Deeper than primes

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The Man said:
This post is a perfect example of Doron’s inability to distinguish his misinterpretations from ‘Standard Mathematics’. It does not matter that we are talking about ‘Standard Mathematics’ (or in this case intervals) Doron will simply assert his misunderstanding as some failing in ‘Standard Mathematics’. Again Doron uses a notation that indicates his point ‘y’ is included in both of his red and blue intervals and presents his misinterpretation that this indicates point ‘y’ is “in more than a one location (blue AND red)” . Doron’s misunderstanding is simply a result of him not reading (or understanding) the post he is responding to, indicating that his ascriptions of red and blue, as shown above, both include the same location ‘y’ while the intervals [x,y) (y,z] would not include that location. The illusion Doron is that you understand ‘Standard Mathematics’ or common notation and you are the only one (at least on this thread) succumbing to that illusion. Again a boundary is one of those ‘"well defined" agreed definitions, terms, concepts, etc …” while your application of the words ‘edge’ and ‘direction’ are still undefined.
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If y is a point, ( notated as [x,y) (y,z] ) then it is not blue and not red, because a point does not have a direction (it is not left and not right).

The standard Math wrongly understands [x,y) (y,z] because it does not get that a line segment is not a collection of points.

Since a line segment is not a collection of points, then [x,y) (y,z] means that y point is not the left edge of [x,y] line segment, and y point is not the right edge of [y,z] line segment.

Look how limited is standard math by get anything only in terms of local elements.

Furthermore, by Standard Math [x,y) (y,z] is not accurate because there is no way to define the exact element which is the predecessor of y in the case of [x,y) or the successor of y in the case of (y,z].

In order to ignore this inability Standard Math will tell you about non-countability or ugly creatures like supremum or infimum instead of simply understand that no collection of local elements (points) can be a non-local element (a line segment).
 
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doronshadmi said:
If y is a point, ( notated as [x,y) (y,z] ) then it is not blue and not red, because a point does not have a direction (it is not left and not right).
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I'm not familiar with this notation - [x,y) (y,z]. Can you explain it? It seems rather circular; why do you have to bring in x and z to define y?


ETA: How's that definition of 'crisp' coming on, plus some examples?
 
Little 10 Toes said:
[x,y] means all points between x and y inclusive. (x,y) means all points between x and y, but not x and y.

Final example: [-5,0),(0,5], all numbers between -5 and 5, but not zero.

Don't worry doronshadmi, i'll respond back to you later.
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This is the standard notion, where anything is understood only in terms of local elements like points.

By OM's non-standard notion of [x,y] (where x<y) [x,y] is a non-local element because it is not less than both x AND y element, where x element OR y element cannot be x AND y element.

This notion of the difference between the non-local and the local, saves the problem of the inability to define the immediate predecessor of y in [x,y) case, or the immediate successor of y in (y,z] case (where y<z) (this problem exists iff [x,y) or (y,z] understood in terms of local elements like points).

The solution is based on the notion that [x,y] or [y,z] is not made of points, but it is a difference type of building-block that
it is at x AND y ( = ____) OR y AND z (= ____ ) location, which is a qualitative property that no point has (a point must be in a one and only one location).
 
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doronshadmi said:
If y is a point, ( notated as [x,y) (y,z] ) then it is not blue and not red, because a point does not have a direction (it is not left and not right).
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No it is simply not blue and not red because it is not included in those intervals defining what constitutes blue and red in this consideration.

doronshadmi said:
The standard Math wrongly understands [x,y) (y,z] because it does not get that a line segment is not a collection of points.
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As sets containing, well, points those intervals are by definition a collection of points. However a line segment is defined by (or bounded by) two points such as the interval [x,y] thus the interval [x,y) simply lacks that end point ‘y’ as part of the included interval but is still bounded by that point.

doronshadmi said:
Since a line segment is not a collection of points, then [x,y) (y,z] means that y point is not the left edge of [x,y] line segment, and y point is not the right edge of [y,z] line segment.
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Again simply a matter of the notation indicating which points are included in the given intervals.


doronshadmi said:
Look how limited is standard math by get anything only in terms of local elements.
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Limited? I gave you four different examples of your red-blue line each with specific considerations and utility.

