Deeper than primes

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HatRack said:
You never said that points A and B are distinct. Thus, it is false to assume that a unique line AB has been determined. One flaw in your proof amongst many.
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Wrong, read this:

doronshadmi said:
For this game we need two points, a line and a plane.
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You still do not get that a given line and its non-local property exists, even if no point exists along it.

Furthermore, two points and their local property exist, even in no names are given to them.
 
jsfisher said:
Be that as it may, this is just another example of Doron not being able to express himself with any clarity or precision.



The word you are struggling to find on your keyboard is "oh". Ho is slang for prostitute. Please use the correct word.



Again you blame me for your failure. You have no basis for this bald accusation, and it isn't true. It may be convenient for you to think otherwise, but you are simply lying to yourself.

Really, Doron. Stop lying about me to cover your own blunders and cognitive limitations. If doronetics has any merit, focus on that. Your continual lying and inability to stay on topic only underscores that it doesn't.



As I have said right along. Knock yourself out! Develop a new mathematical foundation. Mathematics has plenty of room for new ideas.

Heck, you even have your first axiom for Doronetics. Admittedly, it is not a very constructive axiom, and it lacks some foundation, but its yours.

On the other hand, stop accusing the parts of Mathematics you can't understand as being wrong. They aren't. They certainly aren't wrong just because you'd like something else. Build your something else; try to avoid the obvious contradictions and inconsistencies that plague all of your work to date; then maybe we can explore its utility.

So far, Doron, all you do harp about how everyone else is wrong and how everyone else just doesn't get it. You really need a mirror.
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You still do not get it jsfisher.

You play a limited game, which is closed under the concept of Collection.

I play with AND beyond the concept of Collection.

Your game is wrong. Actually you can't comprehend the concept of Collection exactly because you are closed under it, and it can really be comprehended only if you get it without being closed by it.

Non-locality\Locality Linkage is the foundation of the Mathematical Science, whether you get it or not.

It is not up to you anymore.
 
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doronshadmi said:
Wrong, read this:



You still do not get that a given line and its non-local property exists, even if no point exists along it.

Furthermore, two points and their local property exist, even in no names are given to them.
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You are using non-standard geometry. None of the "deductions" you spew follow from any known theorems. If you do not wish to obey the rules of Euclid's postulates, then you must specify your own axiomatic system for geometry. Just like you must specify your own axiomatic system for your non-standard analysis.

So, we have one axiom so far. Let's have the rest. This is mathematics Doron, you must be rigorous.
 
HatRack said:
So, we have one axiom so far. Let's have the rest. This is mathematics Doron, you must be rigorous.
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Ah! There, you see, is the beauty of Doronetics. Rigor is not required when you have the power of direct perception. Doron has freed himself from the necessity of consistency or proof through the sheer will of his mind. If he thinks it to be so, then it must be so.

Doron is therefore able to use his time and effort focussed on more important things, like brushing up on his gibberish and his insults.
 
doronshadmi said:
Wrong, read this:
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Yes, doron. Where did you specify that they are distinct? See, this is a big part of your problem. It's a fairly small error, we all know you meant distinct points. But when pointed out to you, instead just saying something like "yes, I meant to say distinct", you just can't admit that you erred.

doronshadmi said:
You still do not get that a given line and its non-local property exists, even if no point exists along it.

Furthermore, two points and their local property exist, even in no names are given to them.
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Whatever doron, until you define your own axiomatic system, you're out of luck, because in every other currently known system your gibberish is contradictory, because its exact negation can be derived from the axioms. Funny, ain't it?

You won't be able to convince anyone with regurgitating the same nonsense and accusing everyone of being "closed under Collection". You need to lay it out so that it is a consistent framework. Of course, even if you manage to choose your axioms so that it is consistent and somehow all your garbage makes sense in view of those axioms (which I'm certain you won't), you still need to show how it is useful.

In view of all this, a rational person would either get to work and start to formalize everything or just quit. I'm predicting you'll choose otherwise.
 
doronshadmi said:
You still do not get it jsfisher.

You play a limited game, which is closed under the concept of Collection.

I play with AND beyond the concept of Collection.
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And I played with my willie until I got old enough. Now it's serious. :D

doronshadmi said:
Your game is wrong. Actually you can't comprehend the concept of Collection exactly because you are closed under it, and it can really be comprehended only if you get it without being closed by it.
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Maybe it's just me, but this is all starting to sound like religion. We just have to accept it. Without a shred of proof or even plausibility. Guess what? We don't.

doronshadmi said:
Non-locality\Locality Linkage is the foundation of the Mathematical Science, whether you get it or not.
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What linkage? You're arguing for locality (points) being fundamentally different from non-locality (lines and higher order spaces).

