Deeper than primes

shuttlt · May 21, 2011

doronshadmi said:
2) Let us say that by some miracle there are many distinct 0-dim elements that have no gaps between them. In that case you still have to provide the formal mathematical proof of line segments with different lengths, which have sets of points with no gaps between them, where those sets have the same cardinality.

My maths is rusty as all hell. But is this like claiming it's a miracle if there aren't gaps in the real numbers and then asking for a proof that you can take the segment of the real numbers between 0 and 1 and then do a 1-1 mapping back onto the whole real line?

The Man · May 21, 2011

doronshadmi said:
Your ignorance of generalization does not change the following:

1) Any smaller dimensional space is local w.r.t to any greater dimensional space.

2) Any greater dimensional space is non-local w.r.t to any smaller dimensional space.

3) 0-dimensional space is the smallest dimensional space and therefore it is local w.r.t the rest of dimensional spaces.

A point isn’t a “dimensional space” it is specifically without dimension(s). None of your nonsense can change that.

So “Any smaller dimensional space is” only one location (how you define your “local”) “w.r.t to any greater dimensional space”. So a line is only one location “w.r.t to” a plane. Looks like a point isn’t your only “location”.

Your simple and deliberate ignorance of your own assertions is what makes you still the staunchest opponent of just your own notions.

doronshadmi said:
You still can't comprehend the involvement of things that save their ids under co-existence, for example:

You still can’t comprehend that your “ids” are just superfluous nonsense.

doronshadmi said:
Stretched 0-dim is not 0-dim anymore, because we get at least 1-dim.

So your claiming you can ‘Stretch’ your “0-dim” into “”at least 1-dim”?

doronshadmi said:
Totally reducible 1-dim is not 1-dim anymore, because we get at most 0-dim.

So your claiming you can ‘reduce’ your “1-dim” into “at most 0-dim”?

doronshadmi said:
In other words, there is no homeomorphism among different dimensional spaces.

That’s not what you claim above, you just said that by ‘stretching’ or ‘reducing’ one becomes ”at least” or “at most” the other.

doronshadmi said:
A point is something that has 0 dimension.

So your point has no dimension(s)?

doronshadmi said:
Do you agree that a point is something that has 0 dimension?

Agian, a point has no dimension(s) or is zero dimensional, this “has 0 dimension” is your own deliberate (as we have been over it before) confusion of a “0 dimension” (a "dimension" that you just label with “0” as an ordinal number).

doronshadmi said:
Please look at http://www.internationalskeptics.com/forums/showpost.php?p=7205990&postcount=15478 .

I already did, before I made the post you've been quoting.

doronshadmi said:
The actuality of nothing is no symbol at all, exactly as the actuality of silence is no sound at all.

Too bad you keep giving it symbols like “nothing”.

doronshadmi said:
You can add "actuality" to the words that you don't understand.

Actuality I do understand it quite well.

doronshadmi said:
Now you demonstrate your inability to understand the actuality of "beyond expressions"

Still you demonstrate your deliberate ignorance of the implications of your own notations and ordering.

doronshadmi said:
In other words, you do not understand that nothing between 1 and 1 is resulted by (1), where redundancy between 1 and 1 (which is a kind of an interval) is resulted by (1,1).

Nope in the exact words I used

“1 and 1”? You’ve only got “(1)”. Yep it is just you that can’t “distinguish between (1) and (1,1)”

“(1,1)” is an interval with no difference and nothing between the limits. Which again simply makes your equivocation of “difference” with “interval” and “nothing between” with “difference” demonstrably false.

So now with your “redundancy” (that you just want to call “a kind of an interval) your “nothing” is proceeded by 1 and succeeded by 1 as you claim it is “between 1 and 1”. So much for your “nothing” having “no predecessor”.

doronshadmi · May 22, 2011

The Man said:
A point isn’t a “dimensional space” it is specifically without dimension(s). None of your nonsense can change that.

So “Any smaller dimensional space is” only one location (how you define your “local”) “w.r.t to any greater dimensional space”. So a line is only one location “w.r.t to” a plane. Looks like a point isn’t your only “location”.

Once again you demonstrate your inability to get the generalization of Non-locality\Locality co-existence, where 0-dimensional space is the smallest dimensional space and therefore it is local w.r.t the rest of dimensional spaces.

The Man said:
You still can’t comprehend that your “ids” are just superfluous nonsense.