doronshadmi said:
Furthermore, by Standard Math [x,y) (y,z] is not accurate because there is no way to define the exact element which is the predecessor of y in the case of [x,y) or the successor of y in the case of (y,z].
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So Doron show us how your notions “define the exact element which is the predecessor of y” “ or the successor of y” on the real number line. By allowing for infinite decimal representation it is as accurate as any number can possibly be and quite accurately excludes ‘y‘ from those intervals as given. The ‘successor’ of the interval [x,y) is ‘y’ just as it is the ‘predecessor’ of the interval (y,z]. How much more exact can you get then one point?



doronshadmi said:
In order to ignore this inability Standard Math will tell you about non-countability or ugly creatures like supremum or infimum instead of simply understand that no collection of local elements (points) can be a non-local element (a line segment).
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As always Doron the ‘instability’ and ignorance remain yours.
 
The Man said:
However a line segment is defined by (or bounded by) two points such as the interval [x,y] thus the interval [x,y) simply lacks that end point ‘y’ as part of the included interval but is still bounded by that point.
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So we take point y ( which is not in [x,y) ) and somehow we look beyond it and claim that y is the boundary of [x,y).

1) The thing that enables us to define y as the boundary of [x,y) is exactly a non-local element (a line segment, which is an element that is not made, defined, etc … by points) that exists both in AND out of [x,y) set of points.

2) No point has this property, and also infinitely many points together do not have this property exactly because it is a qualitative difference and not a quantitative difference.

3) Standard Math cheating because it claims that a line segment is the result of 'dragging' a point. This is a fundamental failure exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=4709081&postcount=2811 , and this cheating has to be stopped as soon as possible.
The Man said:
Limited? I gave you four different examples of your red-blue line each with specific considerations and utility.
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Because of these four different examples, the universe of infinitely many examples, which are the result of the bridging between Non-locality and Locality, cannot be defined.
The Man said:
The ‘successor’ of the interval [x,y) is ‘y’ just as it is the ‘predecessor’ of the interval (y,z].
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y is not in [x,y) or (y,z] so it cannot be the successor of [x,y) or the predecessor of (y,z] (see (1),(2),(3) above).
The Man said:
So Doron show us how your notions “define the exact element which is the predecessor of y” “ or the successor of y” on the real number line.
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Very simple, by using the non-local element, which is both any arbitrary local element in [x,y) AND out [x,y) (on local y element) there cannot be an immediate predecessor of y ( in the case of in [x,y) AND out [x,y) ) and there cannot be an immediate successor of y ( in the case of out (y,z] AND in (y,z] ) exactly because a non-local element is not made of local elements.

This notion is possible exactly because there is a qualitative difference between non-local and local elements.

On the contrary, Standard Math has no rigorous answer for this case, and it claims that there is a function that somehow enables to "visit" any real number along the real line, including the immediate predecessor or the immediate successor of y.
 
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doronshadmi said:
So we take point y ( which is not in [x,y) ) and somehow we look beyond it and claim that y is the boundary of [x,y).
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You have such trouble with basic concepts. You invent your convoluted set of inconsistent, contradictory notions just because you "can't get" something as simple as half-open intervals.
 
jsfisher said:
You have such trouble with basic concepts. You invent your convoluted set of inconsistent, contradictory notions just because you "can't get" something as simple as half-open intervals.
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Not at all, because I understand the fundamental failure of the reasoning of clopen or open set, I can provide the solution to this fundamental failure by distinguish between the qualitative difference between local and non-local elements, and how exactly they are bridged without derived from each other.

By your fundamental failure a line is the result of a dragged point, which is an utter nonsense that does not hold water, as I clearly show in http://www.internationalskeptics.com/forums/showpost.php?p=4709081&postcount=2811 .

The whole idea of clopen or open set is based on this utter nonsense.
 
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zooterkin said:
Sorry? What is the successor of [x,y), then?
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I show that there is not such a thing like the immediate local successor or the local immediate predecessor of local y.

Also I show that y has an immediate non-local successor or an immediate non-local predecessor, where local y cannot belong both to the immediate non-local successor AND the immediate non-local predecessor (the local y belongs to the immediate non-local successor OR to the immediate non-local predecessor, and in both cases it is not a building-block of any one of them).
 
