A question about the empty set

Organic · Feb 3, 2004

I did not failed because I have a very interesting results, which clearly and simply showing the internal symmetry of the number concept, based on Complementary Logic.

For example:

I still waiting for you in:
https://www.physicsforums.com/showthread.php?s=&threadid=12942&perpage=12&pagenumber=3

Also I still wating to Hurkyl in:
https://www.physicsforums.com/showthread.php?s=&threadid=12436

matt grime · Feb 3, 2004

erm, at whihi point did you define locality?

as for the other post. you adequately answered my question about entropy - a number is entropic iff it is composite - there is a non-trivial partition of n into r equal parts. 1<r<n.

ok, i;ll go over there and write more do not answer to that in this thread

Hurkyl · Feb 3, 2004

Hurkyl wrote:

By "set's content", are you referring to the text that is between '{' and '}' when we write a set in that notation?

Organic replied:

A text is nothing but a representation of some idea.

please look at my previous post, thank you.

The words "yes" and "no" are typically very useful words for responding to questions.

Organic · Feb 3, 2004

Matt,

Again:

1) x is (model of nothing)
2) x is . (model of locality)
3) x is __ (model of non-locality)

Please look at:

http://www.geocities.com/complementarytheory/P0is1.pdf

Organic · Feb 3, 2004

Dear Hurkyl,

No.

matt grime · Feb 3, 2004

Organic, again, wtf are locality and non-locality?

Organic · Feb 3, 2004

Matt,

Please look at the link in my previous post, thank you.

matt grime · Feb 3, 2004

the link does not contain any reference to the locaity. moreoever all the consrtuctions there are self contradictory as you use the empty set, which you mantain makes no sense.

in fact, and i reserve the right to correct myself later, it appears that pdf is almost entirely complete and utter bull****. non-technical term.

you say clearly there are | and _ structures. sorry, but 'clear' in whose deluded mind?

and btw you are misusing the term 'base'.

and you are misusing the * in Z*. * usually means the multiplicative group, which in Z would be {1,-1}

but apart from those gross errors the rest is just specious drivel.

and yes, you've exhausted my patience.

Organic · Feb 3, 2004

Matt,

Have a nice run after your scholastic tail.

matt grime · Feb 3, 2004

so, if i get this right, you are allowed to use whatever definition you want for some object/concept, without saying what that object/concept is, and then, when someone says you are wrong to do so, you throw a tantrum about them not seeing the correct bigger picture, and that they are 'scholastic'? why on Earth post your ideas in math forum if you aren't going to adhere to the basics of mathematics? you say something exhibits property of locality but won't say what locality is! is it unreasonalbe to ask you to explain that? apparently.

Hurkyl · Feb 3, 2004

I'm going to leave the bit about logic aside for a moment.

Let's start with some basics.

ZF gives us an axiomatic definition of a set.

Is what you call a set the same as what ZF calls a set?

There exists what I would call a set that is denoted by the string of symbols

{5, q, apple, unicorn, gazorninplat}

.

Does this string of symbols denote what you would call a set? What is the content of this set, by your meaning?

HallsofIvy · Feb 3, 2004

Ah, c'mon matt, you are starting to sound like me!

I thought I had the "grumpy old man" concession on this forum!

(You may have noticed that I have stopped making any response to Organic whatsoever. Blood pressure problem.)

Organic · Feb 4, 2004

Dear Hurkyl,

It is a very good question.

Answer:

Code:

{5, q, apple, unicorn, gazorninplat}
 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

Or more general:

Code:

{., .,  .,      .,        .}
 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

If any '.' in this set is some unique object with no common property to the other
objects (accept 'uniqueness'), then we can change the order of '.' in the set without changing the information structure, for example:

Code:

{q, 5, unicorn, apple, gazorninplat}
 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

If '.' can be ordered by some common property we get:

Code:

{q, 5, unicorn, apple, gazorninplat}
 |  |    |       |           |  
 |__|    |       |           | 
    |    |       |           |  
    |____________|           |
    |    |                   |
    |____|                   |
    |                        |
    |________________________|
    |
    |

If there are identical objects in some non-ordered collection, we can get for example:

Code:

{5, 5,  q,   unicorn, apple, gazorninplat}
 |  |   |       |         |     |  
 |__|_  |       |         |     | 
 |      |       |         |     |
 |______|       |         |     |
 |              |         |     |
 |______________|         |     |
 |                        |     |
 |________________________|     |
 |                              |   
 |______________________________|
 |
 |

And if there is a common order we have:

Code:

 q  q 
{5, 5, apple, unicorn, gazorninplat}
 |  |   |       |         |  
 |__|_  |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

matt grime · Feb 4, 2004

Originally posted by HallsofIvy
Ah, c'mon matt, you are starting to sound like me!

