Deeper than primes

[doronshadmi]

Your formula for eternal youth has a bug in it, Doron.

Your understanding of the the minimal locations that are needed to define a point and a line segment, has a bug in it, because you can't grasp that only one location is needed in order to define a point, and at least two locations are needed in order to define a line segment.

By your reasoning 1=2.

 

[doronshadmi]

The answer is still the same.

Location, location and location!!!

http://www.internationalskeptics.com/forums/showpost.php?p=7075868&postcount=15001

 

[doronshadmi]

If you drag an orange from one corner of the table to the other, do you get at least two oranges to peel?

If you drag an orange to some location, does its also stay at the initial location?

The answer is no if you are focused on the orange.

The answer is yes if you are focused on the line segment, which actually exists at once in both locations.

 

[punshhh]

Exactly.

Yes, I have come across this in other threads, the materialist mind cannot see the problem on the end of its nose. It is too short sighted (pun..shhh).

A point is + or - infinity in dimension.

There is no way of deriving a second point from the properties of this point, which is required to produce a unit of measurement.

 

[doronshadmi]

Yes, I have come across this in other threads, the materialist mind cannot see the problem on the end of its nose. It is too short sighted (pun..shhh).

The materialist nose has a size of a point, so he does not see any problem.

A point is + or - infinity in dimension.

Please explain.

There is no way of deriving a second point from the properties of this point, which is required to produce a unit of measurement.

Deriving a second point produces a line segment, which is irreducible into a point.

 

[laca]

Yes, I have come across this in other threads, the materialist mind cannot see the problem on the end of its nose. It is too short sighted (pun..shhh).

Please stop trying to come off as anything other than an ignorant, delusional, dishonest liar. The threads are there for all to see.

A point is + or - infinity in dimension.

There is no way of deriving a second point from the properties of this point, which is required to produce a unit of measurement.

Classic punshhh gibberish.

 

[punshhh]

The materialist nose has a size of a point, so he does not see any problem.

Please explain.

A point is + or - infinity in size

Deriving a second point produces a line segment, which is irreducible into a point.

Yes, this line segment is infinitely longer than the size of the point/s.

 

[epix]

No, you simply jump from an element that needs at least two different locations in order to be defined ([0,0],[5,0] element, in this case, which is known as line segment), to an element that needs only one location in order to be defined (([0,0] element, in this case, which is known as point).

You constrict the construction of a line: One definition calls for defining two points a and b on the plane in order to draw a unique line, which intersect both points thus creating line segment a,b. But there are lines called "vectors" defined by direction and magnitude. You define point a on the plane, then chose angular direction and magnitude (length) of the line that represents the vector.

The former definition of line accents the function of the points, but the latter enables the manipulation of the length. You can see bellow a vector with 0 magnitude, which can be a vector with magnitude m>0 that was reduced through subtraction to equal zero, and the vector exists as a point.

Your manipulation of the length of line segments that involves arguments of irreducibility clearly overlooks all definitions that apply to the shortest distance between two points.

 

[epix]

A point is + or - infinity in size

Your potential mental energy (measured in joules per eureka) seems to exceed Doron's. But that point, the singularity that expanded to become the universe, wasn't infinite in size neither it possessed potential energy to create an organization of matter that would expand ad infinitum, as Stephen Hawking found out when shuffling numbers in his head.

Now I don't know whom to believe . . .

 

[ehcks]

A point is + or - infinity in size

If by "infinity in size" you mean "infinitely large," no. A point is quite the opposite. It is infinitely small.

 

[The Man]

Your understanding of the the minimal locations that are needed to define a point and a line segment, has a bug in it, because you can't grasp that only one location is needed in order to define a point, and at least two locations are needed in order to define a line segment.

By your reasoning 1=2.

Locations? Please locate a single point without reference to some other point or points. Locations are relative Doron. A single point has no location, but we can locate some point relative to some other point. So it seems the “bug” remains entirely yours.

ETA:

Oh I forgot to paste this..

http://www.internationalskeptics.com/forums/showpost.php?p=7075868&postcount=15001

So you make a post simply referencing your own post above?

 

[The Man]

If you drag an orange to some location, does its also stay at the initial location?

Try it, you might find that the orange ends up distributed along the way, depending on how you drag it.

The answer is no if you are focused on the orange.

Focus on your orange all you want and depending on how you drag it you might actually notice its distribution.

The answer is yes if you are focused on the line segment, which actually exists at once in both locations.

“both locations”? A line segment is defined by at least two points it isn’t just two locations, drag your orange harder, with more focus and you might just see that.

 

[The Man]

Again please show the set of all infinitely many different points that exist along a line segment,without ever smaller sub-line segments between them.

“Again" what? I have never claimed “different points that exist along a line segment, without ever smaller sub-line segments between them” in a continuous space. So ask “Again” of someone else that has, like, well, you.

It does matter how many times you repeat your “covered” nonsense when you can’t show anything that is the closest AND different points.

That’s your problem Doron as “closest AND different points” (in a continuous space) is only your assertion.

Again you are using a finite reasoning in order to understand the infinite reasoning of the ever smaller.

Nope

The uncovered space is exactly the continuum itself as an ever smaller sub-line segment, which is irreducible to a discrete existing thing like a point.

Nope by your own assertions….

Your understanding of the the minimal locations that are needed to define a point and a line segment, has a bug in it, because you can't grasp that only one location is needed in order to define a point, and at least two locations are needed in order to define a line segment.

By your reasoning 1=2.

Your “smaller sub-line segment” needs some closer, well, points.