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doronshadmi said:
Not at all, because I understand the fundamental failure of the reasoning of clopen or open set...
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Oh, dear! You've circled back to topology. That ended so tragically for you before, Doron. Do you really want to venture there again? There really is no need. We were discussing intervals, remember? Let's stay focused on one topic at a time, please.

I can provide the solution to this fundamental failure by distinguish between the qualitative difference between local and non-local elements, and how exactly they are bridged without derived from each other.
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And, yet, you cannot demonstrate any failure. You are grossly ignorant of so many simple mathematical concepts - probably willfully in many cases. You then use whatever misunderstandings you concoct from your misunderstandings to "disprove" unrelated mathematical facts as faulty.

You now seem fixated on the simple fact for any given number, y, there is no largest number, x < y. Big deal. You may not like the fact, but it doesn't discount it in any way. Nor can you disprove it. Nor can you use it to reject something simple like half-open intervals.

The set { x : 0 <= x < 1 } is perfectly acceptable with no demonstrable failure, as you put it. (And since you are not particularly fond of the real numbers, we can consider the set over just the rationals, if you like.)


...<more Doronetics nonsense>...
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doronshadmi said:
y is not in [x,y) or (y,z] so it cannot be the successor of [x,y) or the predecessor of (y,z]
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Rubbish. Absolute illogical rubbish.

Were we to apply this example of doronetics to the integers, say, we'd find that 7 cannot be a successor to 6 because 7 is not in 6.

By any reasonable meaning of the Doron-tortured terms successor and predecessor, y is a successor (but not the successor) to [x,y) and y is a predecessor to (y,z]. The fact y isn't included in either interval is a requirement for this - exactly the reverse of what Doron alleges. (No surprise there.)
 
jsfisher said:
You now seem fixated on the simple fact for any given number, y, there is no largest number, x < y. Big deal. You may not like the fact, but it doesn't discount it in any way. Nor can you disprove it. Nor can you use it to reject something simple like half-open intervals.
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No.

I provide the exact reason of why local y (an element that has a single value) cannot be also x (an element that has a single value) , because no one of them is the non-local element that is both on x AND y, but it is not made of (not derived from) x or y.
jsfisher said:
The set { x : 0 <= x < 1 } is perfectly acceptable with no demonstrable failure, as you put it. (And since you are not particularly fond of the real numbers, we can consider the set over just the rationales, if you like.)
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I do not care if set { x : 0 <= x < 1 } is perfectly acceptable or not.

I clearly show that x is a local element that cannot be = AND > 0 , which is a property that only a non-local element has.
 
jsfisher said:
Rubbish. Absolute illogical rubbish.

Were we to apply this example of doronetics to the integers, say, we'd find that 7 cannot be a successor to 6 because 7 is not in 6.
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Rubbish. Absolute illogical rubbish.

The real-line is not limited to whole numbers, so, for example, the set of [0,7) can't take 7 as the immediate successor of 6, because there are infinitely many local numbers between 6 and 7.

Furthermore, 7 is not a member of the collection of local elements of [0,7).

The immediate successor of 6 is the non-local element that is both on 6 AND 7.

Let us notate this notion like this:

[0,6_]7
 
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doronshadmi said:
I show that there is not such a thing like the immediate local successor or the local immediate predecessor of local y.

Also I show that y has an immediate non-local successor or an immediate non-local predecessor, where local y cannot belong both to the immediate non-local successor AND the immediate non-local predecessor (the local y belongs to the immediate non-local successor OR to the immediate non-local predecessor, and in both cases it is not a building-block of any one of them).
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If I understand what was described before, by definition, y is the successor of [x, y). If it isn't, then what is [x,y)?
 
zooterkin said:
If I understand what was described before, by definition, y is the successor of [x, y). If it isn't, then what is [x,y)?
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[x,y) = [x ]y

The immediate successor of any local element in [ ] is __ ( and so is the case of [x,y] that is = [x y] )
 
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doronshadmi said:
So we take point y ( which is not in [x,y) ) and somehow we look beyond it and claim that y is the boundary of [x,y).
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Look beyond? No, it is quite specifically defined as the boundary in that interval notation.

