Ahh, ok. I see the problem now. You just don't understand English. The problem is, if it contains no elements, that means there is nothing in it. Here is a hint: you cannot distort definitions to fit your mathematics. If a urelement contains nothing within it, an arguement about the "s" at the end of the word "elements" does not change the fact that you're wrong.

Can somebody please delete this entire thread? It's going nowhere, and somebody who reads this will be completely confused and may be lead to believe false ideas because certain people are distorting definitions for their own use.

No dear Keeblergiant,


You simply do not grasp yet the power that stands in the basis of this fine interpretation of the Urelement concept, which is based on Liebniz' Monad's idea.

If you want to understan it, then please read:

http://www.geocities.com/complementa...loisDialog.pdf


Do you see Keeblergiant?

Because English is not my first Language, I interpreted the Urelement definition differently from a person that English is his first Language.

And the result is a totally new insight about the most fundamental elements of the Language of Mathematics.

And this is exactly the positive interpretation of Godel's Incompleteness Theorems, which actually lead us to understand that no consistent system is necessarily completed, and no competed system is necessarily consistent.

If there is nothing in it, then it is identical to the empty set, but you see dear Keeblergiant, a Urelement is not identical to the Empty set by definition, see for your self in http://mathworld.wolfram.com/Urelement.html .
Here is a hint: you cannot distort definitions to fit your mathematics, becusue this is exectly what you did, by cut out half of the Urelement definiton.



Yours,


Monad

Ah, so you admit to twisting the definitions of words to fit your fancy?

I never said it was identical to the empty set, nor would I have said such a thing, as a urelement IS NOT A SET. I merely said that a urelement did not contain anything.

I didn't cut out anything. You were the one that was using a false definition, I was merely telling you the parts of the definition you were using that were wrong.

The definition of the Urelement is:

"An urelement contains no elements, belongs to some set, and is not identical with the empty set" ( http://mathworld.wolfram.com/Urelement.html )

The element that we get from this definition fits exactly to my 3 non-composed building-blocks,
which are {.}(Point), {._.}(Segment), {__}(Fullness).

No dear, you still do not understand how beautiful and full of surprises thing is a Language (any language, formal or informal).

A language is so beautiful thing because it has a tremendous deep influence on our insights, which sometimes lead us to discover new internal/external worlds which we can live and create there.

The parallel thing in the physical world (which is analogous to my original interpretation of the Urelement definition) is what is called in biology "positive mutation", where some DNA code interpreted differently from the usual way, and constructs a better animal, which gradually substitutes the old animal.

And in our case the better animal is the Non-Euclidian Mathematics (which is NOT what is called Non-Euclidean Geomtry).

.....zzzzzzz...... :cowsleep: :sleeping: :sleep:
/me tried in vain to keep his burning eyes open while browsing this thread

Then Good Night, sleep tight. :2thumbs:

Ok, so you also do not understand the idea of an arbitrary definition. I recommend you read the book "Modern Algebra" for a complete definition of the urelement. It has the same definition as mathworld, except for it does not word it in terms with an "s" at the end of "elements." I just can't understand how you don't understand this. MATHWORLD IS NOT A SUBSTITUTE FOR A GOOD PEER-REVIEWED TEXTBOOK anyways. And, just to agree with Dutchie, this is getting quite old.

HOLY SHIT! Monad...I've found something just for you: http://insti.physics.sunysb.edu/~siegel/quack.html

You do not understand it yet, do you?

I do not care about the standard interpretation of the Urelement definition, because my Urelement is based on Liebniz' Monad's, which are non-composed elements.

You see, you want the language of Mathematics to freeze according to some current point of view, but I find this point of view (which is based on 0_XOR_1 logical reasoning) too weak to deal with real complexity, because no Black/White system can touch the colored and dynamic properties of reality.

Actually, no theoretical framework can do that, but Monadic Mathematics, which is based on Included-Middle reasoning, is richer than Standard Mathematics and its Excluded-Middle reasoning.

