Deeper than primes

[doronshadmi]

No, the content of that post is easily understood: Therein Doron makes a ridiculous statement and leaps to an incorrect conclusion. Included also is a generous dose of gibberish delicately spiced with contradiction.

The comprehension problem, Doron, is yours.

Where exactly is your detailed raply to http://www.internationalskeptics.com/forums/showpost.php?p=6592095&postcount=12597 which is not closed under the concept of Collection?

 

[doronshadmi]

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.

I am very clear about the meaning of "closed under", all you have is to read http://www.internationalskeptics.com/forums/showpost.php?p=6593026&postcount=12603 .

 

[doronshadmi]

And stop telling people they are "closed under collection". We're not mathematical operators.

We are mathematical observers and participators, in case that you are missing it.

This time plase read all of http://www.internationalskeptics.com/forums/showpost.php?p=6591235&postcount=12584 .

 

[doronshadmi]

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.

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.

 

[jsfisher]

No problem, let us start to write the first axioms, for example:

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

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.

Ditto.

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

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.

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.

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.

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?

 

[jsfisher]

Where exactly is your detailed raply to http://www.internationalskeptics.com/forums/showpost.php?p=6592095&postcount=12597 which is not closed under the concept of Collection?

Read up.

 

[jsfisher]

And let's not overlook this:

...x = 1 to ∞...

Doron has abandoned his prohibition on universal quantification, at least when it is convenient for him.

 

[laca]

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.

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.

 

[laca]

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.

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.

 

[doronshadmi]

You're stuck at natural numbers that have successors and predecessors. No wonder you're arguing nonsense.

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.

 

[doronshadmi]

This is not an axiom. It could be a definition for "emptiness", but you'd need to define predecessor, first.

Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.

So emptiness, defined above, doesn't exist.

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

How do you define that order operation?

Simply as less than or more than.

Ok, so you assume the real numbers in you axiom set?

All is assumed at this level is a collection that is ordered by as less than or more than.

So, there we have it.

No, we have a person that can't grasp simple notions, and does his best to miss them.

 

[HatRack]

No problem, let us start to write the first axioms, for example:

Doron, nowhere in your axioms to do assert the existence of anything. I will explain why in detail below.

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

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

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.

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

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

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.

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.

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.

 

[laca]

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.

So define successors and predecessors for real numbers. I dare you.

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.

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?

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.

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.

 

[laca]

Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.

So predecessor means less than and successor means greater than. How totally useless.

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


Simply as less than or more than.

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...

 

[doronshadmi]

And let's not overlook this:




Doron has abandoned his prohibition on universal quantification, at least when it is convenient for him.

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.

 

[doronshadmi]

Oh, and btw., your first two "axioms" are essentially annihilated by the next two.

In other words, you can't get Emptiness, Fullness, and the intermediate existence of collections between Emptiness and Fullness.

 

[doronshadmi]

So predecessor means less than and successor means greater than. How totally useless.

How poor understanding about order (at its most general aspect) you have.

 

[doronshadmi]

So define successors and predecessors for real numbers. I dare you.

0 is a predecessor for pi and pi is a successor for 0.

 

[doronshadmi]

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.

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.

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.

The next two axioms are at the level of the existence of collections, which is > Emptiness AND < Fullness.

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.

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.

 

[doronshadmi]

What is x? What is y?

y and x are place holders for an intermediate state of existence between Emptiness and Fullness.