framework defines actual infinity beyond the notion of collection, by defining the existence of, at least, non-composed _____ (1-dim object), as given by (1).
More details can be found in
http://www.internationalskeptics.com...postcount=3068
Classical Mathematics tries to get to Actual Infinity from the finite by collecting all the points on a line. It begins with the notion that Infinity is composed of an infinite collection of discreet points. But you see between any "discrete" point there must be another infinity of points. The closer you look, the more there are, so you can't possibly complete any process of addition and get to this so-called composed Infinity. You can only talk in terms of a potentiality, but not a reality.
What Classical Mathematics has done is create a special version of Infinity. It still speaks of an "Absolute Infinity" that is Doron's non-composed Infinity, but for its own convenience it sets out a composed Infinity, beginning with the notion of an infinite line of infinite points each a discrete number. With a verbal-symbolic leap this specially brewed Infinity (called "Mathematical Infinity) is a gathered whole of all these discrete point numbers.
Doron's objection is that this concept of Infinity is verbal_symbolic only. The construction exists only in the fantasy world of head-only imagination.
By his above active process demonstration, you are to see (visually-spatially, Directly Perceptionally, that ___________ in reality, that is, the Non-Complex Ground, is not, cannot become, a composed collection of objects. This mathematical bastard of "Mathematical Infinity" is not a result of correct thinking. Correct thinking is verbal_symbolic AND visual_spatial. More generally it is of the organizational principle of X/Y Complementarity. "Mathematical Infinity" is a one parent, unwed mother, child of symbolic_verbal only where the organizational principle of thought is primarily by classes of things, rather than real concrete things.
According to Doron, this kind of thinking spawns separation: us vs them, exclusive classes that are racist and bigoted, and all sorts of prejudice.
What's more "Mathematical Infinity" becomes an imposter of Genuine Infinity, the true Ground of Being. Using it substitutes a toxic concept for Being. We fail to participate in Being and get lost in the fragments.
So symbolic_verbal only just contributes to the ills of the world. "Mathematical Infinity" perpetuates the ills by being an incorrect thinking that keeps us from UNITY awareness and living in the Ground of Being.
He insists this kind of mathematics must stop or we'll all be nuclear toast.