So, as you see, Monadic Mathematics is totally a different framework from the common framework.

And I have something for you: http://www.quantonics.com/Level_5_QT...ean_Logic.html I do not agree with every word that is written there, but it is nice to see a different way of thinking about the Boolean Logic.

On the contrary, this is getting quite new, you are the one who forces the old point of view here (and you are only 17) so think about that.

If you have the guts, than look at http://www.iidb.org/vbb/showthread.p...82#post1935282 where you can find my new point of view about the Function concept (please read this thread until the end of it, including its links).

THEN THERE WE GO! Congratulations, you've given birth to a healthy, 8-lb contradiction. In your paper you specifically use the definition from mathworld, so are you changing definitions on me now because you've realized that your mathematics actually does have holes? Fucking snakes. Oh, and you've once again admitted to changing the definition and meaning of a well defined mathematical object to fit into your mathematics. Nice job.

I'm not forcing views on anyone...I AM MERELY CORRECTING FALSE STATEMENTS. It is not my opinion that you are pushing a bunch of bullshit mathematics, it's a fact. Oh, and I'm 16...your mathematical skills once again amaze me.

Oh, and I'm not even going to bother with your "function concept" (once again, changing real mathematics to fit your fantasy world, as a function is a well-defined object).

PS- I hope you read the link I posted. If not, here it is again: http://insti.physics.sunysb.edu/~siegel/quack.html

Sure, and I gave it my new interpretation, without changing even a single letter of it, So what is your problem, do you want to control the insights of other people?

No dear Keeblergiant, the fact is that your rude language and your bad emotions simply blocking your ability to understand fine and new things about the most fundamental concepts of the language of Mathematics.


Any definition can be changed (or differently understood) by new insights including my system, and no living language (formal or informal) is protected from changes in the long range.

Only cowards and old souls believe that they can stop things from being changed, so if you are already an old soul, it does not matter if your biological age is 16 or 17.

Here are some parts of my dialog about the Function concept.

I'm tired of fucking repeating myself...

Good! :2thumbs:



So give yourself the chance to see familiar things from a new point of view. :scatter:

Ah, so you've admitted that your mathematics is nothing new...

No dear, my system is the new point of view.

"Math, in my opinion, is first of all a rigorous agreement that based on language.

Symmetry is maybe the best tool that can be used to measure simplicity, where simplicity is the best platform for stable agreement.

In any agreement we must be aware to the fact that no model of simplicity is simplicity itself.

This awareness to the difference between x-model and x-itself is the first condition for any stable agreement, because it gives it the ability to be changed."

(http://www.geocities.com/complementa...y/CATpage.html)

Keebler is right...

Coming from a Math major.

An original point of view about 0*oo (post #17):

Let us think about another option.

Let us say that any positive number is based on the Length concept.

It means that if the Length concept itself is omitted, then our set is Empty and we get {}, which is the Empty set.

By saying “0 length” we are using the Length concept and in this case we get number 0, which is equivalent to a Point.

Any other number, which is not a point, is at least some Segment, which is always longer than a Point.

We can take any arbitrary segment and call it 1.

Now we have two building-blocks that can help use to define any given positive R member that we wish.

From this point of view any given positive number, which is not 0 can be represented as the right edge of a segment, which its value defined relatively to the left 0 edge of the segment, and relatively of what has been chosen by us to represent 0_1, which is number one.

So our positive R members are based on the Length concept, and each one of these numbers has a unique length, that can be represented by a point {.} or by a segment {._.} .

Now let us check what is infinity according to this approach.

We know that {} means that the Length concept itself is omitted from our framework.

Can we define a state, which is the opposite of {}?

The answer is: Yes, and we can call this state Fullness which is the totality of the length concept itself, or in other words it is an infinitely long element that can be represented by us as {__} or {.__}.

It means that we cannot define its length and use it to get a particular number, or in other words, the Length concept itself is too strong to be used by us.

