Deeper than primes

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doronshadmi said:
An ambiguity you have not yet resolved, by the way, jsfisher, which is a direct result of your limited Weak Emergence viewpoint, which is also a notionless mechanic action.
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What are you on to now? You really need to stop going off on these tangents instead of addressing the issue at hand. The question was about a poorly worded sentence of yours. It is not at all clear what you meant by the following:

doronshadmi said:
it is derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion).
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If you don't like the interpretation I gave to it -- an interpretation I have already described along with my reasons for adopting that interpretation -- then provide some clarity about what you think you meant.

Be careful, though, because it needs to be consistent with the early declaration that the collection need only have a cardinality > 1. Also, it somehow needs to support your claim that completeness will be a "must have" property of any such collection.
 
The Man said:
Now you are claiming a “notionless” “notion”, how uncharacteristic of you.
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Dragging a point, isn't it?


Some facts:

A point does not have sides as a line segment has.

Let us research these line segments:


________



The blue line left side is the red line right side (and vice versa), but since a point has no sides it is not blue and not red.

Furthermore, since a point has no sides, then the claim that it is both blue AND red does not hold, because being blue or red depends on the existence of sides.

To any given R member along the real-line there is an immediate successor or predecessor with sides, for example:

________ , in this case we have 3 R members, and two immediate successors\predecessors.
 
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doronshadmi said:
Let us research these line segments:


________
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All you did was put two line segments next to each other. That doesn't demonstrate a single line segment having sides. Moreover, the concepts of left and right (sides) require a reference. That reference would be a hidden assumption, Doron. We all know your disdain for hidden assumptions, so you may want to address this.
 
jsfisher said:
All you did was put two line segments next to each other. That doesn't demonstrate a single line segment having sides. Moreover, the concepts of left and right (sides) require a reference. That reference would be a hidden assumption, Doron. We all know your disdain for hidden assumptions, so you may want to address this.
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______ has two sides, each one w.r.t the other (the names of the sides are not important).

No point has this property.

No hidden assumption is used here.
 
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doronshadmi said:
Dragging a point, isn't it?
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Isn’t what?

doronshadmi said:
Some facts:

A point does not have sides as a line segment has.

Let us research these line segments:


________



The blue line left side is the red line right side (and vice versa), but since a point has no sides it is not blue and not red.

Furthermore, since a point has no sides, then the claim that it is both blue AND red does not hold, because being blue or red depends on the existence of sides.

To any given R member along the real-line there is an immediate successor or predecessor with sides, for example:

________ , in this case we have 3 R members, and two immediate successors\predecessors.
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The facts are, as stated before it depends on the intervals you assign as blue or red. Introducing a new word like ‘sides’ does not change those facts; if by side you mean boundaries then you should just say boundaries. Of course that goes against your ‘soggy’ style to actually say what you mean. Please define your ‘sides’.
 
The Man said:
Isn’t what?
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Has no notion.


The Man said:
The facts are, as stated before it depends on the intervals you assign as blue or red. Introducing a new word like ‘sides’ does not change those facts; if by side you mean boundaries then you should just say boundaries. Of course that goes against your ‘soggy’ style to actually say what you mean. Please define your ‘sides’.
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The facts are that a point has no sides, but a line segemnt has.
 
"magnitude of existence" definition

doronshadmi said:
[v]Yes (but instead of "distinct objects" I use "the existence of objects")

0 magnitude = no existing objects (Emptiness (the totality of non-existence)).

∞ magnitude = beyond existing objects (Fullness (the totality of existence)).

0 < n < ∞ , n magnitude = existing objects (the non-total existence).
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Yes you did use the term "distenct[sic] elements".

doronshadmi said:
This is a beautiful question.

As I get it, Measuring is the notion that stands at the basis of the determination to understand many things by using a common principle that help us to compare them with each other.


According to http://en.wikipedia.org/wiki/Measure_theory the common principle is a collection of distenct elements (a set).
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So how does one find/determine "the existence of objects"?
 
A single element that there is more than a one location on it, each one of those locations is called a side w.r.t this single element.

Furthermore, no amount of the sides is exactly this single element (the Whole is greater than the sum of the Parts).

For example:

A line segment is the minimal example of a single element that has sides.

A point is en example of a single element that has no sides.
 
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Little 10 Toes said:
Yes you did use the term "distenct[sic] elements".
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No, I did not.

