Deeper than primes

[The Man]

Let's use your reasoning, which asserts that non-dimensional is exactly the negation of dimensional.

It is the definition of a point which asserts that, Doron.

Do you claim that 0-dimensional space is the negation of dimensional space?

Again, a point by definition lacks dimension(s). No dimensions exist for a singular point. It is the denial of the existence of dimension(s) for a singular point (the negation of dimension) that makes a point 0 dimensional.

 

[doronshadmi]

You haven’t shown anything, but what you have claimed is that you can ‘stretch’ your "0-dimensional space" into “at least 1-dimensional space” and that you can ‘reduce’ your “1-dimensional space" into “at most 0-dimensional space”. If that is not what you wanted to claim then you should make a better effort to make better claims.

Let's make it simple for you:

"stretched 0-dim" is "different than 0-dim".

"totally reduced 1-dim" is "different than 1-dim".

The difference is saved under co-existence and prevents homeomorphism between 0-dim and 1-dim spaces.

Therefore under co-existence there is always 1-dimensional space between more than one 0-dimensional element, which prevents the existence of more than one 0-dimensional element in the same 0-dimensional space.

Let's generalize it:

1) 0-dimension is the smallest existing dimensional space.

2) x = 0 approaching ∞ and x<y, where y approaching ∞.

3) There is always y-dimensional space between more than one x-dimensional element, which prevents the existence of more than one x-dimensional element in the same x-dimensional space.

So, a point’s lack of dimensions(s) doesn’t make it your “smallest existing local thing”? Are you claiming your “smallest existing local thing” has some dimension(s)? How many dimensions does it have?

It is the definition of a point which asserts that, Doron.

Again, a point by definition lacks dimension(s). No dimensions exist for a singular point. It is the denial of the existence of dimension(s) for a singular point (the negation of dimension) that makes a point 0 dimensional.

Since 0-dimensional element (known as a point) is an existing thing, it can't be used as the negation of the existence of Dimension.

In other words, the assertion that a point is the negation of Dimension is equivalent to the assertion that an existing thing is the negation of Existence.

By simply and deliberately ignoring the details of “Hilbert's Hotel” what you posted is “anything but” a version of “Hilbert's Hotel”

It is a different version of “Hilbert's Hotel”. Do you have some problems to understand the word different?

No problem…

http://dictionary.reference.com/browse/Actually

http://en.wiktionary.org/wiki/actually

Actuality is not limited to existing things, for example:

The actuality of nothing can be considered as the negation of Existence.

You simply and deliberately fail to get the meaning of the word “between”

Since you have problems to get the actuality of nothing, you can't comprehend assertions like "There is nothing between A and B".

 

[doronshadmi]

Here is an example of how Pseudo-Mathematics "works":

In mathematics, a pseudometric space is a generalized metric space in which the distance between two distinct points can be zero.

( http://en.wikipedia.org/wiki/Pseudometric_space )

The assertion "the distance between two distinct points is zero" is equivalent to the assertion "there is only one point in a given location".

In other words, the following ( http://en.wikipedia.org/wiki/Pseudometric_space )

Unlike a metric space, points in a pseudometric space need not be distinguishable; that is, one may have d(x,y) = 0 for distinct values x≠y.

is Pseudo-Mathematics nonsense simply because "need not be distinguishable" AND "distinct values x≠y" is a contradiction exactly because points are the smallest existing elements, and therefore two distinct x and y points can't be distinct AND indistinguishable at the same location (it is the same location because according to pseudometric space, there is 0 distance between x and y).

 

[doronshadmi]

Here is more nonsense by Pseudo-Mathematics:

A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors.

( http://en.wikipedia.org/wiki/Seminorm )

 

[doronshadmi]

More nonsense by Pseudo-Mathematics:

Note, however, that this is not an example of a metric space, since we can have two distinct points that are distance 0 from each other, e.g. d((2,3),(2,5))=|2-2|=0

( http://planetmath.org/?op=getobj&from=objects&id=6275 )

This poor example ignores the Y-axis difference (which is 2) between (2,3) and (2,5) points.