From this point of view we get these 4 basic building-blocks {} (Emptiness, which its “content” is too weak to be used as an input in this framework), {.} (Point, which is 0 length), {._.} (Segment, which is any R member > 0) and {__} or {.__} (Fullness, which its length cannot be used as an input in this framework).

Now let us examine Point*Fullness, which is equivalent to the original question, which is:

Zero*Infinity

My answer (according to the Length-concept framework) is:

What is the result of Point*Emptiness?

What is the result of Point*Fullness?

In both cases we can clearly see that we cannot get any meaningful result within this framework, because neither Fullness nor Emptiness can be used as input (or legitimate participators) in these multiplication operation.

(By the way, if we add the Direction concept to the above framework, we can represent the entire R members, by using x_0, 0, 0_x froms).

As you can see, the answer to this question from this point of view, is very simple.

Coming from a Math major of the Standard language of Mathematics.

But my framework is a totally a new one, so please show your skills and point out (in details) some problem that you find in my system.

But before you to thet you have to understand that you cannot do that from an Excluded-Middle point of view, because my framework is based on an included-Middle point of view, where the Contradiction concept is not used at all (please read all of this post to understand this).


Some explanation about Included-Middle reasoning:

The meaning of A and not A in Included-middle reasoning, is understood differently from Excluded-middle reasoning point of view, and the meaning is:

a) Two opposites are not defined by each other, which means that each state exists independently of the other opposite, and each opposite exists by its own self similarity.

b) From this point of view A and not A is any product that exist in the middle-domain between A and not A, and it is the outcome of constructive associations between A and not A.

As you see ex-xian, you look on A and not A from an Excluded-Middle point of view (where two opposites are simultaneously contradicting each other) and by staying in this point of view, you force the Excluded-middle conclusions on Included-Middle point of view (where A and not A are simultaneously preventing/defining their middle-domain).

Because of this forcing approach you simply prevent from yourself to understand what is A and not A from Included-middle point of view.

The “paradox” that you see from Excluded-middle point of view, does not exist in Included-middle framework.

c) not A in Included-middle logical reasoning is any other thing which is not A, AND NOT NECCERRILY the opposite of A, as it is found in Excluded-middle logical reasoning.

d) The contradiction concept does not exist in Included-middle reasoning:

If the contradiction concept does not exist in Included-middle reasoning, then how can we check the consistency of its axioms?

After all, if there is no contradiction then there is no limit to anything and we cannot determine the consistency of anything in this framework.

My answer is this:

In Included-Middle reasoning any product is the result of constructive interactions between at least two opposites, so if something exists because of this interaction, it cannot be anything but a consistent product of this interaction, or in other words, inconsistent products simply do not exist in this framework, and all we have is consistent elements.

An axiomatic system which is based on an Included-middle reasoning, is based on the identity of a thing to itself, which is the new and simple meaning of the tautology concept in an Included-middle reasoning framework ('if, then' propositions are not needed here).

In short, all the "Energy" in an Included-middle reasoning goes to research what we can do with our existing elements, and we do not spend our "Energy" checking the existence of each element in our framework, because if it survives the interaction between two opposites, it cannot be but an existing (and consistent) thing in our mathematical framework.

For more details, please look at: http://www.geocities.com/complementa.../CompLogic.pdf

In short dear stewey, you can be evan a Math professor, but if you do not understand Included-Middle reasoning, then you cannot say any meaningful thing about my new framework.

Thank you.

Well, I would try to decipher what you wrote, but I would rather work on my master's thesis :)

blah blah blah
 

:drool: uhhhh....i think i actually feel stoopider now... :argue:

:sleeping:

Dear stewey,


First, I wish you the best with your master's thesis.

When you are ready, I am here to communicate with you.


Yours,

Monad

Dear PunkRockMaL7, :prin:

I am sure that you can understand the main things of my Mathematical theory, take a chance and ask any crazy question about it :2thumbs: