Deeper than primes

[jsfisher]

It does not matter, only the Distinction among the <0,1> forms is significant.

Great! So, do we now have step #1? Is it:

1. Pick any element, any element at all from the collection. Call it E₁.​

Is that our step #1?

What next? Do we select an arbitrary bit from that element, or do we need to pick something more specific. We all eagerly await step #2.

 

[epix]

Originally Posted by epix
m^2 < 2^m for any positive integer m except 2, 3, and 4.

This is a false proposition.

what is false and what is true?
ask the colors red and blue
what is more and what is less?
if you don't know, take a guess

Anyway:

|N| < |x|

x² < 2^x, where x² is not isolated from 2^x, otherwise you can't conclude that x² < 2^x.

The cardinality |N| of the set of natural numbers is aleph null, so that |x| is greater than that. That means either you annotate aleph one as |x|, or you have been fantasizing profusely once again, where the second option is the bettable one.

Furthermore, x² is not the same as 2^x, and this conclusion can't be concluded if x² is isolated from 2^x, and vice versa.

That's right. If x^2 is isolated from 2^x, you can't see the similarity between both expressions -- and that's the only true part of your conclusion.

 

[doronshadmi]

That's right. If x^2 is isolated from 2^x, you can't see the similarity between both expressions -- and that's the only true part of your conclusion.

The true is the ability to get both x^2 and 2^x, and it is possible only if they are different AND also there is a higher level that enables their comparison with each other.

In other word, at the level of collection, things are not totally connected AND not totally isolated.

 

[doronshadmi]

Great! So, do we now have step #1? Is it:

1. Pick any element, any element at all from the collection. Call it E₁.​

Is that our step #1?

What next? Do we select an arbitrary bit from that element, or do we need to pick something more specific. We all eagerly await step #2.

Let me help you.

The index is the Distinct code of any given <0,1> form.

Given any collection (finite or not) of <0,1> distinct codes, there is always a distinct <0,1> inverse code of the diagonal of the given collection, which is not in the range of the given collection of <0,1> distinct codes.

This fact is not limited to N, P(N) ,P(P(N), P(P(P(N), etc. ... ad infinitum ...

 

[jsfisher]

Let me help you.

The index is the Distinct code of any given <0,1> form.

So, what would be the index of 10000000..., 01000000..., and 10101010..., just as examples?

Then, given we can determine an index for each of the bit maps, what purpose do these indices serve? Are you claiming the index decides the selection order for the elements?

 

[epix]

In other word, at the level of collection, things are not totally connected AND not totally isolated.

Too bad that you didn't supply an example connected to the real world, coz natural numbers are the subset of the real numbers and are themselves connected to the Nature, which can be painfully real, especially when genetic inheritance is concerned.

There are two logical outcomes in the world of mathematical logic: True and False. Or are there?

True: 00
False: 11
---------
Adjusted diagonal: 10

The implications is

True AND False: 10

for example.

The consequence is that all the well-known mathematical proofs starting with Archimedes and Euclid are just illusions. There may be infinitude of primes but at the same time there may be the last prime number. In the case of Pythagorean Theorem, one of the consequences via the calculus is that there are no functional missiles or rockets, as a minuscule of an example, even though some things have been known to work without a theoretical proof that they can.

 

[The Man]

This is the beautiful thing of being mutually exclusive, they are disjoint at their level but also have a common environment for both of them on a higher level.

You still don’t get it Doron, they are still mutually exclusive even at your “common environment for both of them on a higher level” so you are just using your term “disjoint” inconsistently (go figure). That they can both be parts of something else has nothing to do with them being mutually exclusive no matter how “beautiful” you think it is.

Because there is only sameness about the concept of Time, and therefore no process. It is called parallel observation.

No, again it just means ‘at the same time’ it makes no assertions about any “process” lacking or otherwise regardless of what you want to call it. You do understand that processes can happen, well, simultaneously, don’t you?

 

[doronshadmi]

You still don’t get it Doron, they are still mutually exclusive even at your “common environment for both of them on a higher level” so you are just using your term “disjoint” inconsistently (go figure). That they can both be parts of something else has nothing to do with them being mutually exclusive no matter how “beautiful” you think it is.

You still don’t get it The Man, being mutually exclusive is not less then being disjoint at the same lave AND being connected at the higher level.

Your one level flat reasoning actually can't comprehend what mutually exclusive really is.

You do understand that processes can happen, well, simultaneously, don’t you?

In that case both parallel AND serial observations are considered.

 

[doronshadmi]

Too bad that you didn't supply an example connected to the real world,

In the real world we can see how forms are born from already existing forms, such that each existing form of a given collection contributes some bit of information in order to construct the form that is beyond the existence of the forms of the given collection, exactly as shown in the case of the inverse of the diagonal form along the given collection of distinct <0,1> forms.

Isn't it beautiful?

for example.

The consequence is that all the well-known mathematical proofs starting with Archimedes and Euclid are just illusions.

If they are understood as partial, then there is no problem with these proofs.

There may be infinitude of primes but at the same time there may be the last prime number. In the case of Pythagorean Theorem, one of the consequences via the calculus is that there are no functional missiles or rockets, as a minuscule of an example, even though some things have been known to work without a theoretical proof that they can.

epix, the mathematical science of the past 3,500 years works exactly because it is based on the essential incompleteness of any given collection.

Again at the level of collections things are not totally isolated AND not totally connected, and so are the proofs that are related to collections.

 

[epix]

epix, the mathematical science of the past 3,500 years works exactly because it is based on the essential incompleteness of any given collection.

Too bad that you can't imagine the implications of your idea of incomplete finite sets. But that's to be expected.