doronshadmi said:
1) The thing that enables us to define y as the boundary of [x,y) is exactly a non-local element (a line segment, which is an element that is not made, defined, etc … by points) that exists both in AND out of [x,y) set of points.
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No just the interval allows us and requires us to define the boundaries of that interval and that interval can represent a line segment.

doronshadmi said:
2) No point has this property, and also infinitely many points together do not have this property exactly because it is a qualitative difference and not a quantitative difference.
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By your own assertions Not red is blue. Thus in the example I gave with the closed intervals [x,y] is red and [y,z] is blue (or not red by your ascriptions) the point ‘y’ is both in red and not in red (or blue by your own assertions). The only difference Doron is self-consistency, standard math has it while your notions do not.

doronshadmi said:
3) Standard Math cheating because it claims that a line segment is the result of 'dragging' a point. This is a fundamental failure exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=4709081&postcount=2811 , and this cheating has to be stopped as soon as possible.
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Again Doron simply claiming is not ‘showing’

doronshadmi said:
Because of these four different examples, the universe of infinitely many examples, which are the result of the bridging between Non-locality and Locality, cannot be defined.
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What, so you can’t define any of the ‘infinitely many examples’ in your notions? That sounds like your notions are extremely limited.

doronshadmi said:
y is not in [x,y) or (y,z] so it cannot be the successor of [x,y) or the predecessor of (y,z] (see (1),(2),(3) above).
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The fact that it is not included makes it the successor and predecessor to those intervals, as jsfisher also noted.

doronshadmi said:
Very simple, by using the non-local element, which is both any arbitrary local element in [x,y) AND out [x,y) (on local y element) there cannot be an immediate predecessor of y ( in the case of in [x,y) AND out [x,y) ) and there cannot be an immediate successor of y ( in the case of out (y,z] AND in (y,z] ) exactly because a non-local element is not made of local elements.
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So you can not define ‘y’ as a successor and a boundary to the interval [x,y) in your notions, again it makes your notions extremely limited.

doronshadmi said:
This notion is possible exactly because there is a qualitative difference between non-local and local elements.

On the contrary, Standard Math has no rigorous answer for this case, and it claims that there is a function that somehow enables to "visit" any real number along the real line, including the immediate predecessor or the immediate successor of y.
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No function that I am aware of just the result of defining your interval properly so that there is an isolated point as I have already said. Which was basically your claim about your blue-red line segment.
 
doronshadmi said:
I provide the exact reason of why local y (an element that has a single value) cannot be also x (an element that has a single value) , because no one of them is the non-local element that is both on x AND y, but it is not made of (not derived from) x or y.
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No, local and non-local are these bogus terms you introduce without definition. Even if they were defined, however, they cannot be used to disprove something else when that something else is outside their provence.

I do not care if set { x : 0 <= x < 1 } is perfectly acceptable or not.

I clearly show that x is a local element that cannot be = AND > 0 , which is a property that only a non-local element has.
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No, you didn't. Local and non-local are your inventions, supposedly to "fix" a deficency in Mathematics. If Mathematics is truly deficient, then you need to show that there is an inconsistency or contradiction within the existing Mathematics. All you have done is invent something different (which is itself inconsistent and contradictory) then claimed since regular Mathematics isn't doronetics, that regular math must be in error. There is another, more likely possibility.

There is nothing wrong with the interval, [0,1), and 1 is one of its boundaries. If you have a problem with either of those statements, show how they generate a problem within the "pre-doronetics" world.
 
doronshadmi said:
Rubbish. Absolute illogical rubbish.

The real-line is not limited to whole numbers, so, for example, the set of [0,7) can't take 7 as the immediate successor of 6, because there are infinitely many local numbers between 6 and 7.
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The only person who has tried to equate whole numbers to the interval [0,7) is you, doron. The "absolute illogical rubbish" is entirely yours. The rest of us agree with you.

Furthermore, 7 is not a member of the collection of local elements of [0,7).
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This is more of the same "absolute illogical rubbish". Perhaps if you actually read and understood what I had written you wouldn't have gone off on this ridiculous aside.

The immediate successor of 6 is the non-local element that is both on 6 AND 7.
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Since the original post restricted the domain to the integers (and was about successors, not immediate successors), your statement above is just that much more ludicrous. Try to pay attention. You will never keep up if not.
 
doronshadmi said:
Rubbish. Absolute illogical rubbish.