Please define homeomorphism among, for example 0-dimensional space and 1-dimensional space, or among 1-dimensional space and 2-dimensional space.

The Man said:
So your claiming you can ‘Stretch’ your “0-dim” into “”at least 1-dim”?

So your claiming you can ‘reduce’ your “1-dim” into “at most 0-dim”?

Your weak reasoning interprets what I say as the negation of what I actually say. Since you can't comprehend "Actuality" there is no wonder that you can't understand what I actually say.

The Man said:
That’s not what you claim above, you just said that by ‘stretching’ or ‘reducing’ one becomes ”at least” or “at most” the other.

You sipmly ignore "is not 1-dim anymore" or "is not 0-dim anymore" parts of what I actually says, in order to fit it to your limited boxes-reasoning, by brutally cut what does not fit to your boxes.

The Man said:
So your point has no dimension(s)?

It does not changes the fact that a point is something, and this is the important notion that your boxes-reasoning can't comprehend exactly because an integral property of your boxes-reasoning is brutally cut what does not fit to it.

The Man said:
Agian, a point has no dimension(s) or is zero dimensional, this “has 0 dimension” is your own deliberate (as we have been over it before) confusion of a “0 dimension” (a "dimension" that you just label with “0” as an ordinal number).

Your twisted reply on this subject has no impact on the fact that a point is something. In other words you simply avoided a straightforward answer to my question.

The Man said:
I already did, before I made the post you've been quoting.

And what is your detailed reply about it?

The Man said:
Too bad you keep giving it symbols like “nothing”.

You simply can't transcendent a given representation of X in order to actually get it.

The Man said:
Actuality I do understand it quite well.

Evidently you do not understand it.

The Man said:
Still you demonstrate your deliberate ignorance of the implications of your own notations and ordering.

Evidently you are forcing order even if there is no order.

The Man said:
Nope in the exact words I used

“1 and 1”? You’ve only got “(1)”. Yep it is just you that can’t “distinguish between (1) and (1,1)”

“(1,1)” is an interval with no difference and nothing between the limits. Which again simply makes your equivocation of “difference” with “interval” and “nothing between” with “difference” demonstrably false.

You are unable to distinguish between redundancy (which is a kind of an interval) and nothing (now we all aware of your inability to transcendent a representation on order to get the actual).

The Man said:
So now with your “redundancy” (that you just want to call “a kind of an interval) your “nothing” is proceeded by 1 and succeeded by 1 as you claim it is “between 1 and 1”. So much for your “nothing” having “no predecessor”.

Let us do it actual:

a) " between 1 and 1 is resulted as (1)"

b) "Redundancy (which is a kind of an interval) between 1 and 1 is resulted as (1,1)"

Since "actual" is beyond your comprehension, you simply can't comprehend the difference between (a) and (b).

doronshadmi · May 22, 2011

shuttlt said:
My maths is rusty as all hell. But is this like claiming it's a miracle if there aren't gaps in the real numbers and then asking for a proof that you can take the segment of the real numbers between 0 and 1 and then do a 1-1 mapping back onto the whole real line?

If (and I am not sure about it) I understand your question, then please be aware that according to Traditional Math 1-dim elements with different lengths have sets of points along them, which have the same cardinality (notated as |R|).

In that case I ask what enables the different lengths of the considered 1-dim element even if the sets of points along each one of them have the same cardinality?

By disagreeing with Traditional Math about that subject, I claim that no amount of points along a 1-dim element actually completely covers it, and the difference of lengths between the uncovered sub-segments of the considered 1-dim elements with different lengths, actually determine the different lengths of these 1-dim elements.

a) Please read http://www.internationalskeptics.com/forums/showpost.php?p=7205990&postcount=15478 in order to understand my claim about the inability of a set of points to completely cover a given 1-dim element.

b) Please look at the following diagram:

[qimg]http://farm3.static.flickr.com/2691/5736095487_99cb0b393a_b.jpg[/qimg]

As can be seen, the cardinality of the intersection points along the line segments with different lengths is the same, whether it is finite or infinite cardinality. So only the sets of points with the same cardinality can't provide the solution for the existence of 1-dim elements with different lengths.

doronshadmi · May 22, 2011

Euclidean spaces of different dimensions are not homeomorphic, which seems evident, but is not easy to prove.

http://en.wikipedia.org/wiki/Space_(mathematics)

Since it is a self evident truth it does not need any proof.

doronshadmi · May 22, 2011

It is obvious that no Euclidean space can be transformed to a different Euclidean space and still be considered as the Euclidean space before the transformation.

