Deeper than primes

[doronshadmi]

Lines which are parallel and lines which are not parallel are not equivalent.

It is equivalent if you compare between the sub-line segments of the red line segment and the green line segment.

They are smaller or bigger w.r.t each other in the same way as they are smaller or bigger w.r.t each other in my diagram.

In both cases, the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same.

 

[doronshadmi]

Lines which are parallel and lines which are not parallel are not equivalent.

About being parallel, your blue lines and my blue lines are parallel w.r.t each other and also have different lengths w.r.t each other in both diagrams.

The green and red lines in your diagram are equivalent to some pair of black intersection lines in my diagram.

In other words, your second diagram and my diagram are equivalent.


Again, in both cases the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same along the different intersected line segments.

It has to be stressed that if Cardinality is the number of members of a given set that ignores their structure, then talking about Cardinality in terms of the power of the continuum is misleading, because the fundamental property of the continuum is defined by the non-locality given elements w.r.t other elements under locality\non-locality co-existence.

The first existing thing that has the power of the continuum is a 1-dimensional element, which exists simultaneously at least at two different existing locations, where these locations are first at least 0-dimensional elements, where no one of them or any number of them along the 1-dimensional element has the power of the continuum.

The power of the continuum = |1-dimensional element| > |R| = the number of all points along a line segment.

 

[jsfisher]

In both cases, the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same.

Again, in both cases the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same along the different intersected line segments.

Saying basically the same wrong thing twice doesn't make it any less false.

Considering only finite cases often lead to incorrect inferences about the infinite, and that line segments may have different lengths doesn't contradict them being completely coverable by the same (infinite) number of points.

 

[doronshadmi]

... , and that line segments may have different lengths doesn't contradict them being completely coverable by the same (infinite) number of points.

Wrong jsfisher.

A collection of points can't have (the same cardinality) AND (the ability to completely cover 1-dimensional elements with different sizes).

A collection of |R| points does not have the power of the continuum, which is not less than |1-dimensional element|, and this is exactly the reason of why 1-dimensional elements have different sizes even if the number of all points along them is the same.

Jsfisher, your reasoning can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7318292&postcount=15803 .

 

[jsfisher]

Wrong jsfisher.

A collection of points can't have (the same cardinality) AND (the ability to completely cover 1-dimensional elements with different sizes).

Other than your own disbelief, why not?

A collection of |R| points does not have the power of the continuum

Perhaps you should look up the definition of "power of the continuum" before being so certain.

which is not less than |1-dimensional element|

This phrase is nonsense. Dimensional elements don't have cardinality. Sets do.

and this is exactly the reason of why 1-dimensional elements have different sizes even if the number of all points along them is the same.

Gibberish aside, this conclusion has no basis in logic.

 

[epix]

The power of the continuum = |1-dimensional element| > |R| = the number of all points along a line segment.

"The power of continuum" is a very strange idea in the view of the simplicity of the "numerical" proof.

1) The length of line segment is a number x in R, such as x>0
2) Any x is divisible by y in R except zero.

There are two line segments m and n where m ≠ n. If you divide m and n by y, the result is a set of y-1 points drawn on the line segment plus 2 initial endpoints. Example: m = 12, n = 8, y = 4.

m: 12/4 = {0, 3, 6, 9, 12} = M
n: 8/4 = {0, 2, 4, 6, 8} = N

You see that |M| = |N|.

Since R = R, it follows that sets M = m/R and N = n/R must have the same cardinality, and so two line segments m and n of different length contain the same number of points.


Now the serpent was more crafty than any of the wild animals the LORD God had made. He said to the woman, “Did God really say, ‘You must not eat from any tree in the garden’?”
Genesis 3:1


1)SERpenT

or

2) SeRpEnT



You must choose wisely. Use this prefetch: C stands for continuum and R is a set of real numbers. You must computate boldly the "cardinality" of line segment

C________R

to the unabridged joy of the little angels who will gladly blow their trumpets if you miss, so the fowl in the air would flap their wings to AC the world from The Heat of Defeat and other expellents.

 

[doronshadmi]

Dimensional elements don't have cardinality. Sets do.

Wrong.

The set of all points (where each point is 0-dimensional element) has cardinality |R| < |1-dimensional element| = the power of the continuum.

