Sorry, I'm not going to aim at a moving target.
Deeper than primes
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Sorry, I'm not going to aim at a moving target.
doronshadmi
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So why you are using the nonsense of "dragging a point" in order to define a line?doronshadmi said:
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Little 10 Toes
Master Poster
Asking for the second time:
You went back and edited several posts and you had problems understanding the word "I" so I ask the same questions without using the word I.
The Man
Unbanned zombie poster
Again…
So a set containing no dimensions would have a “cardinality 0 if the considered universe” is dimension?
Again the analogy was “0 apples” to “0 dimensions”. If you want it to be “0 apples” to “0 points” that‘s a different analogy as I addressed in my pervious post.
Again..
I thought you said you were going to try to “do it clearer”, not just repeat the same claims I addressed in my previous post?
OK so now your “point” does not have “a dimension” as you claimed before?
So you think simply repeating the same things from your pervious post, verbatim, is doing “it clearer”?
Your “direct perception” has failed you yet again.
Doron if the answer to how much (by mass) of a 1 kg apple pie is apples, is 0.75 kg and each apple used was about 0.125 kg (excluding the core, skin and seeds), how many apples were used in that pie?
In case you haven’t realized it yet the answer to how much of the apple pie is apples (by mass) is answered both by how many apples were used and how much mass (excluding the core, skin and seeds) each had. How much mass each apple has is represented by how many kgs of matter each contains (excluding the core, skin and seeds). So how much is directly dependent on how many of some given units of measure, whether it be apples, kgs or whatever.
How much apple can your pie have when how many apples you have is 0?
Doron, “How much” is just a question of “How many” of some unit representation.
How much (in apples) of an apple is apple? How many apples is that? Take half of that and how much (in apples) is that now? How many apples would that be now?
So you still simply have not or can not answer the question of how many dimensions your “point” has.
The same “exercises” for you, that you have as yet to directly answer.
Size is an aspect of dimension, as a point has no dimension(s) it thus has no size.
A point is an abstract concept with no dimension and thus no size, it “exists” specifically as that abstract concept.
A set with only one member has a cardinality of one, so “a set that have at least a point as its member” has a cardinality of at least one. You still seem to be, perhaps deliberately, ignoring that it is a set containing the ordinate or co-ordinates of some point that represents dimension (in this consideration) not a set containing a point. So I guess you’re simply not done comparing apples to oranges.
So how much (in apples) of an apple is apple? More specifically to your assertion above, what is the “size” of an apple in apples? How many apples is that? Take half of that and what is the “size” of that in apples? How many apples is that now?
Again dimension is represented (in this consideration) by a set containing the ordinate or coordinates needed to located that point in some space or object, not a set containing just a point. Your continued and apparently deliberate ignorance of the fact does not change that fact.
You still seem to be confusing, most likely deliberately, no dimension with no point.
Yes, to what? That now your “point” is 0 dimensional?
Would this “concept of Dimension” of yours be similar to the one that is defined by points, specifically the ordinate or coordinates needed to locate some point in a given space or object?
Again “included NXOR excluded w.r.t a point” is always false as inclusion and exclusion are mutually exclusive.
You still seem to be ignoring the obvious fact , again apparently deliberately so, that it is the ordinate or coordinates needed to located a point in some space or object that defines dimension (in this consideration).
Doron, the ‘elements’ “of the concept of Dimension” are again the ordinate or coordinates needed to located a point in some space or object. Having no ordinate or coordinates does not infer no point, but it does define no dimension(s). Again you shifted your “universe based on dimension” to one based on point(s), which again means that you might actually be learning some geometry in spite of yourself.
See there you go again you specifically claim if your “universe of apples has no apples, then we deal with the empty set” yet for your “universe of dimensions” you do not specifically state if it “has no” dimension“, then we deal with the empty set”. Once again you are simply trying to infer no point from no dimension when a point is specifically defined as having no dimensions.
