Deeper than primes

[doronshadmi]

Is there a spot in the circumference of the circle for which a point doesn't exist, meaning the spot cannot be located. YES or NO?

1) A circumference of a given circle exists even if there is not even a single 0() along it.

2) If there are 0() along a circumference of a given circle, each one of them is different than any other 0(), no matter how many scale levels are researched.

In other words, 0(x)≠0 is an invariant fact, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0 distinction) and an integration (enables the existence of 0(x),0 as a pair).

 

[doronshadmi]

Once again, indentify the locations on a line you think is not covered by points.

0(x)≠0 is invariant upon infinitely many scale levels, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0 distinction) and an integration (enables the existence of 0(x),0 as a pair).

In other words, Traditional Math can't comprehend 1(0(x)≠0).

Ok so “energy” is yet another word that you evidently simply don’t understand.

The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, which your false model of collection of only 0() evidently can't comprehend.

 

[epix]

1) A circumference of a given circle exists even if there is not even a single 0() along it.

You can axiomize the heck out of Virgin Mary and declare anything you want, but you can't make that self-evident. You can stand on the pulpit and hold your sermon 24/7 and it's still no-go, coz there is a requirement for statements of this nature called "acceptance." Even God had to utter something like "let there be light" to make things happen. Your circle appears by itself and its size cannot be determined, coz there are no points of intersection on its circumference and therefore you can't measure its diameter. See, the end points of the diameter line must share the same location with two opposite points on the circumference in order to measure the diameter. So you can't define that phantom circle, and as such, the circle is useless for anything except the halo over the saints.

 

[The Man]

0(x)≠0 is invariant upon infinitely many scale levels, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0 distinction) and an integration (enables the existence of 0(x),0 as a pair).

In other words, Traditional Math can't comprehend 1(0(x)≠0).

No Doron it simply demonstrates that you can't comprehend that "≠" is not a location on a line. So you still simply can not show any location or locations on a line that are not or can not be covered by points.

The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, which your false model of collection of only 0() evidently can't comprehend.

Ok so “energy” is still just another word that you evidently simply don’t understand and “evidently can't comprehend”.

 

[jsfisher]

By traditional reasoning you are unable to define the fundamentals that enable collections.

Wrong again. But that's no surprise.

 

[doronshadmi]

No Doron it simply demonstrates that you can't comprehend that "≠" is not a location on a line.

No The Man it simply demonstrates that you can't comprehend that "≠" is the non-local property of 1() w.r.t 0().

By using Traditional Math, please prove that variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0.

 

[doronshadmi]

You can axiomize the heck out of Virgin Mary and declare anything you want, but you can't make that self-evident.

http://www.internationalskeptics.com/forums/showpost.php?p=6422678&postcount=11927

http://www.internationalskeptics.com/forums/showpost.php?p=6425352&postcount=11946

 

[zooterkin]

Really?

So the sum of a geometric series with a common ratio less than 1 does not have a limit?

...

Please look at S in http://www.internationalskeptics.com/forums/showpost.php?p=6400287&postcount=11858.

Its does not have a sum if the series 2(a+b+c+d+...) is infinite.

He didn't say 'sum', he said 'limit', which is what you originally said.


ETA: Ah, I see it was yet another example of your ninja editing skills; you've been told about the dishonesty of that before.

 

[zooterkin]

epix, Pointless_topology is also under Non-locality\Locality Linkage, because whenever multiplicity is used, there is Non-locality among the considered elements. so?

A very apt description, as I'm sure has been noted before. "Pointless" is exactly the word to describe OM.

 

[doronshadmi]

He didn't say 'sum', he said 'limit', which is what you originally said.

He assumed a sum of convergent series, but I show that this is a false assumption ( http://www.internationalskeptics.com/forums/showpost.php?p=6400287&postcount=11858 ).

 

[doronshadmi]

A very apt description, as I'm sure has been noted before. "Pointless" is exactly the word to describe OM.

Wrong, the complex 1(0()) is not pointless.

 

[doronshadmi]

Your circle appears by itself and its size cannot be determined,

We do not need to know the size of a given circle, in order to know that it is 1().

In order to know the size of a given circle, the complexity 1(0()) is used.