There were different number systems used in the past, but modern math literature uses base 10 system. It's a collection of 10 symbols

0 1 2 3 4 5 6 7 8 9

Attach to it the provably incomplete part, which you call <0,1>, and voila -- the set of those ten digits becomes incomplete as well. But who knows?

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...

No one has ever checked them all, right?

 

[The Man]

You still don’t get it The Man, being mutually exclusive is not less then being disjoint at the same lave AND being connected at the higher level.

Your one level flat reasoning actually can't comprehend what mutually exclusive really is.

No Doron again being mutually exclusive simply means they exclude each other. It has nothing to do with all the superfluous “disjoint at the same lave AND being connected at the higher level” nonsense you want to add into it. Again they are still mutually exclusive when included in your “higher level” whatever, so you are just using your terms “disjoint” and “connected” inconsistently.

In that case both parallel AND serial observations are considered.

So now your previous assertion…

Simultaneity means that no step-by-step observation is involved.

And this one..

Because there is only sameness about the concept of Time, and therefore no process. It is called parallel observation.

Are simply false as I have pointed out?

 

[epix]

Enjoy the incompleteness of Q :

http://www-bcf.usc.edu/~fbonahon/Images/FareyPoincareMovie.gif

Well, every selected series of the radii of the circles is convergent, so there is incompleteness breathing from the animation, even though some believe that a limit can be reached. For example, this sequence in red.

Given radius R=1 for the enclosing circle, the radius of circle n_i is

r_i = 1/(n_i² - 2n_i + 3)


We must computate, Doron, before the atheists steal our numbers. LOL.

 

[doronshadmi]

No Doron again being mutually exclusive simply means they exclude each other. It has nothing to do with all the superfluous “disjoint at the same lave AND being connected at the higher level” nonsense you want to add into it. Again they are still mutually exclusive when included in your “higher level” whatever, so you are just using your terms “disjoint” and “connected” inconsistently.

No The Man, being mutually exclusive is not less than being disjoint (or exclude each other) at the same level AND being connected (mutual) at a higher level. There is no contradiction here because at least two different levels are involved.

This is a simple fact that your one-level flat reasoning can't comprehend, The Man.

So now your previous assertion…

And this one..

Are simply false as I have pointed out?

This is my answer about your "simultaneous process" proposition.

In this case at least parallel (simultaneity) AND serial step-by-step (process) reasoning is involved, but also in the case your flat reasoning can't comprehend it The Man.

 

[doronshadmi]

Too bad that you can't imagine the implications of your idea of incomplete finite sets.

The implication is very simple.

Given any finite or infinite collection of distinct <0,1> forms, there is an object that has the structure of these forms, but it is not in the range of the given collection of these distinct <0,1> forms.

As a result given any collection of distinct <0,1> codes, they provide a new code.

I think that this fact is beautiful because it shows how development is an essential property of any given data.

 

[doronshadmi]

Well, every selected series of the radii of the circles is convergent, so there is incompleteness breathing from the animation, even though some believe that a limit can be reached. For example, this sequence in red.

[qimg]http://img40.imageshack.us/img40/9174/circles1.png[/qimg]

Given radius R=1 for the enclosing circle, the radius of circle n_i is

r_i = 1/(n_i² - 2n_i + 3)


We must computate, Doron, before the atheists steal our numbers. LOL.

epix please show me Pi (circumference/radius) when radius=0.

If you can't show that Pi=circumference/0, then you have no choice but to conclude that your collection of red circles is incomplete, exactly because Pi≠circumference/0 (the convergences of circles is incomplete as long as there are circles, where each circle has a measurable Pi=circumference/radius).

 

[jsfisher]

epix please show me Pi (circumference/radius) when radius=0.

Yeah! And while you are at it, show him a circle with radius = -17, and how about one with radius = banana! Incomplete, incomplete, incomplete!

 

[doronshadmi]

Yeah! And while you are at it, show him a circle with radius = -17, and how about one with radius = banana! Incomplete, incomplete, incomplete!

We also can show radius = jsfisher , and we get the perfect solution.

 

[zooterkin]

epix please show me Pi (circumference/radius) when radius=0.

Well, I don't know what font you're using, but on my screen that's not a circle, it's an ellipse.

 

[doronshadmi]

Well, I don't know what font you're using, but on my screen that's not a circle, it's an ellipse.

You are so right, let us correct it:

radius=°

 

[epix]

The implication is very simple.

Given any finite or infinite collection of distinct <0,1> forms, there is an object that has the structure of these forms, but it is not in the range of the given collection of these distinct <0,1> forms.

As a result given any collection of distinct <0,1> codes, they provide a new code.

I think that this fact is beautiful because it shows how development is an essential property of any given data.

Too bad that you can't imagine the implications of your idea of incomplete finite sets. But that's to be expected.

There were different number systems used in the past, but modern math literature uses base 10 system. It's a collection of 10 symbols

0 1 2 3 4 5 6 7 8 9

Attach to it the provably incomplete part, which you call <0,1>, and voila -- the set of those ten digits becomes incomplete as well. But who knows?

2011 AD: 3.141592653589793238462643383279502884197169399375 10582097494459230781640628620899862803482534211706 79821480865132823066470938446095505822317253594081...


8012 AD:
Moshe! Moshe!

Whaaat?

Com'ere! Quick! Take a look.

...284811174502841027019385211051905596446229489

Whattf is that?

How are we going to call that round digit with a tongue?

How about "doron?"

Right. So, let me complete the decimal-based system:
0 1 2 3 4 5 6 7 8 9

But what if other digits similar to this show up? How are we going to call them?

I think, doron-doron, doron-doron-doron, and so on.