Deeper than primes

[doronshadmi]

Wrong. You really regard infinity as a point on the line. That's why you said that pi doesn't exist when diameter is equal to infinity

Nonsense.

An infinity long straight line has 0 curvature, that's all (pi does not exist at 0 curvature).

No points along a line are needed in order to get this simple and straightforward fact.

 

[epix]

Nonsense.

An infinity long straight line has 0 curvature, that's all (pi does not exist at 0 curvature).

No points along a line are needed in order to get this simple and straightforward fact.

How do you know that the straight line has 0 curvature? Because there is "no presence of pi?"

Why don't you use pi to compute the curvature of f(x) = x^2 at point x=3? That would be quite hard, coz in that process pi is not present, and since f(x) draws a curve, it has a curvature at that given point. So the absence of pi in connection with the straight line doesn't cause the curvature of straight line to be 0. Why don't you compute the curvature of the straight line the way you imagine it goes? I'm really curious given the fact that your straight line is free of any points. See, if you compute the slope on a curve at various points, the slope changes and so you know you dealing with a curve, as opposed to a straight line where the slope is the same at any point. Since your line is a point-free edition, how would you compute its slope at various points? The slope is very particular to the computing of the curvature of various lines.

Btw, The Man said that you were supposed to do some basic geometry, but you didn't do anything. I wonder if you can tell what is happening bellow.

 

[jsfisher]

Now is the good time.

http://www.internationalskeptics.com/forums/showpost.php?p=7023228&postcount=14756 is the exact answer to your last post.

You have a unique usage of the word, exact. To be an exact answer in the normal sense of that phrase, you'd need to either (1) present a bijection between the members of {} and {{}} (or {A} and {A,{A}}) or (2) retract your claim.

You didn't neither. You have again dodged the question. Please try again.

 

[epix]

You have a unique usage of the word, exact. To be an exact answer in the normal sense of that phrase, you'd need to either (1) present a bijection between the members of {} and {{}} [...]

Looking at the first braces with nothing to enclose, a question showed up regarding the null set. Suppose that {} stands for the null set, whose cardinality is zero. The power set of of the null set contains only one member and that's the null set. What is the cardinality of that power set?

If I had to call it, I would say that the answer is |{{}}|=1, coz it is the membership that makes the size of a set. If I'm right, then the relationship |S|< |P(S)| holds also for S = {}. What do you think?

Note: There is a chance that Doron trips over this, looks down and bijects that thing with ease indigenous just to him. LOL.

{ {} }
..{}..

 

[jsfisher]

Note: There is a chance that Doron trips over this, looks down and bijects that thing with ease indigenous just to him. LOL.

{ {} }
..{}..

I guarantee it.

 

[The Man]

This is another demonstration of your weak reasoning, which translates anything into points.

As a result you simply can't comprehend the permanently smaller and uncovered line between any arbitrary closer pair of points.

So I guess you’re just deliberately ignoring the part in what you even quote where it specifically says “not “one point” but one line segment (a smallest line segment)”? Another demonstration of your weak reading and as a result you simply can not understand what you read or apparently what you write.

Once again Doron if your line segment can’t be covered by smaller line segments then it is your de-facto smallest line segment. Nothing is “permanently smaller” because any smaller line segment could cover part of your so called “uncovered” line segment and one or more equally as small, smaller or not quite that much smaller could cover the rest of your segment. Also you have no points “arbitrary closer” than the ends of your “uncovered” thus de-facto smallest line segment as they would define a smaller line segment and your “uncovered” line segment remains covered still. So you can ‘translate’ it any way you want (points, line segments or even concentric circles as before) geometry’s still got you covered.

You want to try squares or other polygons next?

Again you remain the staunchest opponent of just your own notions.

The Man, a line is one of the building-blocks (together with a point).

A building-block is not constructed by other building-block (otherwise it can't be considered as a building-block).

You still do not get 0 (actually finite building-block) < ∞ (infinite collection) < ∞ (actually infinite building-block) in terms of existence.