So now your “empty set” that has no apples in your “universe of apples” has a “property of apple”?
Yet you still do not specifically assert the empty set for “no dimension” in your “universe of dimensions” as you did for your “universe of apples”. Once again you are simply ignoring no dimension in your “universe of dimensions” while proclaiming the empty set for no apples in your “universe of apples”.
Yet “no apples” is under your “universe of apples” as the empty set. Once again you are simply ignoring “no dimension" as the empty set in your “universe of dimensions”. Once again you seem to be confusing, and at this point it can only be deliberate, a set containing a point with the definition of dimension (in this consideration) as the (or a set containing the) ordinate or coordinates need to locate a point in some space or object. As I said before a point is a defining element of dimesion, specifically the ordinate or coordinates need to locate a point in some space or object. So no point means no dimension(s) as there is nothing to locate. However, having just a single point also means no dimension(s) as although you now have something to locate you have no way of locating it (the ordinate or coordinates of that point is the empty set). In order to locate it you need at least one other point in a discrete space and if your space is continuous then between those two points are an infinite number of points, both giving a dimension with in which to locate that point or any of those points.
Do you have any evidence to support your claim? (The notorious Q. LOL.)
How much money do I need to buy a pipe like that?
26 dollars and 99 cents plus tax.
Hmm. I guess you do.
It doesn't go like that. The number of dependent variables defines the dimensionality of drawn objects:
f(x,y) = 0 draws a 2D object:
f(x) = 0 draws a 1D object -- a horizontal line
Now, which function would draw the 0-D object, which the point?
It's a function with no dependent variable. But such a function doesn't exist and therefore a point cannot be drawn at a specified location, coz there is no function to do so. But a point can be located by a set of two functions. A point of intersection, for example, is a a solution of f(x) - g(x) = 0. Points are just imaginary reference points.
You need to be careful though when you go the other way. Remember that
y = f(x)
z = f(x,y)
and so on.
When you start to manipulate the independent variables the dimensional objects will respond according to the dependent variable y, z, and so on. The changes can be detected with the help of co-ordinates y, z, and so on. Here is an example:
Looks familiar?
If you rewrite the equation in the graph to satisfy certain conditions that exist in the Gamma-Rho phase space, then . . .
Yep. It's the four-legged mischievous demon Ekklund.
The higher dimensions are virtually infested with deities of peculiar varieties, so be careful -- unless you are an atheist with limited, local-only reasoning that is closed to the isomorphic algebra of multi-dimensional manifolds.
doronshadmi
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EDIT:The Man said:
Let us get it this way:
An element of a given universe has the most basic property of that universe.
The property can be "Apple", "Dimension", … etc …
------------------------
By following your argument:
If "no apples" is not the lack of the most basic property of the universe of apples (because, afrer all, the term "apples" is used), then this universe has an empty set as one of its members, known as "no apples".
If "no dimension" is not the lack the most basic property of the universe of dimensions (because, afrer all, the term "dimension" is used), then this universe has an empty set as one of its members, known as "no dimension".
--------------------------
In that case there is an exclusive empty set for each given universe, which is a false claim, because empty set is not an exclusive element of any given universe.
--------------------------
Let us follow your argument about a point:
An element that has "no dimension" is equivalent to empty set under the universe of dimensions, and a point is such an element.
--------------------------
But this is a false claim because empty set is not an exclusive element of any given universe, and since "no dimension" is an exclusive element then a point is not equivalent to empty set.
A point (which is not equivalent to empty set) and a line are elements of the universe of dimensions, where a point is a dimensional element that has 0 degrees of freedom and a line is a dimensional element that has more than 0 degrees of freedom.
By getting this simple fact, a point is located XOR not-located w.r.t to a given line, where a line is located NXOR not-located w.r.t a given point.
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doronshadmi
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A pair of coordinates is related to 0 dimensional space under 2 dimensional space, so?