 

[doronshadmi]

Unfortunately

http://www.internationalskeptics.com/forums/showpost.php?p=7221899&postcount=15503

http://www.internationalskeptics.com/forums/showpost.php?p=7222092&postcount=15504

http://www.internationalskeptics.com/forums/showpost.php?p=7222131&postcount=15505

are considered as valid frameworks by the current community of mathematicians.

 

[doronshadmi]

It has to be stressed that if the second values of (x₁,y₁) and (x₂,y₂) - which are notated as y₁ and y₂ - are not metric values (for example: they are used to define different weights of a given location), then we have a one point with different properties in the same location (which is determined by x₁ and x₂ values).

In this case the interval between (x₁,y₁) and (x₂,y₂) is not entirely determined by distance in terms of metric space, but it does not change the fact that there is an interval between (x₁,y₁) and (x₂,y₂).

But this is not the case with the current community of mathematicians about this subject, as clearly can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7221899&postcount=15503 .

 

[zooterkin]

Here is more nonsense by Pseudo-Mathematics:

( http://en.wikipedia.org/wiki/Seminorm )

Just because you don't understand it, that doesn't make it nonsense.

 

[doronshadmi]

Just because you don't understand it, that doesn't make it nonsense.

Please demonstrate in details that I do not understand it.

 

[doronshadmi]

In addition to http://www.internationalskeptics.com/forums/showpost.php?p=7222092&postcount=15504 it is trivial to define that a vector space has zero width AND non-zero length.

 

[zooterkin]

Please demonstrate in details that I do not understand it.

The part where you said it was nonsense.

 

[doronshadmi]

The part where you said it was nonsense.

If the x and y components of a given vector space in R² are considered, then it is trivial that y-component (the width of the given vector) has zero magnitude and the x-component (the length of the given vector) has non-zero magnitude.

If one ignores the width, then only the length of the vector is considered.

Otherwise both width and length are considered, which does not change the fact that y-component is zero, whether one ignores it or not.

Furthermore, a zero vector space is actually an element with components (0,0,0, ... ,0), and once again we can see how Modern Mathematics uses different names for the same actual element, which in this case is simply a point (where a point has no directions) by forcing "perpendicular" directions of zero magnitudes and calling them "a zero vector space".

By these twisted maneuvers with names Modern Mathematics prevents the mind's ability to distinguish between a point (an element that naturally does not have directions) and an element that is different than a point exactly because it actually has a direction.

One of the results of these twisted maneuvers with names is the inability of Modern Mathematics to distinguish between the actual properties of 0-dimensional element (and its locality w.r.t, for example, 1-dimensional element) and 1-dimensional element (and its non-locality w.r.t, for example, 0-dimensional element) under co-existence.

The twisted maneuvers with names is a load of nonsense.

 

[doronshadmi]

As for the nonsense in http://www.internationalskeptics.com/forums/showpost.php?p=7221899&postcount=15503, please read carefully http://www.internationalskeptics.com/forums/showpost.php?p=7211335&postcount=15494 .

Two points can't be at the same location and still be considered as two points, so the whole idea of pseudometric space is based on contradiction.

 

[jsfisher]

Last week I ran into an old friend I hadn't seen in a very long time. Who'd have thought it. There we were in exactly the same place at the same time after all those years.

 

[doronshadmi]

Last week I ran into an old friend I hadn't seen in a very long time. Who'd have thought it. There we were in exactly the same place at the same time after all those years.

Like two points at the same location, isn't it jsfisher?

 

[jsfisher]

Like two points at the same location, isn't it jsfisher?

It's not my problem that your thinking is so rigid.

By the way, where in the definition of pseudo-metric space do you see any mention of location? Distance, yes, but location?

 

[epix]

If the x and y components of a given vector space in R² are considered, then it is trivial that y-component (the width of the given vector) has zero magnitude and the x-component (the length of the given vector) has non-zero magnitude.

The twisted maneuvers with names is a load of nonsense.

We all live in a yellow submarine, yellow submarine, yellow submarine...

I wonder what caused such an explosion of self-criticism. Was it "the width of the vector" that set it off kaboom? LOL.