For example:

a) A stretched "0-dimensional space" is actually at least 1-dimensional space that actually can't be considered as 0-dimensional space.

b) A totally shrunken "1-dimensional space" is actually at most 0-dimensional space that actually can't be considered as 1-dimensional space.

In other words:

"Euclidean spaces of different dimensions are not homeomorphic ..."

( http://en.wikipedia.org/wiki/Space_(mathematics) )

-------------------------

In http://planetmath.org/encyclopedia/InvarianceOfDimension.html you can find Brouwer's theorem about this subject ( as we know, Brouwer rejected the Cantorien transfinite system and the law of excluded middle ).

The Man · May 22, 2011

doronshadmi said:
Once again you demonstrate your inability to get the generalization of Non-locality\Locality co-existence, where 0-dimensional space is the smallest dimensional space and therefore it is local w.r.t the rest of dimensional spaces.

Once again you demonstrate your inability to get that you just typing “generalization” doesn’t make a point a “dimensional space”. It is again specifically non-dimensional.

doronshadmi said:
Please define homeomorphism among, for example 0-dimensional space and 1-dimensional space, or among 1-dimensional space and 2-dimensional space.

Define it yourself since you’re the one who claimed you could ‘stretch’ or ‘reduce’ one into the other.

doronshadmi said:
Your weak reasoning interprets what I say as the negation of what I actually say. Since you can't comprehend "Actuality" there is no wonder that you can't understand what I actually say.

Nope Doron, again we can only go be what you write. If what you write is not what you actually want to say I would recommend that you take more care with what you do write.

doronshadmi said:
You sipmly ignore "is not 1-dim anymore" or "is not 0-dim anymore" parts of what I actually says, in order to fit it to your limited boxes-reasoning, by brutally cut what does not fit to your boxes.

No I didn’t, that is where you specify that your ‘stretching’ or ‘reducing’ makes one into the other.

doronshadmi said:
It does not changes the fact that a point is something, and this is the important notion that your boxes-reasoning can't comprehend exactly because an integral property of your boxes-reasoning is brutally cut what does not fit to it.

No one said that a point wasn’t something. So are you claiming that your point has no dimension(s).

doronshadmi said:
Your twisted reply on this subject has no impact on the fact that a point is something. In other words you simply avoided a straightforward answer to my question.

Again, no one said that a point wasn’t something and I gave you a straightforward answer to your deliberately loaded question.

doronshadmi said:
And what is your detailed reply about it?

You have simply and deliberately ignored the details of “Hilbert's Hotel”

doronshadmi said:
You simply can't transcendent a given representation of X in order to actually get it.

You simply can't “transcendent” your way out of your own representation, notations, notions and orderings (much that you would like to).

doronshadmi said:
Evidently you do not understand it.

Actually I do, and I can cite references if that still confuses you.

doronshadmi said:
Evidently you are forcing order even if there is no order.

It’s your ordering Doron, so stop forcing it yourself

doronshadmi said:
You are unable to distinguish between redundancy (which is a kind of an interval) and nothing (now we all aware of your inability to transcendent a representation on order to get the actual).

I have made no such assertions

doronshadmi said:
Let us do it actual:

a) " between 1 and 1 is resulted as (1)"

“(1)” or “1” is not “between 1 and 1”. You fail right off the bat as usual

doronshadmi said:
b) "Redundancy (which is a kind of an interval) between 1 and 1 is resulted as (1,1)"

“Redundancy” isn’t an interval but “(1,1)” is and the result isn’t “(1,1)” it is the empty set.

doronshadmi said:
Since "actual" is beyond your comprehension, you simply can't comprehend the difference between (a) and (b).

Since anything but your fantasies are evidently beyond your comprehension you simply can't comprehend that there is no fundamental difference between your nonsense “(a) and (b)” assertions.

epix · May 22, 2011

doronshadmi said:
If (and I am not sure about it) I understand your question, then please be aware that according to Traditional Math 1-dim elements with different lengths have sets of points along them, which have the same cardinality (notated as |R|).

In that case I ask what enables the different lengths of the considered 1-dim element even if the sets of points along each one of them have the same cardinality?

In this case "the same" doesn't refer to a finite concept of sameness. You can use Cantor's diagonal argument when "stretching" set of reals x in [0, a] to x in [0, b] where a<b.