A single ordinate is related to 0 dimensional space under 1 dimensional space (where the term "horizontal" is insignificant), so?
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So, once again, you demonstrate your ignorance.
What, exactly, is "0 dimensional space"? Is that just you struggling to understand what a point is? As epix says, a point is just an imaginary reference point; you specify it with co-ordinates; it is a location.
doronshadmi
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The Man said:
The Man, in addition to post http://www.internationalskeptics.com/forums/showpost.php?p=6270709&postcount=11327 :
{} is not equivalent to {no apples}
{} is not equivalent to {no dimension} is equivalent to {.}
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doronshadmi
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You can't use the word "point" as a part of its definition ("a point is just an imaginary reference point"), because you get a circular reasoning, which is invalid.
You'll be the expert on what constitutes a definition, then?
Yes, you are correct, a different word should be used; I was quoting epix, and missed the reuse of the word. Does that stop you from understanding what a point is, though, or a co-ordinate?
doronshadmi
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You get the notion of point under the universe of dimensional spaces:
A point is an existing dimensional space that has 0 degrees of freedom (no coordinates are related to points).
A line is an existing dimensional space that has 1 degrees of freedom (singletons of ordinates are related to points).
A plan is an existing dimensional space that has 2 degrees of freedom (pairs of coordinates are related to points).
A sphere is an existing dimensional space that has 3 degrees of freedom (triples of coordinates are related to points).
Etc... ad infinituum.
EDIT:
By the way, by understanding a dimensional space and its related coordinates, we are able to get the notion of Mutual Independency, because each value of pair of, triple of (or any greater finite amount of) coordinates can be changed independently of each other, and yet they are all related to given dimensional spaces (which is the property of mutuality), which have 2 or more degrees of freedom (where a point and its related values under a given dimensional space, is the local aspect of this dimensional space).
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Little 10 Toes
Master Poster
Asking for the third time:
You went back and edited several posts and you had problems understanding the word "I" so I ask the same questions without using the word I.[/QUOTE]
You went back and edited several posts and you had problems understanding the word "I" so I ask the same questions without using the word I.[/QUOTE]
doronshadmi
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Who is I that asks the same questions without using the word I?
http://www.internationalskeptics.com/forums/showpost.php?p=6267027&postcount=11316
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doronshadmi
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Some details that support your "No", please.
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What would be the point?
doronshadmi
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Maybe you tell us.
Also be aware of the fact that
AND
is a contradiction.
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Little 10 Toes
Master Poster
Fourth time asking a very simple question:
Are you sure that English is a second language for you? The way you can't comprehend it makes me wonder.
Not answering your ever changing posts (That is what zooterkin is referring to in the second quoted message) and dragging a point (the third quoted message) is not a contradiction.
Are you sure that English is a second language for you? The way you can't comprehend it makes me wonder.
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The Man
Unbanned zombie poster
Where did I ever make such a ridiculous “argument”? Again Doron stop trying to just pawn off asspects of your own failed reasoning onto others.
What the heck are you talking about? The empty set is by definition, well, empty becouse it excludes all "elements". This “exclusive empty set for each given universe” is just some ridiculous aspect of your own failed reasoning that again you're just trying to attribute to someone else.
No Doron the set of an ordinate or coordinates locating a point, when the space is that point, is the empty set. This has been explained to your several times yet you still simply ignore it. If you are going to assert “ Let us follow your argument about a point:” then at least try to follow that argument and not some imaginary nonsense you simply want to attribute to someone eles.
Too bad, it’s your claim, if you think it is false then the problem lies simply with you.
Nope again a point is specifically an “element” without dimension.
Simply changing from "included" and "excluded" to “located” and “not-located” does not help you. “located NXOR not-located w.r.t a given point” is still always FALSE as “located” and “not-located” are mutually exclusive.
Who ever said it was?