 

[doronshadmi]

We all live in a yellow submarine, yellow submarine, yellow submarine...

I wonder what caused such an explosion of self-criticism. Was it "the width of the vector" that set it off kaboom? LOL.

EDIT:

I wonder why you do not read the entire http://www.internationalskeptics.com/forums/showpost.php?p=7227833&postcount=15512 before you reply.

Maybe your inability to get http://www.internationalskeptics.com/forums/showpost.php?p=7211335&postcount=15494 stands at the basis of your "yellow submarine, yellow submarine, yellow submarine..." ( please read also the new post http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 on this subject, for better clarification).

Anyway, the twisted maneuvers with names, as used by Modern Mathematics, is a load of nonsense, because it leads to contradiction, for example:

1) http://www.internationalskeptics.com/forums/showpost.php?p=7221899&postcount=15503 .

2) Again, Modern Mathematics uses different names for the same actual element, which in this case is simply a point (where a point has no directions) by forcing "perpendicular" directions of zero magnitudes and calling them "a zero vector space".

By these twisted maneuvers with names Modern Mathematics prevents the mind's ability to distinguish between a point (an element that naturally does not have directions) and an element that is different than a point exactly because it actually has a direction.

One of the results of these twisted maneuvers with names is the inability of Modern Mathematics to distinguish between the actual properties of 0-dimensional element (and its locality w.r.t, for example, 1-dimensional element) and 1-dimensional element (and its non-locality w.r.t, for example, 0-dimensional element) under co-existence.

3) My different names (as used, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=7211335&postcount=15494) do not lead to contradiction and do not prevent the distinction of the local and the non-local under co-existence.

4) Another result of the Modern Mathematics twisted maneuvers with names, is its inability to distinguish between something and nothing.

This devastating result can be seen in The Man's mind that can't comprehend that "nothing between A and B" is equivalent to "there is one and only one object".

--------


As for you epix, the devastating result of Modern Mathematics twisted maneuvers with names on your mind, clearly can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7212115&postcount=15499 .

 

[doronshadmi]

It's not my problem that your thinking is so rigid.

By the way, where in the definition of pseudo-metric space do you see any mention of location? Distance, yes, but location?

EDIT:

Do you have some problem to understand that if x and y points have zero distance between them, then they are actually at least 3 distinct points ?

Acceding to Modern Mathematics' pseudometric space reasoning "need not be distinguishable" AND "distinct values x≠y" is a contradiction exactly because x and y points are indistinguishable AND distinct in the same space, no matter what name is given to that space (pseudo-metric or whatever).

The last part of http://www.internationalskeptics.com/forums/showpost.php?p=7221899&postcount=15503 needs some clarification:

In other words, the following ( http://en.wikipedia.org/wiki/Pseudometric_space )

Unlike a metric space, points in a pseudometric space need not be distinguishable; that is, one may have d(x,y) = 0 for distinct values x≠y.

is Pseudo-Mathematics nonsense simply because "need not be distinguishable" AND "distinct values x≠y" is a contradiction exactly because points are the smallest existing elements, and therefore two distinct x and y points can't be distinct AND indistinguishable at the same location (it is the same location because according to pseudometric space, there is 0 distance between x and y).

In other words, since according to pseudometric space points "need not be distinguishable" and 0 distance is a point, then by following this reasoning also x and y must be indistinguishable from each other, and in this case we have exactly one point.

But according to pseudometric space reasoning, x and y are also distinct from each other (x≠y), so by following this reasoning zero distance (which is actually a point) between x and y is actually at least 3 distinct points.

So according to pseudometric space reasoning 1=3.

Nice reasoning, isn't it? (and this time I did not use location).

It's not my problem that your thinking is so rigid.

So now, jsfidher, you do not distinguish between being consistent and being rigid.

 

[epix]

I think of all the education that you've missed.
But then your homework was never quite like this!

Furthermore, a zero vector space is actually an element with components (0,0,0, ... ,0), and once again we can see how Modern Mathematics uses different names for the same actual element, which in this case is simply a point (where a point has no directions) by forcing "perpendicular" directions of zero magnitudes and calling them "a zero vector space".