The real-line is not limited to whole numbers, so, for example, the set of [0,7) can't take 7 as the immediate successor of 6, because there are infinitely many local numbers between 6 and 7.
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Do you not know what an integer is, since jsfisher specifically referred to integers?


doronshadmi said:
Furthermore, 7 is not a member of the collection of local elements of [0,7).

The immediate successor of 6 is the non-local element that is both on 6 AND 7.

Let us notate this notion like this:

[0,6_]7
Click to expand...




doronshadmi said:
[x,y) = [x ]y

The immediate successor of any local element in [ ] is __ ( and so is the case of [x,y] that is = [x y] )
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Well typical Doron problem solving just claim that it “is both on 6 AND 7” and make up some equally undefined representation.

doronshadmi said:
Furthermore, by Standard Math [x,y) (y,z] is not accurate because there is no way to define the exact element which is the predecessor of y in the case of [x,y) or the successor of y in the case of (y,z].
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.

So unlike standard math, even in the case of integers, Doron can not “define the exact element which is the” “ the successor of y in the case of (y,z]” since his ‘immediate successor’ is both y and y+1.
 
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doronshadmi said:
[x,y) = [x ]y

The immediate successor of any local element in [ ] is __ ( and so is the case of [x,y] that is = [x y] )
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I see, doron, that you continue to substitute meaningless notation for any substantive ideas. Notation is to be used as a convenience, a shorthand. You use it as an excuse to not think.
 
The Man said:
So unlike standard math, even in the case of integers, Doron can not “define the exact element which is the” “ the successor of y in the case of (y,z]” since his ‘immediate successor’ is both y and y+1.
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So unlike standard math that totally ignores the exact notion of +1 (which is the non-local element between local y and local z) , where z value is based on local y value and +1 non-local value.

By the way – or + determines the direction of the non-local element from one local element to another local element.

Moreover, there is a non-local element between any given pair of any collection, which can be used in at least two ways:

{12, -pi, 14, 7, 8}

Example 1: Order has no significance

In this case the non-local element is used to simply notate the fact that each local element has a different value, for example:

12 -pi 14 7 8

Example 1: Order has significance

In this case the non-local element is used to notate the exact difference and direction between different local values, for example:

-pi_____7_8__12__14


Furthermore, by ignoring the exact value of each local element, we are able to show (by using Non-locality\Locality bridging) exactly how a collection is a Non-local\Local mathematical object of superposition\non superposition of ids.

Standard Math has no ability to get that because it is closed under Locality (and uses Non-locality (for example: +1) as its hidden assumption).

The Man said:
By your own assertions Not red is blue. Thus in the example I gave with the closed intervals [x,y] is red and [y,z] is blue (or not red by your ascriptions) the point ‘y’ is both in red and not in red (or blue by your own assertions). The only difference Doron is self-consistency, standard math has it while your notions do not.
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First let us observe an ordered collection:

A color is possible iff the given element has a direction.

A point itself has no direction and therefore no color.

A line segment has a direction and therefore color.


Now, let us observe an unordered collection:

A point indirectly has a color iff it is observed through a line segment which actually gather transparent (colorless) local elements by a specific color, where this color notates the simultaneous bi-directional parallel property of the non-local element.

Standard Math has no ability to research this universe.
The Man said:
What, so you can’t define any of the ‘infinitely many examples’ in your notions?
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The Organic Numbers.

The Man said:
The fact that it is not included makes it the successor and predecessor to those intervals, as jsfisher also noted.
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Nonsense.

It does not matter if we deal with [x,y] or [x,y), in both cases y is not the immediate successor of any given local element.

Only a non-local element is the immediate successor or predecessor of local elements.

--------------------------------------

The Man and jsfisher continue to lie to themselves because they have no clue with what they are dealing.

--------------------------------------

Generally, any immediate successor or predecessor must be a non-local element, and it does not matter if we deal with ordered or unordered collections.
 
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doronshadmi said:
It does not matter if we deal with [x,y] or [x,y), in both cases y is not the immediate successor of any given local element.
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You have moved the goal posts, I see. You have also failed to comprehend what others have written.

Assuming X < Y < Z, and any reasonable definition for "immediate successor", then, like it or not, doron, Y is in fact an immediate successor to [X,Y). So is [Y,Z]. So is ....