In other words, no set of points has the power of the continuum, exactly because each point is local w.r.t 1-dimensional element.

As long as your reasoning is limited to localities, it can't comprehend the power of the continuum, and this is exactly Cantor's failure of this profound and highly important subject (traditional Formalist and Platonist mathematicians are the followers of Cantor's failure of this profound and highly important subject, and you, jsfisher, simply one of them, no less, no more).

Generally (by not limited only to metric space) the power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.

Please look at the following analogy:

Each given curvature is local w.r.t the 1-dimensional space, which is the common and non-local property of the collection of all these infinity many curvatures.

Only the 1-dimensional space exists at once at all these infinity many curvatures, which is a property that no given curvature has w.r.t 1-dimensional space.

By going beyond this analogy, no amount of localities has the property of non-locality, and only that has the property of non-locality has the power of the continuum.

 

[doronshadmi]

"The power of continuum" is a very strange idea in the view of the simplicity of the "numerical" proof.

The power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.

 

[doronshadmi]

The notion of Cardinality (in the traditional way), which actually ignores the structure of the considered members, is equivalent to the set of points, because no point has structure.

Yet |R| points do not have the power of the continuum, as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=7318292&postcount=15803.

Furthermore, by using Cardinality (in the traditional way) the power of the continuum of 1-dimensional element can't be defined,
because |{___}| = 1 by Cardinality traditional way.

 

[jsfisher]

Wrong.

The set of all points (where each point is 0-dimensional element) has cardinality |R| < |1-dimensional element| = the power of the continuum.

Repeating your gibberish doesn't make it any less false. And stop trying to disprove definitions. It serves no real purpose other than to flaunt your confusion.

 

[doronshadmi]

Repeating your gibberish doesn't make it any less false. And stop trying to disprove definitions. It serves no real purpose other than to flaunt your confusion.

Staying in your limited box is resulted by getting what I say as gibberish.

For example your reasoning can't get the power of the continuum of _____ w.r.t to all |R| points along it, exactly because your reasoning can't comprehend the non-locality of _____ w.r.t the collection of |R| localities (points) along it.

I really do care about your limitations to get it, exactly because persons like you stand at the basis of our technological development, which is currently context-dependent-only technology, which has no cross-contexts reasoning of the technological results.

Without also cross-contexts reasoning of the results, context-dependent-only technology and disconnected reductionist-only specialization is going to fulfill itself by smashing its developers\ushers into pieces, because there is no common base ground that supplies the needed balance for the context-dependent aspect of the technological development.

The natural cross-contexts reasoning is exactly the non-subjective state of our awareness, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=7255966&postcount=15594 and http://www.internationalskeptics.com/forums/showpost.php?p=7241076&postcount=15569, which is resulted by new fundamental insights of the mathematical science ( for example: http://www.internationalskeptics.com/forums/showpost.php?p=7289466&postcount=15706 ) that can't be comprehended by context-dependent-only reasoning, which is currently the main stream of the mathematical science, which is stuck at the thinking process level that is the subjective-only level of one's awareness.

 

[jsfisher]

Staying in your limited box is resulted by getting what I say as gibberish.

No, it is gibberish because you misuse words you simply do not understand. It does you no good to blame me for your own lack of knowledge.

Please stop trying to disprove definitions. It doesn't help you demonstrate anything approaching intelligence.

 

[doronshadmi]

No, it is gibberish because you misuse words you simply do not understand. It does you no good to blame me for your own lack of knowledge.

Please stop trying to disprove definitions. It doesn't help you demonstrate anything approaching intelligence.

jsfisher, you are blind to what is written in http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831.

I hope that soon minds like you, which are stuck at their thinking process level, will no longer be the majority.

 

[jsfisher]

jsfisher, you are blind to what is written in http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831.

You continue to accuse others of your own failings. It is you who is blind to what you have written, your abuse of meaning, your abandonment of logic.

By the way, how is that example of some actual, tangible, significant result from this olio of gibberish you call OM coming along? Will you likely have anything soon, or is another 20+ years of wasted effort required?

 

[doronshadmi]

You continue to accuse others of your own failings.

jsfisher, we are all in the same boat, called planet Earth, so context-dependent only reasoning is definitely not the way for our survival on this planet.