I thought I had the "grumpy old man" concession on this forum!

(You may have noticed that I have stopped making any response to Organic whatsoever. Blood pressure problem.)

I know, yet another young idealist comes up against a pig-headed refusal to learn and eventually cracks under the stress. It's why I should never become a teacher.

This is a temporary thing I hope - I will go back to simply pointing things out without losing it. The new tactic will be one objection at a time so Organic can't wander off topic as he tends to.

Hurkyl · Feb 4, 2004

It is a very good question.

Answer:...

My best guess is that you're trying to demonstrate content, via the pictures like

Code:

{5, q, apple, unicorn, gazorninplat}
 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

Well, what is content? Is it this entire picture? Is it just

Code:

 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

?

Is it

Code:

5, q, apple, unicorn, gazorninplat

?

Is it actually one of these, or simply denoted by one of these?

What is '.'? It looks as if you're trying to use the five '.' as logical variables. Is this correct? Why not just say something like:

----------------------------------------------
Or more general:

Code:

{a, b,  c,      d,        e}
 |  |   |       |         |  
 |__|   |       |         | 
 |      |       |         |
 |______|       |         |
 |              |         |
 |______________|         |
 |                        |
 |________________________|
 |
 |

where a, b, c, d, and e are any 5 distinct objects
----------------------------------------------

I would still like an answer to my other questions:

ZF gives us an axiomatic definition of a set.

Is what you call a set the same as what ZF calls a set?

There exists what I would call a set that is denoted by the string of symbols

{5, q, apple, unicorn, gazorninplat}

.

Does this string of symbols denote what you would call a set?

Organic · Feb 4, 2004

As I wrote, for me a set's content is the model of some x, where '{' and '}' is the framework, which we use to examine x-model.

1) x is (model of nothing)
2) x is . (model of locality)
3) x is __ (model of non-locality)

a,b,c,... is like 5, q, apple,... but I go simpler than that and use '.' as general notation for some singleton, and '_' for general notation for non-singleton.

To understand singleton, non-singleton please read:

http://www.geocities.com/complementarytheory/P0is1.pdf

matt grime · Feb 4, 2004

so __ is your notation for some 'collection' of elements (note the plural). You also use it for some limit of everything elsewhere (in aspirating I seem to recall; still not changed the name, eh?), and you say that |{_}| =1 so how can a set with more than one element have cardinality 1? no wonder you're struggling to understand this stuff.

what is x?

Organic · Feb 4, 2004

No Matt,

__ is not a collection and also . . . is not a collection.

Code:

Only the association between _ and . is a collection, 
for exemple:

{.,.,.}
 | | | 
 |_|_|_
 |

'{' and '}' is the framework, which we use to explore these collections.

x is any thing that can be thinkable by us.

matt grime · Feb 4, 2004

I was attempting to say, and I think I implied it, that . is a single element of some 'set' and __ denotes contents of some non-singleton 'set' ie the collection of elements in the 'set'. Is that how we're supposed to interpret your statement?

I now also choose x to be all those things that do not have a model as contents for some set in organic's theory. that is thinkable. i just thought it.

that seems to be about a problem there doesn't it? seeing as a set's contents is some x-model

Organic · Feb 4, 2004

Then x = the model of "all not x-models"

Please read AGAIN:

http://www.geocities.com/complementarytheory/P0is1.pdf

matt grime · Feb 4, 2004

so it is a model that isn't a model?

Organic · Feb 4, 2004

x content cannot be but a model of the content.

No content has any impact on this hierarchy.

Organic · Feb 4, 2004

Let x1 = the model of "all not x-models"

Let x2 = the model of "the model of "all not x-models""

x1 not= x2

general notation:

x=model(x)

x = x only if x is actual(= not theoretical, or not a model)

matt grime · Feb 4, 2004

x=x is a tautology.

you know, you might want to define what you mean by model at some point, as even you seem confused by it.

Organic · Feb 4, 2004

I am not confused, you are the one because your point of view does not distinguish between the theoretical and the actual.

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