So you just don’t know or just don’t want to say “what “objects” of what “collection” define your line as being your “actual infinity (∞)”?” Color me unsurprised.

 

[The Man]

Btw, The Man said that you were supposed to do some basic geometry, but you didn't do anything. I wonder if you can tell what is happening bellow.


[qimg]http://img215.imageshack.us/img215/7943/congruent1.png[/qimg]



[qimg]http://img34.imageshack.us/img34/7161/rateofchange.png[/qimg]

Actually I just recommend that he learn some (and still do). Perhaps then he might be able to do something other than just fantasize.

Nice graphics though epix.

 

[epix]

A line is not defined by points.

Too bad that some of your denials are not followed by alternative definitions accompanied by graphics. Since the passing of Salvador Dali, there has been nothing much to marvel over.

The most frequent usage of the line (meaning the straight line) adheres to a property of the line; that is, it is the shortest distance between two points. Two points on the plane define a unique line, which is also frequently used as a vector which has A) a magnitude and B) a direction. By some "sheer coincidence," the connecting link between points A and B (from A to B) creates a unique vector.

Daily skirmishes shall commence soon right after Doron brushes his set of teeth including the wisdom subset with its cardinality equal to 4 . . . .

 

[doronshadmi]

Once again Doron if your line segment can’t be covered by smaller line segments...

The Man, the collection of all sub line segments that exist between the opposite edges of any arbitrary line segment, which follow each other by 0 gaps between them, cover that line segment if the opposite sub line segments of that collection have common edges with the considered line segment.

In the case of finite amount of sub line segments, one of the sub line segments can be the smallest one.

In the case of infinite amount of sub line segments, on one of the sub line segments can be the smallest one (we have ever smaller sub line segments).

We are not talking about a collection of sub line segments, where each one of them > point, whether there is finite or infinite amount of them along the considered line segment.

We are explicitly talking about the collection of points along the considered line segment, and this collection does not completely cover the considered line segment, whether the smallest sub line segment exists along the considered line (and in this case it is a finite collection of sub line segments along the considered line segment, which completely covers it) or only an ever smaller sub line segment exists along the considered line (and in this case it is an infinite collection of sub line segments along the considered line segment, which completely covers it).

In other words The Man, you still do not get the simple fact about the collection of infinitely many points (and not lines, whatever their size is, where all lines > 0) that can't completely cover any arbitrary given line segment.

 

[doronshadmi]

The most frequent usage of the line (meaning the straight line) adheres to a property of the line; that is, it is the shortest distance between two points.

So what? still its size is bigger than any of these points (each point has exactly 0 size), or the sum of infinitely many 0 sizes along it.

 

[doronshadmi]

You have a unique usage of the word, exact. To be an exact answer in the normal sense of that phrase, you'd need to either (1) present a bijection between the members of {} and {{}} (or {A} and {A,{A}}) or (2) retract your claim.

You didn't neither. You have again dodged the question. Please try again.

Wrong again jsfisher.

To be exact means that one is not limited to only partial case of the considered subject, and as can clearly be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7020203&postcount=14722, the range of all possible mappings between S and P(S) members is always from no mapping to bijection.

Your "either (1) or (2)" is too weak in order to deal with the range of all possible mappings between S and P(S) members.

 

[jsfisher]

Wrong again jsfisher.

Still no bijection. Do continue.

 

[epix]

So what? still its size is bigger than any of these points (each point has exactly 0 size), or the sum of infinitely many 0 sizes along it.

The "size" of a line (please use "length" the next time) is not comparable to any points, coz points are 0-dim objects. You just added another bead such as this one I refered to,

Originally Posted by doronshadmi
A line is not defined by points.

to the neckless of arguments that may scare the witt out of any evolutionary scientist. Fortunately, it doesn't matter at all when you're wrong on a grand scale not easily imaginable, but the question is whether your mind is unique.

As far as your "gaps" are concerned, p and q in R cannot be adjacent, so there is "vacuum" of sort, but that region is not closed -- it can be occupied by any real number, which is available upon detection. That creates an image of a two-gallon bucket that can accommodate the whole water mass of the Atlantic Ocean, but remember that points are dimensionless objects.