Fortunately there are other voices in your community, which are aware of the impotence of cross-contexts reasoning development, in addition to context-dependent reasoning , as can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576 .

So I am optimistic about current and future development of the mathematical science, which is not going to be developed anymore by minds like you.

 

[jsfisher]

jsfisher, we are all in the same boat, called planet Earth, so context-dependent only reasoning is definitely not the way for our survival on this planet.

My, but you do inflate things, don't you? You also continue to reflect your failings onto others. They remain your failings.

Fortunately there are other voices in your community, which are aware of the impotence of cross-contexts reasoning development, in addition to context-dependent reasoning , as can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576 .

I see you again misunderstand things others have written. The article you cite raised a point (30+ years ago, by the way) not completely unlike the point Hilbert raised over a century back. You misunderstood Hilbert, too. In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.

It in no way supports your gibberish, your confusion, your blatant denial of logic and reason, and certainly not the chaotic failure you call OM.

 

[doronshadmi]

My, but you do inflate things, don't you? You also continue to reflect your failings onto others. They remain your failings.

I see you again misunderstand things others have written. The article you cite raised a point (30+ years ago, by the way) not completely unlike the point Hilbert raised over a century back. You misunderstood Hilbert, too. In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.

It in no way supports your gibberish, your confusion, your blatant denial of logic and reason, and certainly not the chaotic failure you call OM.

A typical trivial reply of context-dependent-only mind, which can't get anything beyond his context-dependent-only reasoning.

Again, I am optimistic about current and future development of the mathematical science, which is not going to be developed anymore by minds like you, which can't get http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831 or http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576.

 

[doronshadmi]

In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.

Speaking about the overall beauty of Mathematics does not fulfill this beauty without actually using cross-contexts reasoning among context-dependent reasoning.

Your context-dependent-only reasoning missing it all along this thread.

For example, Cantor set elements are irreducible into disjoint points, simply because no 1-dimensional element is reducible to 0-dimensional element, so the assertion that Cantor set has Lebesgue measure 0 is false.

 

[jsfisher]

A typical trivial reply of context-dependent-only mind, which can't get anything beyond his context-dependent-only reasoning.

Please, just stop, Doron. The failures are completely your own, not those of anyone else. You are not helping your cause by continually exposing your inabilities.

 

[epix]

The power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.

Your definition of "the power of the continuum" -- a substitute for |R| or aleph1 -- remains, like anything else you've come up with, unwrapped. How far do you think it gets when it encounters real enemy tanks?

Obviously, you don't get a bit of the essence of anything that is connected with "=". That's why you hate "traditional math," coz it supports it's statements with that particular symbol, and here is the evidence:

You are not aware of the fact that a set can divide a real number. Any math software returns a result to m/{a, b, c, d}, for example. Using some constants,

8/{1, 2, 3, 4} = {8, 4, 8/3, 2}.

That means m/A = B, where m is a real number and A and B are sets with the same size, or cardinality. When the dividing sets are finite, things are boring. The fun starts when the dividing set is the continuum, or set R.

m/R = ?

The expression on the left side divides m, which can be the length of a line segment, with the set of real numbers. R has a membership, but that cannot be put in 1 to 1 correspondence with the set of natural numbers. That's why the size of R is hypothetical aleph1 and not aleph0, which is the cardinality of the set of natural numbers and holds the set countably infinite. But that doesn't prevent you to indicate the intended . . .

m/R: m/{pi, √2, 9/8, e, Log(5), Sin(pi/7), ...}

If the cardinality of the denominator R is aleph1, then the result of the division must be set S which has the same cardinality as R, namely aleph1. It follows that

|m/R| = |n/R| where m≠n.

That means if m=2 and n=pi, for example, there is a 1 to 1 correspondence between all points on m and all points on n, which can be seen below through a consistent vertical mapping.

And that concludes the non-rigorous proof that the number of all points, which satisfy the definition of the real number and which are positioned alongside a 1-dim object, is independent of the magnitude of such an object.

Btw, how does OM find the magnitude of finite curves? Care to demonstrate the essence of the "power of the continuum?" How does OM figure the length of this object?