And it does matter if we deal with [X,Y] or [X,Y).

Only a non-local element is the immediate successor or predecessor of local elements.
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In the psychotic world of doronetics perhaps, and as has been shown repeatedly, doronetics is just a convoluted collection of unnecessary notions that are contradictory and inconsistent and lead no where.
 
doronshadmi said:
Moreover, there is a non-local element between any given pair of any collection
jsfisher said:
Blatantly false. Consider, for example, the collection of the color blue, the number seventeen, and the continent of Antarctica.
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No problem:

a=color blue
b=the number seventeen
c=continent of Antarctica

a b c = a c b = b c a = b a c = c b a = c a b
 
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jsfisher said:
You have moved the goal posts, I see. You have also failed to comprehend what others have written.

Assuming X < Y < Z, and any reasonable definition for "immediate successor", then, like it or not, doron, Y is in fact an immediate successor to [X,Y). So is [Y,Z]. So is ....

And it does matter if we deal with [X,Y] or [X,Y).
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Since you do not get that a successor or a predecessor is only a non-local element, you can't get that for any given immediate successor of some collection that its cardinal > 1 there must be an immediate predecessor, and for any given immediate predecessor of some collection that its cardinal > 1 there must be an immediate successor.

Since you can't show it, your reasoning is nothing but an illusion that does not hold water.

On the contrary by show that any successor or predecessor is a non-local element it is easy to show how it is an immediate successor or predecessor of any given value.

jsfisher said:
In the psychotic world of doronetics perhaps, and as has been shown repeatedly, doronetics is just a convoluted collection of unnecessary notions that are contradictory and inconsistent and lead no where.
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In the psychotic world of Cantor and his followers, we can clearly see that they have no clue what a successor or a predecessor really are.

For the past 130 they sell to the world a defective merchandise that is based on lies and hidden assumptions.
 
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doronshadmi said:
No problem:

a=color blue
b=the number seventeen
c=continent of Antarctica

a b c
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Setting your meaningless glyphs one side, what are you alleging is between blue and Antarctica.

Simple question: What's between blue and Antarctica?
 
doronshadmi said:
Since you do not get that a successor or a predecessor is only a non-local element...
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I understand successor and predecessor just fine. You, however, clearly do not, so you have imaged some bizarre alternate. Don't fault me for not accepting your contradictions and inconsistencies as fact.

you can't get that any immediate successor of some collection that its cardinal > 1...
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I don't suppose it would be possible to get you to stop abusing that term. Catholics have cardinals, not collections. It really looks bad for you if you can't even get these simple things correct.

there must be an immediate predecessor, and any immediate predecessor of some collection that its cardinal > 1 there must be an immediate successors.
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Why must there be? This is just something you have decided must be true yet you have no basis for that belief. Your wants and desires about what you'd like Mathematics to be aren't relevant.

Since you can't show it, your reasoning is nothing but an illusion that does not hold water.
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It's your fantasy; the obligation falls to you to "show it". So far, though, you haven't.


In the psychotic world of Cantor and his followers, we can clearly see that they have no clue what is really a successor or a predecessor.

For the past 130 they sell to the world a defective merchandise that is based on lies and hidden assumptions.
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And yet, you can't point out any defects, lies, or hidden assumptions. You can only claim they are there with no proof.
 
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jsfisher said:
I understand successor and predecessor just fine. You, however, clearly do not, so you have imaged some bizarre alternate.
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No you don't, as long as you do not get non-locality.

jsfisher said:
And yet, you can't point out any defects, lies, or hidden assumptions. You can only claim they are there with no proof.
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jsfisher , please show us how you define a line by dragging a point.
 
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doronshadmi said:
jsfisher said:
Setting your meaningless glyphs one side, what are you alleging is between blue and Antarctica.

Simple question: What's between blue and Antarctica?
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The thing that gathers them into a collection.
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You are evading the question, not answering it. Moreover, there was no collection involved in this question, just a pair of elements taken from a collection.