Doron “{no dimension}” or “{.}” are still not a set of the ordinate or coordinates needed to locate a point in that point. You’re still just jerking yourself around claiming apples aren’t the same as oranges.
The Man
Unbanned zombie poster
Nice one epix. Say, that guy does look familiar. Wasn’t he in that movie “Pirates of the Caribbean Plain: The Curse of the Buckled Surface“?
I don't think so. That universe, as any other universe, develops a very dense objects that generate such a strong gravitational pull that even the photon cannot overcome, so the very dense object is invisible. But there is no black juice, is there?
So?
Well, an "inductive reasoning" leads you to a conclusion that no ordinate is related to a point. Since the specific relation means, and has always meant, 'ordinate <--> variable' you can't draw a point at a specified location. But a line is a collection of points organized according to y=f(x). That means a property of a point can be established only when it exist in a multitude. A point is not a free particle like the neutrino; it manifest itself only through a 1-D object. It is like investigating the property of a quark which manifest itself only when proton forms an imaginary line by travelling fast inside a particle collider where it collides with another proton. The high energy fender-bender releases a quark. Now you can see the property of the quark/point.
You can see the lines where two protons were traveling along, and the point of impact is the point of intersection. The impact releases a quark/point so you can see it and investigate its property. You are establishing the property of a point through some philosophies foreign to this universe. By doing so, you are missing the very concept that the existence of Higgs boson relies upon.
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Who? The mischievous demon Ekklund?
I think he got a cameo in the sequel "Pirates of the Caribbean Plain: The Curse of the Swashbuckled Surface."
doronshadmi
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No The Man, you ignore the fact that a point is an existing element of the set of dimensional spaces, where the amount of its coordinates is 0.
This set looks like this:
{0,1,2,3,4,5,..}, where each value is the number of ordinates or coordinates that is related to each existing dimensional space.
Before you jump and replace each number by a set ( for example: {{},{{}},{{},{{}}}, …} ) be aware that according to OM each dimensional space is a non-composed element (or ur-element, if you wish) which is not a set, so the whole idea of Membership as defined among sets, is changed to Membership as defined among ur-elements, where this membership is based on sharing a common property ("Dimension", in this case).
EDIT:
A point and a line are ur-elements that shares the proprty of Dimension.
By understanding the Membership among ur-elements, which is based on shared property, a point is included XOR excluded w.r.t a line and a line is included NXOR excluded w.r.t a point (where no one of them is the component of the other).
A point is an existing dimensional space that has 0 degrees of freedom (0 coordinates are related to points).
A line is an existing dimensional space that has 1 degrees of freedom (singletons of ordinates are related to points).
A plan is an existing dimensional space that has 2 degrees of freedom (pairs of coordinates are related to points).
A sphere is an existing dimensional space that has 3 degrees of freedom (triples of coordinates are related to points).
Etc... ad infinituum.
Here it is:
{0, ...} , where 0 ( which is a member of {0,1,2,3,4,5,..} ) is the number of ordinates or coordinates needed to locate a point in 0 dimensional space.
The dimensional spaces can be also represented as { . , __ , ... } but we have a problem to represent dimensional spaces > 3 in this way.
By the way, by understanding a dimensional space and its related coordinates, we are able to get the notion of Mutual Independency, because each value of pair of, triple of (or any greater finite amount of) coordinates can be changed independently of each other, and yet they are all related to given dimensional spaces (which is the property of mutuality), which have 2 or more degrees of freedom (where a point and its related values under a given dimensional space, is the local aspect of this dimensional space).
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Let me stop you there. You appear to be still confused about what co-ordinates are. They tell you where the point is, not its size or extent. The number of (co-)ordinates needed to specify where a point (or anything else) is depends on the number of dimensions of the space it is located in, not the number of dimensions the point has.
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doronshadmi
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EDIT:
You appear to be still confused about what co-ordinates are. A dimensional space that has 0 degrees of freedom has an amount of coordinates that are derive from the difference of degrees of freedom that each dimensional space has w.r.t it.
