Deeper than primes

[shuttlt]

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]

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.

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.

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”?

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”?

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.

A point is something that has 0 dimension.

So your point has no dimension(s)?

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).

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.

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”.

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

Actuality I do understand it quite well.

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.

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]

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.

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.

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.

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.

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.

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.

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

And what is your detailed reply about it?

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.

Actuality I do understand it quite well.

Evidently you do not understand it.

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.

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).

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]

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]

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]

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]

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.

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.

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.

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.

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).

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.

And what is your detailed reply about it?

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

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).

Evidently you do not understand it.

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

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

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

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

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

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.

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]

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]

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.

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]

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.

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.

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.

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

Please cite the references.

“(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".

“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).

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]

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]

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]

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]

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]

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]

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]

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]

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

Yes they are, look:

... . < . < . ...

____ = ____

. = .


... _____ ... ≠ ... . < . < . ...

 

[doronshadmi]

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]

Yes they are, look:

... . < . < . ...

____ = ____

. = .


... _____ ... ≠ ... . < . < . ...

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

 

[The Man]

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.

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?

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”

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.

Please cite the references.

No problem…

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

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

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

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

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.

Really?

Acctually.

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….

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.