Deeper than primes

[doronshadmi]

Now you say that 0() and 1() are BOTH STRICT NUMBERS.

EDIT:

0() or 1() are strict, where, for example, 0.999...[base 10]() is non-strict.

You still do not get X() as a measurement unite of existence, which can be strict or non-strict.

The same holds for some location w.r.t a given existence, for example:

0.999...[base 10](0(1)) means that there is a strict location 0(1) along the non-strict existence 0.999...[base 10]().

If 1() is considered w.r.t some given 0() along it in terms of location, then the location of 1() w.r.t 0() is non-strict, such that 1(0()).

Please do not mix between 1() as a strict number in terms of existence and 0(1) as a strict number in terms of location
under 1(0(1)), where 1() does not have a strict relation (in terms of location) w.r.t 0(1) and 0(1) has a strict relation (in terms of location) w.r.t 1().

But there is a tiny light at the end of the tunnel. I have an impression from your scribble that you don't agree with the idea that "0.999999..." actually equals 1. Am I right or not?

1(0.999...[base 10](0()))

You also have missed the logical aspect of 0(),1() as seen in http://www.internationalskeptics.com/forums/showpost.php?p=6444698&postcount=12016.

 

[doronshadmi]

Let us carefully look at the general form X(x).

X is the measurement of existence and x is the name of X under X', such that X'>X, where x is strict if X=0().

He can't provide an example of such two real numbers, though. Instead, he uses the strict and the non-strict arguments to show that such numbers do exist.

R set is the form 1(0(x)), such that x is strict (for example: x can be Pi, but it can't be 3.14…[base 10]).

Please do not mix between x and X because, for example, Pi(3.14…[base 10]()) or 1(0(Pi)) are valid, where 1(0(3.14…[base 10])) is invalid.

Non-strict x are defined under X>0.

 

[epix]

It does not have an immediate successor exactly because no amount of distinct 0() is 1().

The reason why √2 doesn't have an "immediate" successor is that the line that models the set of real numbers is a collection of points whose number approaches infinity and there is no segment on that line that cannot correspond to a real number. This can be proven without inventing a strange symbolism, like 0() and 1().

Let s be the immediate successor of √2. In that case √2 < s with the consequnce of |√2 - s| > 0. That means |√2 - s| = m, where m is the length of a line segment. Since the length of a line segment can be divided by any positive real number except zero, it follows that

|√2 - s|/d = r

where d is any positive real number greater than 1. The consequence of such a division is

r < s

and therefore s cannot be the immediate successor to √2.

A proof by a contradiction such as that one was invented by the same species who also invented various pagan gods. That's why you try to invent other ways to proof stuff, so you would feel more "advanced."

 

[doronshadmi]

A proof by a contradiction such as that one was invented by the same species who also invented various pagan gods. That's why you try to invent other ways to proof stuff, so you would feel more "advanced."

It is more advanced, because it discovers the fact that 1() is not a collection of 0(), where the proof by contradiction stays at the level of collection of 0().

 

[epix]

It is more advanced, because it discovers the fact that 1() is not a collection of 0(), where the proof by contradiction stays at the level of collection of 0().

No, it's not advanced, coz it states among other things that a straight line cannot be fully covered by points. That means there exists a line segment A_____B on that line where there are no points between A and B. But since (B - A) > 0, the line segment has length m where m>0. There are many special points, and one of them is called "the mean," or the average. In this particular case, the average of A and B is

P_mean = m/2

A_____P_____B

Any line segment must have such a point. So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution. In other words, 6/2, for example, has indeterminable result -- the fraction does not equal 3. That, of course, doesn't apply in those happy moments when you cut salami to feed your face. LOL.


What? You don't cut salami? How come?



Wow!

 

[doronshadmi]

No, it's not advanced, coz it states among other things that a straight line cannot be fully covered by points. That means there exists a line segment A_____B on that line where there are no points between A and B. But since (B - A) > 0, the line segment has length m where m>0. There are many special points, and one of them is called "the mean," or the average. In this particular case, the average of A and B is

P_mean = m/2

A_____P_____B

Any line segment must have such a point. So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution. In other words, 6/2, for example, has indeterminable result -- the fraction does not equal 3. That, of course, doesn't apply in those happy moments when you cut salami to feed your face. LOL.


What? You don't cut salami? How come?



Wow!

Under complex 1(0()) 0() is the minimal existing space of strict Locality, where 1() is the minimal existing space of strict Non-locality.

you can cut salami to infinitely many slides, which does not change the fact that 1(0(x)≠0), such that ≠ is 1() at AND beyond 0(x) OR 0 upon infinitely many "cutting" levels.

Again, your notion is limited to the concept of collection of 0(), without understanding 1() as an existence that is at AND beyond 0(), as expressed by 1(0()).

 

[doronshadmi]

So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution.

There are strict or non-strict solutions, for example:

Under 1(0.999...[base 10]()), 1()-0.999...[base 10]() = 0.000...1[base 10](), where 0.000...1[base 10]() is a non-strict solution,
and 0.999...[base 10]()+0.000...1[base 10]() = 1(), where 1() is a strict solution.