By the way, how do you figure that lines cannot completely cover a 2-dim space, since according to you they're both possessing non-locality? :confused:
 
doronshadmi said:
this axiom is strictly not ZFC, because ZFC is closed under the concept of Collection.
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Doron,

Your axiom is a contradiction in the ZFC system. ZFC is widely used and is considered a rigorous basis for a wide variety of mathematics, including and most importantly analysis.

Now, read this next part carefully:

In order for anyone to even consider accepting your axiom, you have to show us which ZFC axiom we should drop. The ZFC axioms state some very basic properties and existences of sets. For example, one guarantees the existence of unordered pairs. Another essentially guarantees the existence of the natural numbers. Another guarantees that unions exist, and so on.

In fact, I believe it is not even necessary to use at least two of the ZFC axioms (choice/regularity) to deduce the negation of your axiom, but I could be wrong, and I will stand corrected if I am. Basically, any system of logic which implies the Peano Axioms along with some elementary set theory puts the spike in your axiom.

So, you have to explain to us which ZFC axiom is wrong and why. Until then, there's no point in continuing, because no one will ever take you seriously if you throw away ZFC without reason.
 
jsfisher said:
Ah! There, you see, is the beauty of Doronetics. Rigor is not required when you have the power of direct perception. Doron has freed himself from the necessity of consistency or proof through the sheer will of his mind. If he thinks it to be so, then it must be so.

Doron is therefore able to use his time and effort focussed on more important things, like brushing up on his gibberish and his insults.
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My mistake. Let's add that to the list of axioms in Doron's theory.

The Axiom of Direct Perception

Whatever Doron Shadmi directly perceives as being correct, is correct, and should be accepted by all others without question.
 
doronshadmi said:
Your game is wrong. Actually you can't comprehend the concept of Collection exactly because you are closed under it, and it can really be comprehended only if you get it without being closed by it.
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And stop telling people they are "closed under collection". We're not mathematical operators.
 
laca said:
And I played with my willie

...

By the way, how do you figure that lines cannot completely cover a 2-dim space, since according to you they're both possessing non-locality? :confused:
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No, you still continue to play with your willie instead of fully read http://www.internationalskeptics.com/forums/showpost.php?p=6592095&postcount=12597

laca said:
What linkage? You're arguing for locality (points) being fundamentally different from non-locality (lines and higher order spaces).
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And yet both of them have a common property, they exist as non-composed spaces.
 
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laca said:
Edited by jhunter1163: 
Edited moderated content.
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Edited by jhunter1163: 
Edited for civility.


laca said:
What linkage? You're arguing for locality (points) being fundamentally different from non-locality (lines and higher order spaces).
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And yet both of them have a common property, they exist as non-composed spaces.
 
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doronshadmi said:
Edited by jhunter1163: 
Edited moderated content.


And yet both of them have a common property, they exist as non-composed spaces.
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doron, you know what you have to do. Start working and present a rational argument. Until you do, you're just looking silly.
 
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HatRack said:
And stop telling people they are "closed under collection". We're not mathematical operators.
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He is not knowledgeable of the mathematical meaning of "closed under". I am guessing he is freely translating something from his native tongue. But as jsfisher noted, all he really needs is a mirror.
 
jsfisher said:
Ah! There, you see, is the beauty of Doronetics. Rigor is not required when you have the power of direct perception. Doron has freed himself from the necessity of consistency or proof through the sheer will of his mind. If he thinks it to be so, then it must be so.

Doron is therefore able to use his time and effort focussed on more important things, like brushing up on his gibberish and his insults.
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jsfisher, since when one has to prove an axiom (no matter what name is given to it)?
 
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HatRack said:
You are using non-standard geometry. None of the "deductions" you spew follow from any known theorems. If you do not wish to obey the rules of Euclid's postulates, then you must specify your own axiomatic system for geometry. Just like you must specify your own axiomatic system for your non-standard analysis.
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No problem, let us start to write the first axioms, for example:

The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.

The axiom of existence:
Any existing thing has a predecessor.

The axiom of infinite collection:
If x exists then y>x exists.

The axiom of Locality:
y, such that x = 1 to ∞ and ((y≥0)<x), is simultaneously at most at one location w.r.t all x.

The axiom of Non-Locality:
y, such that x = 0 to ∞ and x < y, is simultaneously at least at two locations w.r.t all x.
 