 

[doronshadmi]

http://hypatia.math.uri.edu/~kulenm/honprsp02/interpolation.html

Here you are using 2(1(0())), where 2() is irreducible to 1() or 0(), and 1() is irreducible to 0().

 

[epix]

http://www.internationalskeptics.com/forums/showpost.php?p=6422678&postcount=11927

Collection is a process, not an amount. You made it synonym to plural. You collect data and if you manage to get only one, then you still collected data.
Altering the meaning of words to suit your needs will not sit well with your attempt to reorganize math.

Let's practice extrapolation: 1, 2, 3, 9, 24, 76, 236, ...

Where does it go? These numbers are you invention, remember?

 

[epix]

We do not need to know the size of a given circle, in order to know that it is 1().

We don't draw a circle to know its dimensionality; there are much more useful things you can do with circles. The dimensionality of a circle is not important and is rarely mentioned. For example the article in Wiki doesn't mention the dimensionality of the circle not even once.
http://en.wikipedia.org/wiki/Circle

You are swimming in the Sea of Irrelevance and the time is getting short.

 

[epix]

Originally Posted by epix
http://hypatia.math.uri.edu/~kulenm/...rpolation.html

Here you are using 2(1(0())), where 2() is irreducible to 1() or 0(), and 1() is irreducible to 0().

I add two
and erase four
low and behold
there is more

 

[doronshadmi]

In addition to this post where you are again asked above to show any locations on a line that you think are not or can not be covered by points, you are also invited to show that you understand any of those papers you cited as well as how and why you think (specifically based on the papers themselves) they are relevant to your OM nonsense.

The function f(x)=1/x on the real line has a singularity at x = 0, where it seems to "explode" to ±∞ and is not defined.

( see http://en.wikipedia.org/wiki/Mathematical_singularities ).

By understanding 1/0 as 1()/0() we actually discover the irreducibility of 1() to 0(), such that 1(0()) where, 1() is non-local w.r.t 0() and 0() is local w.r.t 1().

In other words, the "explosion" to ±∞ is actually the irreducibility of 1() to 0(), such that no amount of 0() is 1().

n=1 to ∞

k= 0 to n-1

The irreducibility of n() to k() stands at the basis of gravitational singularity ( http://en.wikipedia.org/wiki/Gravitational_singularity ).

 

[doronshadmi]

Collection is a process,

No it is not a process, because time is not considered.

The same holds for infinite interpolation\extrapolation.

 

[doronshadmi]

For example the article in Wiki doesn't mention the dimensionality of the circle not even once.
http://en.wikipedia.org/wiki/Circle

So what?

This article was written according to Traditional Math, where the irreducibility of 1() to 0() is not understood.

 

[epix]

In other words, the "explosion" to ±∞ is actually the irreducibility of 1() to 0(), such that no amount of 0() is 1().

The irreducibility of 1() to 0() means that there can't be 1/2() or 1/3()... In other words there can't be no values between 1 and 0 that would lead to the reduction of 1 toward 0. But that's not so, as I already told you once:

In mathematics, the Hausdorff dimension (also known as the Hausdorff–Besicovitch dimension) is an extended non-negative real number associated with any metric space. The Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional vector space equals n. This means, for example the Hausdorff dimension of a point is zero, the Hausdorff dimension of a line is one, and the Hausdorff dimension of the plane is two. There are however many irregular sets that have noninteger Hausdorff dimension.

"Noninteger" means a fraction, such as 1/2, 1/3, 1/4... and therefore 1() is reducible. But it cannot be reduced all the way to 0() through reduction by division, the same way 0() can't be expanded to 1() through multiplication.

If you are in the Euclidean space, then be advised that

Many constructs within Euclidean geometry consist of an infinite collection of points that conform to certain axioms. This is usually represented by a set of points; As an example, a line is an infinite set of points of the form

(see formula)

where (parameter) through (parameter) and (parameter) are constants and 'n' is the dimension of the space. Similar constructions exist that define the plane, line segment and other related concepts.

http://en.wikipedia.org/wiki/Point_(geometry)

If your are not in Euclidean space, where are you then?

Once a 1-D object is defined continuous, then its definition assures that there is no point on the object that cannot be located. f(x) = 1/x or g(x) = Log(x) are not defined continuous in the domain -∞ < x < ∞. If this is what you mean by "not all points can cover 1()," then you just made a "far-reaching discovery."