Once you start stretching, new points are created to fill the "topological gaps" caused by the action. This is similar to disproving the assumption that all real members x in [a, b] have been accounted for.

How many 0-dim objects can fit into a finite 1-dim space?

doronshadmi · May 23, 2011

The Man said:
Nope Doron, again we can only go be what you write. If what you write is not what you actually want to say I would recommend that you take more care with what you do write.

The Man said:
No I didn’t, that is where you specify that your ‘stretching’ or ‘reducing’ makes one into the other.

What I have showed is that changing X names has not impact on the actuality of X, but since your reasoning end at the level of names, you can't comprehend the actuality of the considered things.[/quote]

The Man said:
No one said that a point wasn’t something.

Good, so your "no-dimension" has no impact on the fact that a point is the smallest existing local thing.

The Man said:
You have simply and deliberately ignored the details of “Hilbert's Hotel”

You have simply and deliberately ignored the details of my new version of “Hilbert's Hotel”. This is another example of your boxes-only reasoning style, you simply ignore anything which is not in the agreed box.

The Man said:
You simply can't “transcendent” your way out of your own representation, notations, notions and orderings (much that you would like to).

This is a self contradictory proposition from a person that its reasoning is based on the principle of context-dependent, which is exactly the inability to transcendent context-dependent reasoning (boxes-only reasoning) by using also cross-contexts reasoning.

The Man said:
Actually I do, and I can cite references if that still confuses you.

Please cite the references.

The Man said:
“(1)” or “1” is not “between 1 and 1”. You fail right off the bat as usual

You simply fail to get the actuality of " between".

The Man said:
“Redundancy” isn’t an interval but “(1,1)” is and the result isn’t “(1,1)” it is the empty set.

The empty set is something, so it can't be used as " between 1 and 1" that is resulted by (1).

The Man said:
Since anything but your fantasies are evidently beyond your comprehension you simply can't comprehend that there is no fundamental difference between your nonsense “(a) and (b)” assertions.

Really?

Please define the redundancy of (1) and (1,1) expressions, in order to realize that it is not the same.

doronshadmi · May 23, 2011

epix said:
How many 0-dim objects can fit into a finite 1-dim space?

No amount of 0-dim objects can fully fill (completely cover) 1-dim space, no matter what length it has, exactly as it is shown in http://www.internationalskeptics.com/forums/showpost.php?p=7205990&postcount=15478 .

doronshadmi · May 23, 2011

epix said:
In this case "the same" doesn't refer to a finite concept of sameness. You can use Cantor's diagonal argument when "stretching" set of reals x in [0, a] to x in [0, b] where a<b.

Once you start stretching, new points are created to fill the "topological gaps" caused by the action. This is similar to disproving the assumption that all real members x in [a, b] have been accounted for.

Please look at case (b) in http://www.internationalskeptics.com/forums/showpost.php?p=7207963&postcount=15484 .

zooterkin · May 23, 2011

doronshadmi said:
No finite amount of 0-dim objects can fully fill (completely cover) 1-dim space, no matter what length it has

FTFY.

caps fodder

doronshadmi · May 23, 2011

zooterkin said:
FTFY

No.

You Spoiled That For You (YSTFY) exactly because you can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7207963&postcount=15484 .

doronshadmi · May 23, 2011

The real line R is a connected perfect space, while the Cantor space 2^ω and Baire space ω^ω are perfect, totally disconnected zero dimensional spaces.

http://en.wikipedia.org/wiki/Perfect_space

In other words, Traditional Math can't distinguish between versions a and b of Hilbert's Hotel exactly because it does not understand that "nothing between two points" is "one and only one point":

Version a) http://www.internationalskeptics.com/forums/showpost.php?p=7205685&postcount=15477

Version b) http://www.internationalskeptics.com/forums/showpost.php?p=7205990&postcount=15478

Furthermore, Traditional Math does not enable to distinguish between "nothing between two points" (which is actually "one and only one point") and "something between two points" where this something is any abstract or non-abstract thing, which actually enables the existence of at least two points.

It can be a 1-dimensional space, Distinction, Difference, Redundancy, etc... where all of them are forms of something, which I also call an Interval.

But the names are not important as long as you are able to understand the result of "nothing between ..." .