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doronshadmi said:
No problem, let us start to write the first axioms, for example:

The axiom of minima:
Emptiness is that has no predecessor.
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This is not an axiom. It could be a definition for "emptiness", but you'd need to define predecessor, first.

The axiom of maxima:
Fullness is that has no successor.
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Ditto.

The axiom of existence:
Any existing thing has a predecessor.
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So emptiness, defined above, doesn't exist. Why'd you bother to define it, then?

The axiom of infinite collection:
If x exists then y>x exists.
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How do you define that order operation? Is it partial or is it complete? So, in Doronetics only collections over ordered elements exist? What is a collection in Doronetics? What axiom set are you assuming for your collections?

The axiom of Locality:
y, such that x = 1 to ∞ and ((y≥0)<x), is simultaneously at most at one location w.r.t all x.
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Ok, so you assume the real numbers in you axiom set? Setting yourself up for all sorts of contradictions, I see. You need to define "location" and you need to define "location with respect to" something else.

It looks like you may have meant it to be a definition of "locality", but it is not an axiom.

The axiom of Non-Locality:
y, such that x = 0 to ∞ and x < y, is simultaneously at least at two locations w.r.t all x.
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Ditto.


So, there we have it. A meaningless collection of things that are not axioms. Definitions might help save some of them, but that isn't really your forte, now, is it?
 
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doronshadmi said:
laca, you asked a question.

A simple and clear answer was given in http://www.internationalskeptics.com/forums/showpost.php?p=6592095&postcount=12597.

You can't comprehend it.
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I'm sorry but that answer was neither simple nor clear. You basically assert that points have local property and lines have non-local property and therefore points cannot cover lines completely. All your arguments for why points cannot completely cover lines end up at this. You've got nothing else. So, please define what is a line. Without using the concept of non-local, unless you define that before. Definitions should be clear and unambiguous. I shall wait for your next fail.
 
doronshadmi said:
No problem, let us start to write the first axioms, for example:

The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.

The axiom of existence:
Any existing thing has a predecessor.

The axiom of infinite collection:
If x exists then y>x exists.

The axiom of Locality:
y, such that x = 1 to ∞ and ((y≥0)<x), is simultaneously at most at one location w.r.t all x.

The axiom of Non-Locality:
y, such that x = 0 to ∞ and x < y, is simultaneously at least at two locations w.r.t all x.
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Doron, that's just pathetic and utterly useless. No wonder no one is taking you seriously. That's all you can come up with after all these years? You don't even seem to know what an axiom is or how to formulate one. You've also failed to define successor, predecessor and location w.r.t. something.

By the looks of it though, we were right: you are unable to grasp uncountable infinity or real numbers. You're stuck at natural numbers that have successors and predecessors. No wonder you're arguing nonsense.
 
laca said:
You're stuck at natural numbers that have successors and predecessors. No wonder you're arguing nonsense.
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Poor laca, you can't distinguish between immediate successors or predecessors that are related to whole numbers, and successor or predecessor, which are not immediate and related not to whole numbers.

Also the axioms are partial example, which enables to comprehend the fundamental difference between axiomatic system that is based only on the concept of Collection (for example: ZFC), and an axiomatic system that deals dirctly with Emptiness, Fullness, Non-locality, Locality and the concept of infinite collection w.r.t Non-Locality.

Your poor reasoning, which is closed under the concept of Collection and therefore gets 1-dimensional space as a collection of distinct and uncountable 0-dimensional spaces, can't comprehend even a single axiom of my system.
 
jsfisher said:
This is not an axiom. It could be a definition for "emptiness", but you'd need to define predecessor, first.
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Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.

jsfisher said:
So emptiness, defined above, doesn't exist.
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Yes, do you have some abstraction problems to get such a notion?

jsfisher said:
How do you define that order operation?
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Simply as less than or more than.

jsfisher said:
Ok, so you assume the real numbers in you axiom set?
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All is assumed at this level is a collection that is ordered by as less than or more than.

jsfisher said:
So, there we have it.
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No, we have a person that can't grasp simple notions, and does his best to miss them.
 
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doronshadmi said:
No problem, let us start to write the first axioms, for example:
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Doron, nowhere in your axioms to do assert the existence of anything. I will explain why in detail below.

doronshadmi said:
The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.
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These axioms give two definitions: emptiness and fullness. First of all, it is not the purpose of an axiom to give a definition, it is the purpose of an axiom to assert some type of existence or uniqueness. Furthermore, these axioms definitions define emptiness and fullness in terms of two other undefined terms, which is most unhelpful.

doronshadmi said:
The axiom of existence:
Any existing thing has a predecessor.