 

[jsfisher]

0() is for strict relation....

A simple, "No, I can't explain them," would have sufficed. No need for gibberish.

 

[doronshadmi]

A simple, "No, I can't explain them," would have sufficed. No need for gibberish.

A simple, "No, I can't get them," would have sufficed. No need for your gibberish-loop.

 

[The Man]

"≠" is exactly the non-local property of 1() w.r.t any 0(x),0, such that 1(0(x)≠0).

Still does not make it a location on a line, let alone a location(s) on a line that is not or can not be covered by point(s)

How about you first learn things beyond your 0() only reasoning?

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

 

[The Man]

Ok so you can’t actually get novell notions about those papers.

Again Doron, you simply not understanding those papers does not constitute any "novell notions about those papers".

 

[epix]

There are strict or non-strict solutions, for example:

Under 1(0.999...[base 10]()), 1()-0.999...[base 10]() = 0.000...1[base 10](), where 0.000...1[base 10]() is a non-strict solution,
and 0.999...[base 10]()+0.000...1[base 10]() = 1(), where 1() is a strict solution.

Why do you include the number base in there?

Even without it, there is a strong impression that subtraction yields "non-strict solutions," and addition yields "strict solutions," which not what you intended.

You don't relate the operands well: the expression "0.999..." implies a number where the decimal digits repeat infinitely, whereas the result "0.000...1" implies a very small but finite number. So the subtraction 1 - 0.999... = 0.000...1 is not a good rendition of the idea of non-strictness.

The "obsolete" math uses this syntax:

1 - (1 - 1/10ⁿ) where n → ∞.

The result is then

1 - (1 - 1/10ⁿ) = 1 - 1 + 1/10ⁿ = 1/10ⁿ where n → ∞

and there is no doubt about what is meant.

 

[doronshadmi]

Ok, let us continue to develop OM.

The following diagram demonstrates the notion of nested levels of existence among Non-Locality\Locality Linkage, where the tangent line between each pair of quarter circles represents the Non-locality of a given nested level, and 0() represents the "depth" of Locality w.r.t to Non-Locality, for any given nested level:

This model can be used to understand better the differences between microscopic and macroscopic non-rotating black holes.

 

[doronshadmi]

whereas the result "0.000...1" implies a very small but finite number.

Wrong.

0.000...1 is an example of non-strict (infinitely smaller AND > 0) number.

You still miss the notion of infinite interpolation.

 

[The Man]

Ok, let us continue to develop OM.

The following diagram demonstrates the notion of nested levels of existence among Non-Locality\Locality Linkage, where the tangent line between each pair of quarter circles represents The Non-locality of a given nested level, and 0() represents the "depth" of Locality w.r.t to Non-Locality, for any given nested level:

[qimg]http://farm5.static.flickr.com/4147/5089991451_9b8ccd7ee1_z.jpg[/qimg]

This model can be used to understand better the differences between microscopic or macroscopic black holes.

You can make up as much nonsensical gibberish, drawings and notations as you want Doron, but until you make you "OM" both self-consistent and generally consistent you haven't even started to "develop OM".

We are still waiting for you to identify any locations on a line that are not or can not be covered by points.

 

[doronshadmi]

Still does not make it a location on a line,

Location along 1() is exactly 0().

Since you get 1() only in terms of 0(), your 0()-only reasoning can't comprehend the fact that 1() is at AND beyond any given 0() along 1().

As a result you do not understand the non-local property of ≠ w.r.t any given pair of 0() localities.

 

[doronshadmi]

You can make up as much nonsensical gibberish, drawings and notations as you want Doron, but until you make you "OM" both self-consistent and generally consistent you haven't even started to "develop OM".

We are still waiting for you to identify any locations on a line that are not or can not be covered by points.

I am not with you in your 0()-only game.

Actually I do not care anymore about your 0()-only replies.

 

[The Man]

Location a long 1() is exactly 0().

"≠" still isn't a location.

Are you claiming that any location “a long 1() is exactly” a point?

Since you get 1() only in terms of 0(), your 0()-only reasoning can't comprehend the fact that 1() is at AND beyond ant given 0() along 1().

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Oh and evidently you simply can’t understand that a line segment is specifically not “beyond” its given end points and in the case of segment represented by an interval like (1,2) the line segment isn’t even “at” those two points.

As a result you do not understand the non-local property of ≠ w.r.t any given pair of 0() localities.

You still simply don’t understand that "≠" still isn't a location and “As a result” your “non-local property of ≠ w.r.t any given pair of 0() localities.” is still simply just nonsense.

 

[The Man]

I am not with you in your 0()-only game.

Actually I do not care anymore about your 0()-only replies.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

 

[epix]

Wrong.

0.000...1 is an example of non-strict (infinitely smaller AND > 0) number.

So why did you use 1 - 0.999... instead of 1 - 0.999...9?

I think that the old-fashioned expression 10^-n (n → ∞) is superior in clarity to your version 0.000...1.