Deeper than primes

[jsfisher]

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.

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:

it is derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion).

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.

 

[doronshadmi]

Now you are claiming a “notionless” “notion”, how uncharacteristic of you.

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.

 

[jsfisher]

Let us research these line segments:


________

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.

 

[doronshadmi]

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.

______ 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.

 

[The Man]

Dragging a point, isn't it?

Isn’t what?

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.

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’.

 

[doronshadmi]

Isn’t what?

Has no notion.

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 facts are that a point has no sides, but a line segemnt has.

 

[The Man]

Has no notion.

So it isn’t "Has no notion"?

The facts are that a point has no sides, but a line segemnt has.

First you have to define your 'sides' and only then can you assert any relation or lack thereof with a point, points, a line segment, line segments or whatever.

 

[jsfisher]

...Please define your ‘sides’.

It will never happen. Definitions are far too limiting.

 

[jsfisher]

Lest we drift too far from this, what did you mean by the following, Doron?

any collection of all distinct objects (the standard mathematical notion).

 

[The Man]

It will never happen. Definitions are far too limiting.

Undoubtably, those darn deffinitions just get in the way of Doron's notions and never seem to bode well for him.

 

[Little 10 Toes]

"magnitude of existence" definition

[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).

Yes you did use the term "distenct[sic] elements".

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).

So how does one find/determine "the existence of objects"?

 

[zooterkin]

So, how about that definition of "crisp", and some examples of "crisp ids"?

 

[doronshadmi]

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.

 

[doronshadmi]

Yes you did use the term "distenct[sic] elements".

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.

So how does one find/determine "the existence of objects"?

The non-total existence between Emptiness and Fullness.

 

[The Man]

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.

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‘.

 

[doronshadmi]

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‘.

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.

 

[doronshadmi]

A point is a location and a single element, there are an infinite number of other locations or points ‘with respect to’ that location...

The other locations are not on that point, so that point (or any other point) has no sides.

 

[zooterkin]

Who is saying a point has 'sides'?

 

[Little 10 Toes]

"magnitude of exsistence" definition

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.

So how does one find/determine "the existence of objects"?

The non-total existence between Emptiness and Fullness.

You did not answer the question. Please explain the process to determine "the existence of objects"

 

[doronshadmi]

Who is saying a point has 'sides'?

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].