EDIT:

It has to be stressed that a point is something, but if we are using a point as an interval between points, we do not define the minimal existence of multiple points, which is no more than two points.

epix · May 23, 2011

doronshadmi said:
No amount of 0-dim objects can fully fill (completely cover) 1-dim space, no matter what length it has, exactly as it is shown in http://www.internationalskeptics.com/forums/showpost.php?p=7205990&postcount=15478 .

Your reference doesn't constitute any proof. It wouldn't be accepted as such even by the Sumerians. The implication of your statement is that there doesn't exist p (point) different from zero such as |a|/|p| > 0, where a>p, but you cannot show otherwise, coz your "proofs" never involve the crucial symbols that enters proofs, namely '=', '<', or '>'; your proofs are sermons made of declarations of ideas conceived in the Bzzz-Infested Attic of Rampant Decline of Reason and Perpetual Instability of Mind.

doronshadmi · May 23, 2011

epix said:
Your reference doesn't constitute any proof.

It is a self evident truth, exactly because there is no homeomorphism between different Euclidean dimensional spaces (the points and the line save their ids under co-existence, in this case).

doronshadmi · May 23, 2011

epix said:
coz your "proofs" never involve the crucial symbols that enters proofs, namely '=', '<', or '>'

Yes they are, look:

... . < . < . ...

____ = ____

. = .

... _____ ... ≠ ... . < . < . ...

doronshadmi · May 23, 2011

The Man said:
Once again you demonstrate your inability to get that you just typing “generalization” doesn’t make a point a “dimensional space”. It is again specifically non-dimensional.

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

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

epix · May 23, 2011

doronshadmi said:
Yes they are, look:

... . < . < . ...

____ = ____

. = .

... _____ ... ≠ ... . < . < . ...

Save your "Morse code" for someone else . . .

The Man · May 25, 2011

doronshadmi said:
What I have showed is that changing X names has not impact on the actuality of X, but since your reasoning end at the level of names, you can't comprehend the actuality of the considered things.

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.

doronshadmi said:
Good, so your "no-dimension" has no impact on the fact that a point is the smallest existing local thing.

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?

doronshadmi said:
You have simply and deliberately ignored the details of my new version of “Hilbert's Hotel”. This is another example of your boxes-only reasoning style, you simply ignore anything which is not in the agreed box.

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

doronshadmi said:
This is a self contradictory proposition from a person that its reasoning is based on the principle of context-dependent, which is exactly the inability to transcendent context-dependent reasoning (boxes-only reasoning) by using also cross-contexts reasoning.

Nope, the statement just contradicted you (which you do yourself), not itself.

doronshadmi said:
Please cite the references.

No problem…

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

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

doronshadmi said:
You simply fail to get the actuality of " between".

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

doronshadmi said:
The empty set is something, so it can't be used as " between 1 and 1" that is resulted by (1).

So don’t use it " between 1 and 1" that is resulted by (1)”, since no one else made such an assertion.

doronshadmi said:
Really?

Acctually.

doronshadmi said:
Please define the redundancy of (1) and (1,1) expressions, in order to realize that it is not the same.

Please read the post you quoted as the assertion was….

The Man said:
Since anything but your fantasies are evidently beyond your comprehension you simply can't comprehend that there is no fundamental difference between your nonsense “(a) and (b)” assertions.

The Man · May 25, 2011

doronshadmi said:
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.

doronshadmi said:
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 · May 25, 2011

The Man said:
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.

The Man said:
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?

The Man said:
It is the definition of a point which asserts that, Doron.

The Man said:
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.

The Man said:
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?

The Man said:
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.

The Man said:
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 · May 26, 2011

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 · May 26, 2011

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 · May 26, 2011

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 · May 26, 2011

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 · May 26, 2011

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 · May 26, 2011

doronshadmi said:
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 · May 26, 2011

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

Please demonstrate in details that I do not understand it.

doronshadmi · May 26, 2011

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 · May 27, 2011

doronshadmi said:
Please demonstrate in details that I do not understand it.

The part where you said it was nonsense.

doronshadmi · May 27, 2011

zooterkin said:
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 · May 28, 2011

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 · May 28, 2011

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 · May 28, 2011

jsfisher said:
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 · May 28, 2011

doronshadmi said:
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 · May 28, 2011

doronshadmi said:
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 · May 28, 2011

epix said:
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 · May 28, 2011

jsfisher said:
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:

doronshadmi said:
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.

Click to expand...

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).

jsfisher said:
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 · May 28, 2011

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

doronshadmi said:
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".

Deeper than primes

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