 

[doronshadmi]

Still no bijection. Do continue.

Still "either (1) or (2)" "in the box" reasoning. Do the needed paradigm shift in order to get the range of all possible mappings between S and P(S) members (which is always from no mapping to bijection, according to one's needs. In other words, there is no universality about mapping).

 

[doronshadmi]

As far as your "gaps" are concerned, p and q in R cannot be adjacent, so there is "vacuum" of sort, but that region is not closed -- it can be occupied by any real number, which is available upon detection.

This time please read carefully http://www.internationalskeptics.com/forums/showpost.php?p=7030466&postcount=14789 in order to realize that your post is irrelevant to the considered subject.

 

[punshhh]

This time please read carefully http://www.internationalskeptics.com/forums/showpost.php?p=7030466&postcount=14789 in order to realize that your post is irrelevant to the considered subject.

I have come late to this thread so I may not be in full possession of the arguments for and against.

Your theory makes perfect sense to me, I can't see how you will be able to explain it to the other guys though. The problem is not that you can't explain it to them, rather they can't or won't accept that there may be something in what you say sufficiently to grasp the concept.

I have experienced a similar impasse in another thread in regards of an infinity applied to 3 dimensional space.

Until you have grasped the concept it is incomprehensible or meaningless drivel.

 

[epix]

This time please read carefully http://www.internationalskeptics.com/forums/showpost.php?p=7030466&postcount=14789 in order to realize that your post is irrelevant to the considered subject.

You don't need to read carefully your entire contribution to this thread to realize that it is a foreigner in the subject of number crunching. But if you read it carefully, then it may induce a permanent state of hopelessness.

We are not talking about a collection of sub line segments, where each one of them > point, whether there is finite or infinite amount of them along the considered line segment.

Statements like sub line segment > point clearly suggests that your definition of a point includes a property such as magnitude. But if you happen to adhere to the way point has been defined in general sense and you include point in an inequality the way you did, then by God's mercy and love for his failed adventure in terrestrial evolutionary genetics, you meant that the number of line segments is greater than the number of points, which is still wrong, as you can see below.

|________|_______|__________|


There is no paragraph of yours that any demon of chaos and vague persuasion wouldn't find attractive to move in.

 

[doronshadmi]

Statements like sub line segment > point clearly suggests that your definition of a point includes a property such as magnitude.

Yes, the magnitude of existence of the considered objects, which is not defined by their amount.

But if you happen to adhere to the way point has been defined in general sense and you include point in an inequality the way you did, then by God's mercy and love for his failed adventure in terrestrial evolutionary genetics, you meant that the number of line segments is greater than the number of points, which is still wrong, as you can see below.

|________|_______|__________|

Once again, you get magnitude in terms of the amount of the considered objects, where I get magnitude in terms of the existence of the considered elements, which is defined by their dimensional size.

By understanding this simple fact no amount of 0 sizes completely covers an object with size > 0.


epix, please show me a pair of points with 0 gap between them, and I will agree with Traditional Mathematics about the claim that a line segment is completely covered by a collection of distinct 0-size objects (known as points).

 

[doronshadmi]

I have come late to this thread so I may not be in full possession of the arguments for and against.

Your theory makes perfect sense to me, I can't see how you will be able to explain it to the other guys though. The problem is not that you can't explain it to them, rather they can't or won't accept that there may be something in what you say sufficiently to grasp the concept.

I have experienced a similar impasse in another thread in regards of an infinity applied to 3 dimensional space.

Until you have grasped the concept it is incomprehensible or meaningless drivel.

Hi punshhh,

Please read http://www.internationalskeptics.com/forums/showpost.php?p=7034631&postcount=14798 .

 

[laca]

I have come late to this thread so I may not be in full possession of the arguments for and against.

Your theory makes perfect sense to me,

Finally! Someone who understands what doron is babbling about. So, punshhh, I guess you can provide the bijection between a set and its power set then? I assume it's easy, since it makes perfect sense to you.