The axiom of infinite collection:
If x exists then y>x exists.
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These next two axioms do not suffer from the same problem as the first two. They are more along the lines of proper axioms. However, they only assert the existence of something given that something else already exists. In the first, you assert the existence of a "predecessor", but only given that something else already exists. In the second, you assert the existence of y > x given that x already exists.

doronshadmi said:
The axiom of Locality:
y, such that x = 1 to ∞ and ((y≥0)<x), is simultaneously at most at one location w.r.t all x.

The axiom of Non-Locality:
y, such that x = 0 to ∞ and x < y, is simultaneously at least at two locations w.r.t all x.
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The axiom of locality is particularly troublesome. Here, you introduce several undefined terms and assume the existence of numbers although at this point you've yet to give an axiom that asserts the existence of anything. The axiom of nonlocality is troublesome for the same reason.

So far, your theory is completely empty. One cannot deduce the existence of anything from your given axioms, because you didn't assert the existence of anything.

Before you attempt to correct your axioms or alternatively try to tell me that I'm wrong, let's take a different approach. It's already been explained to you that ZFC is strong enough to deduce the negation of your central result known as the "Axiom of the Continuum". ZFC states some very obvious and intuitive things about the notion of a collection. Tell us, in detail, which ZFC axioms are wrong and why.
 
doronshadmi said:
Poor laca, you can't distinguish between immediate successors or predecessors that are related to whole numbers, and successor or predecessor, which are not immediate and related not to whole numbers.
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So define successors and predecessors for real numbers. I dare you.

doronshadmi said:
Also the axioms are partial example, which enables to comprehend the fundamental difference between axiomatic system that is based only on the concept of Collection (for example: ZFC), and an axiomatic system that deals dirctly with Emptiness, Fullness, Non-locality, Locality and the concept of infinite collection w.r.t Non-Locality.
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Do it better. Define all those terms, because you never had. Get to work.

Oh, and btw., your first two "axioms" are essentially annihilated by the next two. You're not very good at this, are you?

doronshadmi said:
Your poor reasoning, which is closed under the concept of Collection and therefore gets 1-dimensional space as a collection of distinct and uncountable 0-dimensional spaces, can't comprehend even a single axiom of my system.
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Insulting people will get you nowhere. You just need to do the work. Define the terms. Establish the axioms. Start proving theorems. Use them and get some results. You're just being childish.
 
doronshadmi said:
Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.
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So predecessor means less than and successor means greater than. How totally useless.

doronshadmi said:
Yes, do you have some abstraction problems to get such a notion?


Simply as less than or more than.
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What is x? What is y? Did you even understand the questions? I think not, since you left out most of them... And that's another of your main problems. You just ignore questions you cannot mock or understand. And there's a lot of the latter...
 
jsfisher said:
And let's not overlook this:




Doron has abandoned his prohibition on universal quantification, at least when it is convenient for him.
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jsfisher I simply started to use the technique of going with one's notion, instead of confront with it.

By going with your notion about infinite collections I agree with you that no object of such a collection is missing and yet, given any collection, its infinity < non-local infinity.
 
laca said:
Oh, and btw., your first two "axioms" are essentially annihilated by the next two.
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In other words, you can't get Emptiness, Fullness, and the intermediate existence of collections between Emptiness and Fullness.
 
HatRack said:
These axioms give two definitions: emptiness and fullness. First of all, it is not the purpose of an axiom to give a definition, it is the purpose of an axiom to assert some type of existence or uniqueness.
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Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.

Only Emptiness does not have a predecessor in the absolute sense.

Only Fullness does not have a successor in the absolute sense.

Your notion is still closed under the concept of Collection, which is an intermediate state of existence between Emptiness and Fullness.

HatRack said:
These next two axioms do not suffer from the same problem as the first two. They are more along the lines of proper axioms. However, they only assert the existence of something given that something else already exists. In the first, you assert the existence of a "predecessor", but only given that something else already exists. In the second, you assert the existence of y > x given that x already exists.
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The next two axioms are at the level of the existence of collections, which is > Emptiness AND < Fullness.

HatRack said:
The axiom of locality is particularly troublesome. Here, you introduce several undefined terms and assume the existence of numbers although at this point you've yet to give an axiom that asserts the existence of anything. The axiom of nonlocality is troublesome for the same reason.
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I do not assume numbers, I explicitly use numbers as measurements of the intermediate levels of existence between Emptiness and Fullness.

Simultaneity does not need any further definition in order to clearly be understood, exactly as step-by-step (the opposite of Simultaneity) does not need any further definition in order to clearly be understood.
 
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