But this is the particular case that is derive from the difference of dimensional spaces with more than 0 degrees of freedom w.r.t a dimensional space that has 0 degrees of freedom.
The arithmetic of this case is very simple:
Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.
Abs (1 degrees of freedom – 0 degrees of freedom) = 1 amount of (co-)ordinates.
Abs (2 degrees of freedom – 0 degrees of freedom) = 2 amount of (co-)ordinates.
Abs (3 degrees of freedom – 0 degrees of freedom) = 3 amount of (co-)ordinates.
Etc … at infinitum …
In general, the amount of (co-)ordinates is derive from the absolute difference among the degrees of freedom of dimensional spaces.
Another particular case defines the number of (co-)ordinates of dimensional spaces w.r.t themselves, and as we see the result is 0 amount of (co-)ordinates.
Also the arithmetic of this case is very simple:
Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.
Abs (1 degrees of freedom – 1 degrees of freedom) = 0 amount of (co-)ordinates.
Abs (2 degrees of freedom – 2 degrees of freedom) = 0 amount of (co-)ordinates.
Abs (3 degrees of freedom – 3 degrees of freedom) = 0 amount of (co-)ordinates.
Etc … at infinitum …
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Co-ordinates are called "degrees of freedom" in phase space, which is a geometry concept that enables engineers to better understand the mechanics of object assembly -- among other things. The purpose of drawing co-ordinates is to locate a point. But in phase space, co-ordinates are basically lines to be followed. In 3-D space, you have 3 degrees of freedom to move along. So what would you do?
It depends on circumstances. For example, if you have your back against the record machine then you . . . ?
The Man
Unbanned zombie poster
So now you’re now claiming a point has no dimension(s) since you claim it has no coordinates?
Related how, specifically?
Again as this “each dimensional space is a non-composed element (or ur-element, if you wish)” is just your own imposed limitation, it restricts only you.
Please tell us what “elements” the empty set “{}” is “composed” of? How many elements are in the set of coordinates for just a point? Your assertion above says “0”, thus it would be the empty set.
No ordinate or coordinates, no dimension(s) Doron.
Again a point specifically has no dimension(s) thus “the proprty of Dimension” it has is specifically, well, lacking.
Once again as “each dimensional space is a non-composed element (or ur-element, if you wish)” is just your own imposed limitation, it restricts only you. Still, this does not help you as “a line is included NXOR excluded w.r.t a point” is still always FALSE as included and excluded are mutually exclusive.
Again how does your “point” specifically “include” your “line” or your “line” specifically “include” your “point” when you claim both are “a non-composed element”?
Thus it has no dimension(s) as no “coordinates are related to” that point.
“related to points”, how, specifically?
Particularly considering that by your own restriction they are “non-composed element (or ur-element, if you wish)”. My recommendation would be that you simply stop ‘wishing’ that.
How are any of your "spaces" "dimensional" if they do not specifically "include" points?
Again…
How are your 2 and 3 “dimensional” spaces 2 or 3 dimensional if they are not “composed” of those, well, dimensions?
So now you’re now claiming a point has no dimension(s) as no ordinate or coordinates can locate that point when the space is that point?
Too bad, as it’s simply your nonsense it’s just your problem.
By the way, you simply not understanding or just refusing to try to understand dimension does not imbue your pervious “Mutual Independency” nonsense with any validity.
Here it is:
Once again you simply try to substitute your deliberate misuse of a phrase like “Mutual Independency”, your unspecific “related to” and “included” ascriptions, your own self imposed “ur-element” restriction, your always FALSE “included NXOR excluded” assertion, your superfluous “degrees of freedom” and your continued, evidently deliberate, obfuscation of the empty set for the ordinate or coordinates of just a point for an actual understanding and direct discussion of dimension.
The Man
Unbanned zombie poster
Absolutely ridiculous, this superfluous subtracting nonsense of yours did not work for you before and it is no different now that you have just substituted the words “degrees of freedom” for your “k_X - k_Y” designations.
Your own absolutely ridiculous and superfluous subtracting nonsense still shows no coordinates (in both of your ‘cases’) for just a point and thus no dimension(s). Your really are without a clue when even your own absolutely ridiculous and superfluous subtracting nonsense still proves you wrong.
doronshadmi
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No, I claim that a point has 0 degrees of freedom, and any measured case that has 0 degrees of freedom does not have any (co-)ordinates that are related to it.The Man said:
Yet it is not equivalent to the empty set because any given dimensional space is non-composed (also known as ur-element), where the Membership among ur-elements is not based on being sub-elements, but by sharing a common property, where in the case of dimensional spaces, the common property is being a dimension.
Traditional Math gets the concept of Membership only in terms of sets, and as a result the member must be a component (sub-set) of a given set, which is a limitation of the concept of Membership.
On the contrary, OM enables to deal with both cases of Membership, where the traditional Membership deals with complexities, and the novel aspect deals with non-composed elements that share a common property.
The novel aspect of Membership goes beyond the limitations of the traditional approach of the concept of Membership.
Here is the part that clearly shows how the traditional approach can't deal with Membership among ur-elements (which is something that OM enables to do, in addition to the standard Membership among sets):
http://en.wikipedia.org/wiki/Urelemen
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doronshadmi
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The Man, you are stuck with the notion of sets, and can't get any reasoning which goes beyond it.The Man said:
The ridiculous and superfluous nonsense is a direct result of forcing your limited reasoning (which is stuck with the notion of sets) on OM's reasoning.
The fact is this:
1) Dimensional spaces do not need (co-)ordinates in order to be defined.
2) Dimensional spaces need degrees of freedom in order to be defined and here is the set of degrees of freedom of dimensional spaces:
{0,1,2,3,4,5,...}
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Something yet to be demonstrated.
So by your logic, since a point has no co-ordinates, it cannot be at any location?
Of course, the whole statement is nonsense anyway. I'll repeat, just in case that should have an effect; the co-ordinates tell you where the point is, not anything about its size (which is not surprising, since it has none).
What does the empty set have to with the location of a point?
doronshadmi
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By the difference of degrees of freedom among dimensional spaces.The Man said:
doronshadmi
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Any dimensional space w.r.t itself in not local AND not non-local.
The co-ordinates are the result of the difference of degrees of freedom among dimensional spaces.
We?
And who is the other guy who has a hard time to realize that there are other punctuation marks apart from the period and the comma?
Doron, put your human waste together or you won't be able to sneeze again. Never. Ever. You hear?
The Man
Unbanned zombie poster
So how do you define "degrees of freedom"?
Again if you claim the set of coordinates for just a point is not the empty set then give us those coordinates.
No Doran the definition of what constitutes a member is specifically the limitation of membership, it is what limits something (even a set) to, well, its members.
On the contrary, Doron, the demonstrative evidence is that your “OM” has not enabled you to deal with anything.
No Doron it simply makes membership meaningless because that limitation (mutual exclusion) of membership is specifically what makes something a member and something else not a member. Your simple and deliberate ignorance of membership is not a "novel aspect".
Doron “ur-elements” is a membership (A classification of some elements), the only one who evidently can’t deal with that (or evidently just can't understand what he quotes from some reference) is you.
Doron you are still just stuck in your fantasies and the resulting ridiculous and superfluous nonsense you spew is a direct result of you forcing your fantasies onto terminology of actual mathematics.
Then define your “Dimensional space” without “(co-)ordinates”.
So how do you define your “degrees of freedom”?
“related to points” “By the difference of degrees of freedom among dimensional spaces.” how, specifically?
So how do you define your “degrees of freedom”?
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