All I care is the magnitude of the existence, and the distinction between the total and the non-total.

A collection of objects is a non-total existence.

Little 10 Toes said:
So how does one find/determine "the existence of objects"?
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The non-total existence between Emptiness and Fullness.
 
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doronshadmi said:
A single element that there is more than a one location w.r.t it, each one of those locations is called a side w.r.t this single element.

Furthermore, no amount of the sides is exactly this single element.

For example:

A line segment is the minimal example of a single element that has sides.

A point is en example of a single element that has no sides.
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A point is a location and a single element, there are an infinite number of other locations or points ‘with respect to’ that location, thus a point meets your definition (if you could call it that) of a ‘side‘.
 
The Man said:
A point is a location and a single element, there are an infinite number of other locations or points ‘with respect to’ that location, thus a point meets your definition (if you could call it that) of a ‘side‘.
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You are right, let us correct it.

A single element that there is more than a one location on it, each one of those locations is called a side w.r.t this single element.

Furthermore, no amount of the sides is exactly this single element (the Whole is greater than the sum of the Parts).

For example:

A line segment is the minimal example of a single element that has sides.

A point is en example of a single element that has no sides.
 
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The Man said:
A point is a location and a single element, there are an infinite number of other locations or points ‘with respect to’ that location...
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The other locations are not on that point, so that point (or any other point) has no sides.
 
"magnitude of exsistence" definition

doronshadmi said:
All I care is the magnitude of the existence, and the distinction between the total and the non-total.

A collection of objects is a non-total existence.

The non-total existence between Emptiness and Fullness.
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Little 10 Toes said:
So how does one find/determine "the existence of objects"?
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doronshadmi said:
The non-total existence between Emptiness and Fullness.
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You did not answer the question. Please explain the process to determine "the existence of objects"
 
zooterkin said:
Who is saying a point has 'sides'?
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Let us take this case, where the left side of the blue element is the right side of the red element:

________

Any one who claims ( fore example: The Man in http://www.internationalskeptics.com/forums/showpost.php?p=4714591&postcount=2841 ) that the point between the single blue element and the single red element, is both blue AND red, actually claims that a single point has sides, which is wrong.

For example, The Man does not understand that if y of [x,y][y,z] is considered as a point, then it is not blue in the case of [x,y] AND not red in the case of [y,z].

Things are changed if y is a side on [x,y] OR a side on [y,z].

The difference between a point and a side is qualitative and not quantitative.

EDIT:

The qualitative difference can be understood in terms of logical connectives as follows:

If y is a point in the case of [x,y][y,z], then since it has no sides it does not have blue or red sides on it (it is not blue AND not red).

If y is a side in the case of [x,y][y,z], then it is blue w.r.t [x,y] OR red w.r.t [y,z].
 
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doronshadmi said:
Let us take this case, where the left side of the blue element is the right side of the red element:

________

Any one who claims ( fore example: The Man in http://www.internationalskeptics.com/forums/showpost.php?p=4714591&postcount=2841 ) that the point between the single blue element and the single red element, is both blue AND red, actually claims that a single point has sides, which is wrong.
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He was only explaining that that's what you had defined.

For example, The Man does not understand that if y of [x,y][y,z] is considered as a point, then it is not blue in the case of [x,y] and not red in the case of [y,z].
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So what colour do you say it is, if it is on both the blue and the red lines?
 
A point has no sides w.r.t any element, including itself.

A line can have sides, such that no amout of sides that are on this line, is that line.
 
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jsfisher said:
**bump**
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doronshadmi said:
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.
sjfisher said:
Note that the word all appears nowhere in the claim. Note also that Doron cannot support the claim.
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Ok, let us write it like this:

Any element of the collection of all elements of the interval [x,y) including y element, must have an immediate successor OR an immediate predecessor.

This claim must be true, because we are using the universal quantifier "for all" on the interval [x,y).
 
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doronshadmi said:
Ok, let us write it like this:

Any element of the collection of all elements of the interval [x,y) including y element, must have an immediate successor OR an immediate predecessor.

This claim must be true, because we are using the universal quantifier "for all" on the interval [x,y).
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Except that, by definition, [x,y) does not include y.
 
doronshadmi said:
Ok, let us write it like this:

Any element of the collection of all elements of the interval [x,y) including y element, must have an immediate successor OR an immediate predecessor.

This claim must be true, because we are using the universal quantifier "for all" on the interval [x,y).
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This is not your original statement. In it you simply required a collection with cardinality > 1. Are you retracting your original statement?

Moreoever, in the current version of your statement involving "all distinct objects", you have switched from collection to interval. Are you retracting the original version of your second statement.

And moreover, are you assuming the underlying domain for these intervals is the set of real numbers with the common order relationship? This is not implicit in your statement, but it is required to get to your statement about completeness.
 
jsfisher said:
This is not your original statement. In it you simply required a collection with cardinality > 1. Are you retracting your original statement?

Moreoever, in the current version of your statement involving "all distinct objects", you have switched from collection to interval. Are you retracting the original version of your second statement.

And moreover, are you assuming the underlying domain for these intervals is the set of real numbers with the common order relationship? This is not implicit in your statement, but it is required to get to your statement about completeness.
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In the last post I use the standard notion of using the universal quantifier "for all" on the elements of the interval [x,y).

An interval is an ordered collection of R members:
http://en.wikipedia.org/wiki/Interval_(mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them.
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In that case, for example, 1 of [0,1) must have an immediate predecessor by the definitions of Standard Math, but Standard Math cannot explicitly define it.

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

On the contrary, Organic Mathematic explicitly defines the immediate predecessor of 1, as the non-local element that is both on 1 AND on any arbitrary member of [0,1) interval.
 
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doronshadmi said:
In the last post I use the standard notion of using the universal quantifier "for all" on the elements of the interval [x,y).
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Ok, but that does mean you made a sequence of statements that you have abandoned. There are now many, many constraints not present in your original statements. You have wasted a lot of bandwidth by stating something completely different from what you meant in the first place.

An interval is an ordered collection of R members
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There's a little more to it than just that, but ok.

In that case, for example, 1 of [0,1) must have an immediate predecessor by the definitions of Standard Math, but Standard Math cannot explicitly define it.
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This doesn't follow from anything in Mathematics. There is no such requirement. Why do you think otherwise?
 
doronshadmi said:
This is the reason of why I explicitly wrote "including y element".
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The point was that [x,y) doesn't include y, so tacking on "including y" is a contradiction, not an addition. I will assume this is an ESL problem.

If you meant to add y, you should have said something like "[x,y) and y". (That would be equivalent to saying [x,y], by the way.)
 
jsfisher said:
Ok, but that does mean you made a sequence of statements that you have abandoned. There are now many, many constraints not present in your original statements.
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Nonsense.
jsfisher said:
This doesn't follow from anything in Mathematics. There is no such requirement. Why do you think otherwise?
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jsfisher you simply continue with your twisted style, in order to avoid the simple fact that Standard Math uses the universal quantifier "for all" on an interval [x,y) of R members, but cannot explicitly define the immediate predecessor of y.
jsfisher said:
The point was that [x,y) doesn't include y, so tacking on "including y" is a contradiction, not an addition. I will assume this is an ESL problem.

If you meant to add y, you should have said something like "[x,y) and y". (That would be equivalent to saying [x,y], by the way.)
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It does not change the fact that Standard Math cannot explicitly define the immediate predecessor of y, whether we deal with [x,y) or [x,y].

Your twisted legend about 2^aleph0 members that cannot be expressed by aleph0 members is over, because Cantor's second diagonal is a direct proof of the incompleteness of any non-finite collection, ordered or not (the claim that there exists an interval of all non-finite members is false, because the Whole is greater than the sum of the Parts).

Pages 9,12,13 of http://www.geocities.com/complementarytheory/OMPT.pdf explicitly show the new notions about non-finite collections.
 
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doronshadmi said:
jsfisher said:
Ok, but that does mean you made a sequence of statements that you have abandoned. There are now many, many constraints not present in your original statements.
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Nonsense.
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Let's review: First you said it was true for any collection with cardinality > 1. Then you changed it to any collection of all distinct objects. Now, you have morphed it to requiring an interval over the reals along with the normal order property.

Are you honestly saying those different statements are saying the same thing?

jsfisher said:
This doesn't follow from anything in Mathematics. There is no such requirement. Why do you think otherwise?
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jsfisher you simply continue with your twisted style, in order to avoid the simple fact that Standard Math uses the universal quantifier "for all" on an interval [x,y) of R members, but cannot explicitly define the immediate predecessor of y.
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I see your "according to standard mathematics" claim has also morphed. It is now an "according to doron" claim. I also see you have introduced a subtle change. Before, we were discussing whether [X,Y) had an immediate successor. It does, and Y is one such example. But now, you've shifted to the immediate successor of just Y -- the interval has become irrelevant.