So, try again, please. A direct, specific answer would be appreciated: What's between blue and Antarctica?
 
doronshadmi said:
jsfisher said:
I understand successor and predecessor just fine. You, however, clearly do not, so you have imaged some bizarre alternate.
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No you don't, as long as you do not get non-locality.
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I understand the terms just fine. Perhaps, though, if you actually understood them, you might realize that the inconsistent, contradictory alternate reality you've concocted was totally unnecessary.

jsfisher said:
And yet, you can't point out any defects, lies, or hidden assumptions. You can only claim they are there with no proof.
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jsfisher , please show us how you define a line by dragging a point.
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I fail to see how my statement and your response are related. Moreover, I have never made any claims about dragging points to define lines.

Be that as it may, if you'd like to discuss the definition of line in the Euclidean sense because you think you can identify some flaw, we can do that. But be forewarned, the line is defined in Geometry implicitly by its properties. The rest tend to be figurative statements meant to help convey the concept.
 
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Apathia said:
Ah, one of those very telling moments.
What's between blue, Antarctica, and the Thing that gathers them together?
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Hi Apathia,

If you look at the Thing that gathers them together at the same level of the gathered things then:

A= blue
B= Antarctica
C= the thing the gathers them together = --

And you get A B C = A B --

If C is not at the same level of A or B than C = __ , and we get A B (C is simply itself).
 
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jsfisher said:
I understand the terms just fine.
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No, you don't.

Furthermore, you don't have a clue of how much you don't.
jsfisher said:
I fail to see how my statement and your response are related. Moreover, I have never made any claims about dragging points to define lines.
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Good so you and me disagree with The Man, that claims that a given dimension is defined by a lower dimension.
jsfisher said:
Be that as it may, if you'd like to discuss the definition of line in the Euclidean sense because you think you can identify some flaw, we can do that. But be forewarned, the line is defined in Geometry implicitly by its properties. The rest tend to be figurative statements meant to help convey the concept.
Click to expand...

1) Non-locality is not limited to Geometry.

2) If we limit ourselves to Geometry, then the existence of a line is not determined by any collection of points.

This is an utter nonesense to claim such a silly statment.
doronshadmi said:
Since you do not get that a successor or a predecessor is only a non-local element, you can't get that for any given immediate successor of some collection that its cardinal > 1 there must be an immediate predecessor, and for any given immediate predecessor of some collection that its cardinal > 1 there must be an immediate successor.
jsfisher said:
Why must there be? This is just something you have decided must be true yet you have no basis for that belief.
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No, it is derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion).
 
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doronshadmi said:
Hi Apathia,

If you look at the Thing that gathers them together at the same level of the gathered things then:

A= blue
B= Antarctica
C= the thing the gathers them together = --

And you get A B C = A B --

If C is not at the same level of A or B than C = __ , and we get A B (C is simply itself).
Click to expand...

Then "C" is local also?

"Same level"
Is "B" at one level local and another non-local?

Shuffling levels: "C" as itself becomes a non-local level?
 
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doronshadmi said:
Hi Apathia,

If you look at the Thing that gathers them together at the same level of the gathered things then:

A= blue
B= Antarctica
C= the thing the gathers them together = --

And you get A B C = A B --

If C is not at the same level of A or B than C = __ , and we get A B (C is simply itself).
Click to expand...


Ah yes the epitome of Doron’s notions that ‘thing’ ‘that gathers them together’ which may or may not ‘be on the same level’. Another one of those very telling moments Apathia, Doron seems to have this fixation with underlining things as if it makes them more significant, ascribing to that ‘line’ the very function of ‘gathering’ those ‘things’ above it. So much so is this graphical fixation that he takes his own notions of ‘level’ quite literally. When his ‘thing’ is “at the same level” he represents it as – at the same ‘level’ as the letters and I might surmise that he considers it just another of the ‘gathered things’. When he claims it is “not at the same level” then ‘C’ becomes the underline itself and Doron refer to it as “(C is simply itself)”. Of course Doron also underlined his notation when ‘C’ was at the same ‘level’ “And you get A B C = A B --”. So in typical Doronics I might surmise that it is intended to be ‘itself’ (the underline) and ‘not itself’ (just another element of the ‘gathered things’ being ‘gathered’ by that underline). Basically it all comes down to Doron’s magical amorphous anthropomorphic underlining ‘thing’ that does his ‘gathering’, unfortunately it did not bother to gather better or at least self-consistent notions for him.
 
doronshadmi said:
jsfisher said:
I understand the terms just fine.
Click to expand...
No, you don't.