The Man, the collection of all infinitely many different points is not a continuous space,

Well that depends on the space, doesn’t it? The collection of all points in a discontinuous space certainly can’t be a continuous space.

exactly because it is no more than a collection of all different AND smallest elements, where this existence is impossible without the ever smaller actual continuum state between the arbitrary closer smallest (and therefore discrete) collection of points.

Wait so your “continuum” ain’t a “continuum” unless it is continuous? Amazing.

You still can't comprehend the the co-existence of all different AND smallest elements AND all sub-line segments, where the all different AND smallest elements not reach the actual continuum of any ever-smaller sub-line segment, along some considered line segment.

Oh wait, so your “continuum” isn’t continuous? Who would have guessed?

 

[epix]

If by "infinity in size" you mean "infinitely large," no. A point is quite the opposite. It is infinitely small.

That's quite sizable difference in the opinions. I thought that after some fifteen thousand posts of focused deliberation, we would smooth out a wrinkle here and there . . . .

Now this happens. *sigh*

 

[doronshadmi]

You constrict the construction of a line: One definition calls for defining two points a and b on the plane in order to draw a unique line, which intersect both points thus creating line segment a,b. But there are lines called "vectors" defined by direction and magnitude. You define point a on the plane, then chose angular direction and magnitude (length) of the line that represents the vector.

The former definition of line accents the function of the points, but the latter enables the manipulation of the length. You can see bellow a vector with 0 magnitude, which can be a vector with magnitude m>0 that was reduced through subtraction to equal zero, and the vector exists as a point.

[qimg]http://mathworld.wolfram.com/images/eps-gif/ZeroVector_1000.gif[/qimg]

Your manipulation of the length of line segments that involves arguments of irreducibility clearly overlooks all definitions that apply to the shortest distance between two points.

epix, it does not that the fact that [0,A] is an ever smaller element and [0] is the smallest element.

 

[doronshadmi]

Locations? Please locate a single point without reference to some other point or points. Locations are relative Doron. A single point has no location, but we can locate some point relative to some other point. So it seems the “bug” remains entirely yours.

You do not distinguish between the ever smaller element that exists between any pair of some closer smallest elements.

The different names of the smallest elements is possible because of the co-existence of the smallest AND the ever smaller, and it is known by the name "collection".

Actually, without the ever smaller element, the smallest elements can't be related to each other.

So the relative locations of the smallest elements are the result of the ever smaller AND the smallest.

You can add relative to the list of the concepts that you (yet) do not comprehend, by your smallest-only reasoning.

 

[doronshadmi]

Try it, you might find that the orange ends up distributed along the way, depending on how you drag it.

An orange is already a result of the co-existence of the ever smaller element, which exists at once at least at two smallest elements' locations.

No smallest element exists at once at more than one location, which is a property that an ever smaller element has.

Focus on your orange all you want and depending on how you drag it you might actually notice its distribution.

This distribution is a result of the co-existence of the ever smaller AND the smallest.

“both locations”? A line segment is defined by at least two points it isn’t just two locations,

Yet no smallest element has the property of being at once at both given locations, which a property that the ever smaller element has.

You still the not grasp the co-existence of the ever smaller AND the smallest.

 

[doronshadmi]

That’s your problem Doron as “closest AND different points” (in a continuous space) is only your assertion.

That is a challenge that your reasoning simply ignore.

Nope by your own assertions….

Your “smaller sub-line segment” needs some closer, well, points.

By my own determination only an ever smaller element has the property of being at once at lest at two locations of the smallest elements, where no smallest element has this property.

Well that depends on the space, doesn’t it? The collection of all points in a discontinuous space certainly can’t be a continuous space.

The continuum is a property of an ever smaller element. No smallest element has this property.

Wait so your “continuum” ain’t a “continuum” unless it is continuous? Amazing.

Your local-only view, which gets only the smallest elements of some collection, ignores the ever smaller elements between them, with actually have the property of the continuum.

You still to not get the co-existence of the continuum, which is the property of the ever smaller element, and the discrete, which is the property of the smallest element.

Oh wait, so your “continuum” isn’t continuous? Who would have guessed?

You can wait as much as you like, it does not change the fact that your location-only reasoning does not help you the comprehend the co-existence of the continuum, which is the property of the ever smaller element, and the discrete, which is the property of the smallest element.

 

[doronshadmi]

A point is + or - infinity in size

Please provide more details, I still do not understand what you wish to express.

Yes, this line segment is infinitely longer than the size of the point/s.

A line segment is a co-existence of an ever smaller element and at least ever closer points, such that no closer points are at a single location.

The inability of two distinct smallest elements to be at one location, and the ability of an ever smaller element to be at once at least at both locations of some pair of the smallest elements, is resulted by an infinite magnitude of the ever smaller element with respect to the finite magnitude of a smallest element.

 

[epix]

epix, it does not that the fact that [0,A] is an ever smaller element and [0] is the smallest element.

No, it doesn't w.r.t. what you're trying to demonstrate. I just wanted to bring to your attention the fact that your statements about properties of various objects may not be always true as you think they are.

I think that your attempt to prove that the definition

A line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points.

implies nothing but that the points in question are adjacent to each other amounts to saying that the mathematicians who formulated the definition were simply insane.

By "every point," the definition means a magnitude [t] from point [0] where point t exists in its exact format, such as Log[t] or Sin[t], for example. As you keep reducing a line segment through division by repeatedly inserting point t between end points a and b, there is no way that as you keep dividing the line segments infinitely, the points Log[t] or Sin[t] would never mark a location of one of such division. In other words, as you keep dividing infinitely, points Log[t] or Sin[t] must and will show up sooner or later. But points

Log[pi/3] => 0.046117597181...
Sin[pi/3] = √3/2 => 0.8660254003784...

would never show up, as 1, 2, 3, 4, ... would never show up at the end of their voyage into infinity.