Why did you even introduce the interval if you were going to ignore it?

No, Y has no immediate successor. This is true for any real number, and it is also true for any rational number. Why do you think it must be otherwise?

jsfisher said:
The point was that [x,y) doesn't include y, so tacking on "including y" is a contradiction, not an addition. I will assume this is an ESL problem.

If you meant to add y, you should have said something like "[x,y) and y". (That would be equivalent to saying [x,y], by the way.)
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It does not change the fact that Standard Math cannot explicitly define the immediate predecessor of y, whether we deal with [x,y) or [x,y].
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As already pointed out, by asking about the immediate predecessor of Y, you have made irrelevant the intervals.

By the way, you are misusing the word, define. You don't "define the immediate predecessor of Y". You define what "immediate predecessor" means, then the rest follows.

ETA:
On the other hand, if you do want to continue intervals as a vital part of this discussion, then the term, immediate predecessor must include intervals as well. In this case, Y does have immediate predecessors, all of the form [X,Y) or (X,Y).​

Your twisted legend about 2^aleph0 members that cannot be expressed by aleph0 members is over, because Cantor's second diagonal is a direct proof of the incompleteness of any non-finite collection, ordered or not.
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Cantor's second diagonal? Boy you twisted that one, didn't you. Did you mean Cantor's second uncountability proof?

You have alleged this before, and you failed before to prove the allegation. Care to try again? Perhaps you'd like to disprove Cantor's first proof, too.
 
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Little 10 Toes said:
Lets recap what you say about the phrase "magintude of existence":

1) magnitude is a measurement unit
2) it does not measure the number of distinct objects in a collection (aka Set_(mathematics)WP) but it does however measure "the existence of objects"
3) there is no way to determine "the existence of objects"
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http://www.internationalskeptics.com/forums/showpost.php?p=4727965&postcount=2918 is my exact ansewr to your question.

If you don't like it you have to explicitly show why you disagree with it.

So please do it in details.
 
jsfisher said:
Are you honestly saying those different statements are saying the same thing?
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Yes, and your inability to get it is the reason of why you don't get my answers about this case.
jsfisher said:
No, Y has no immediate successor. This is true for any real number, and it is also true for any rational number. Why do you think it must be otherwise?
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This is a good example of how you totally ignore what you read.

I am talking about the immediate predecessor of y, whether we deal with [x,y] or [x,y), and you insist to talk about y's immediate successor.

Actually (and this is the main point of my argument) it does not matter if we are talking about an immediate predecessor or an immediate successor of any arbitrary given R member along the real-line.

My claim is this, if y is an immediate successor of some R member, then this member is the immediate predecessor of y. This claim must be true both in [x,y) or [x,y] cases, since the universal quantifier "for all" is used in both cases.

Standard Math uses the twisted legend, that any representation method is limited to aleph0, and as a result there is no way to represent the immediate successor or the immediate predecessor of any arbitrary given R member along the real-line.

But this twisted legend is collapsed because Standard Math (as you wrote) can't show the immediate successor or the immediate predecessor of any arbitrary given Q member along the real-line, even if there are aleph0 Q members along the real-line.

We do not need more than that in order to show that the use of the universal quantifier "for all" on a collection of non-finite elements, does not hold.
jsfisher said:
Cantor's second diagonal? Boy you twisted that one, didn't you. Did you mean Cantor's second uncountability proof?

You have alleged this before, and you failed before to prove the allegation.
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No, you have failed to get the fact that Cantor explicitly used a way to define the exact member that is not mapped with any member of N, and by using this method, the conclusion and the premise are under a circular reasoning.

jsfisher, as long as your community uses the pinky garbage can called "proper classes" as an ad hoc problems' solver, you are nothing but a religious community that has nothing to do with modern science.
 
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doronshadmi said:
You are right, let us correct it.

A single element that there is more than a one location on it, each one of those locations is called a side w.r.t this single element.

Furthermore, no amount of the sides is exactly this single element (the Whole is greater than the sum of the Parts).

For example:

A line segment is the minimal example of a single element that has sides.

A point is en example of a single element that has no sides.
Click to expand...

OK, so as locations, points still meet your requirement for being your ‘sides’.
 
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