Furthermore, you don't have a clue of how much you don't.
Click to expand...

You meant to say I don't understand it the same way you do. Your understanding is whatever you have invented to fill the void in your knowledge of mathematics.

jsfisher said:
I fail to see how my statement and your response are related. Moreover, I have never made any claims about dragging points to define lines.
Click to expand...
Good so you and me disagree with The Man, that claims that a given dimension is defined by a lower dimension.
Click to expand...

You are wrong again.

jsfisher said:
Be that as it may, if you'd like to discuss the definition of line in the Euclidean sense because you think you can identify some flaw, we can do that. But be forewarned, the line is defined in Geometry implicitly by its properties. The rest tend to be figurative statements meant to help convey the concept.
Click to expand...

1) Non-locality is not limited to Geometry.
Click to expand...

You have shifted topics, again. Please try to say focused.

We were discussing the fact you have repeatedly alleged Mathematics has flaws but you have never demonstrated any. It seemed like you wanted now to explore lines to expose what you think is a flaw. Guess not.

2) If we limit ourselves to Geometry, then the existence of a line is not determined by any collection of points.
Click to expand...

Are you trying to make a point by this statement? You seem to be in a stream of consciousness mode right now, blurting out unconnected statements.

This is an utter nonesense to claim such a silly statment.
Click to expand...

What statement are you claiming is silly?

doronshadmi said:
Since you do not get that a successor or a predecessor is only a non-local element, you can't get that for any given immediate successor of some collection that its cardinal > 1 there must be an immediate predecessor, and for any given immediate predecessor of some collection that its cardinal > 1 there must be an immediate successor.
jsfisher said:
Why must there be? This is just something you have decided must be true yet you have no basis for that belief.
Click to expand...
Click to expand...
No, it is derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion).
Click to expand...

What property of any collection would that be?
 
Apathia said:
Ah yes the epitome of Doron’s notions that ‘thing’ ‘that gathers them together’ which may or may not ‘be on the same level’. Another one of those very telling moments Apathia, Doron seems to have this fixation with underlining things as if it makes them more significant, ascribing to that ‘line’ the very function of ‘gathering’ those ‘things’ above it. So much so is this graphical fixation that he takes his own notions of ‘level’ quite literally. When his ‘thing’ is “at the same level” he represents it as – at the same ‘level’ as the letters and I might surmise that he considers it just another of the ‘gathered things’. When he claims it is “not at the same level” then ‘C’ becomes the underline itself and Doron refer to it as “(C is simply itself)”. Of course Doron also underlined his notation when ‘C’ was at the same ‘level’ “And you get A B C = A B --”. So in typical Doronics I might surmise that it is intended to be ‘itself’ (the underline) and ‘not itself’ (just another element of the ‘gathered things’ being ‘gathered’ by that underline). Basically it all comes down to Doron’s magical amorphous anthropomorphic underlining ‘thing’ that does his ‘gathering’, unfortunately it did not bother to gather better or at least self-consistent notions for him.
Click to expand...
What a low level of abstraction.

The insider can't get that the thing that gathers things is permanently not one of those things.

So if we ask "what’s between the thing that gathers things and the gathered things", we have these options:

This thing is observed by this question as one of the gathered things (it is on the same level of the gathered things, and there is a thing in another level that gathers them into some collection, for example A B –

Another option is that that this question is equivalent to the question of "what exists northern to the north pole?" .

Since the question is meaningless, then the answer is that __ is between A B.


Apathia said:
Then "C" is local also?

"Same level"
Is "B" at one level local and another non-local?

Shuffling levels: "C" as itself becomes a non-local level?
Click to expand...

You do not get the idea.

At the momnet that you ask "what's between bla bla bla" this "bla bla bla" is local w.r.t "what's between the bla bla bla" and "what's between the bla bla bla" is non-local w.r.t "the bla bla bla".

Some analogy:

This is like the horizon, each time new things are not the horizon as long as you go to the horizon, but the line of the horizon is always there in a different level, and it is not made of the things that are gathered by it.

For better understanding, please see page 10 at http://www.geocities.com/complementarytheory/OMPT.pdf .
 
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