Deeper than primes

[ddt]

I have changed definition 5 to:

So what? We're arguing right now about definition 4, which precedes it (I may hope). So, definition 5 is utterly irrelevant at this point.

 

[ddt]

Relation (which is not an element) is between an element to itself or not to itself.

Please show a relation which is not what was written above.

Nonsense. That's not what a relation is.

 

[doronshadmi]

I am trying to build a bridge from my notions to the currently agreed notions.

It is not as easy task but I am not going to give up easily.

Thank you for your patience.

So, since a line can be distinguished from a point by the relation "isn't the same as", a line is therefore local.

You are right.

If x ≠ y or y ≠ x (where ≠ is < or >) then x or y are local w.r.t to each other, where the first object (x or y) is the observer and the second object is the observed.

In this case the non-local is ≠ relation, that enables a simultaneous connection between x and y, in order to conclude that x "is not the same as" y or y "is not the same as" x (please see the top of page 3 in http://www.geocities.com/complementarytheory/UR.pdf ).

This is not the case if x = and ≠ (where ≠ is < or >) w.r.t y.

In that case x is non-local w.r.t y (where y is the observed and x is the observer).

You cannot get things form the observed point of view and still be considered as observed.

Actually x w.r.t y means that x is the observer and y is the observed, where only the observer can get a conclution according to a pre-condition and a given rule.

You switched things around then. Before nothing was local and everything was non-local. Now, with these improved definitions it's the other way around.

Is that really what you meant to do?

Ok, let's try this:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

A point cannot be but Local according to Definition 4.

Example:

x = .
y = __

x is local w.r.t y if:

x < y (example: . __ )

or

x = y (example: ( _. , _._ , ._ )

or

x > y (example: __ . )

Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.

Example:

A line segment can be Non-Local according to Definition 5.

x = __
y = .


x is non-local w.r.t y if:

x < and = y (example: _. )

x < and > y (example: _._ )

x = and > y (example: ._ )

 

[doronshadmi]

By the way: ≠ cannot be < and > , < and = , > and = becase ≠ is a single relation.

 

[doronshadmi]

I have to add that I use "=" as self identity ( http://en.wikipedia.org/wiki/Identity_(philosophy) )

 

[ddt]

I could also show you that any point is non-local to any line or line segment with your ludicrous definition.

Please do it.

Pearl before swine. You wouldn't understand it anyway, and for the rest of the posters I can safely say: left as an exercise for the reader.

How about you showing some honest effort - e.g., post your enrollment in the Open University.

 

[ddt]

I have to add that I use "=" as self identity ( http://en.wikipedia.org/wiki/Identity_(philosophy) )

You claim to be doing math, and then you refer to an article about philosophy???

 

[jsfisher]

This is not the case if x = and ≠ (where ≠ is < or >) w.r.t y.

"W.r.t" doesn't mean what you think it means. Your sentence is nonsense. If you intended to say two objects are equal, then just do so. Don't make a totally unnecessary shift to symbols that do not add any clarity, and don't throw in mathematical-sounding phrase abbreviations that render it gibberish.

And, why, oh why are you introducing less-than and greater-than relations? Or do you mean something totally nonstandard and bizarre for your comparison operators? Do the formulae, X = Y and X ≠ Y, not carry their conventional meanings?

Ok, let's try this:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

We are again back to everything being local. This is assured because equality is a reflexive relation. (In doron-speak, object x = w.r.t. object x.)

 

[The Man]

By the way: ≠ cannot be < and > , < and = , > and = becase ≠ is a single relation.

Why? If considering a circle taken from some X Y origin and defined by X² + Y² = R². Any Radius R_Xn,Yn that is not equal to R_X1,Y1 would be defined as all radii both greater to and less then R_X1,Y1 or R_Xn,Yn ≠R_X1,Y1 is the same as R_Xn,Yn < and > R_X1,Y1.

 

[ddt]

I am trying to build a bridge from my notions to the currently agreed notions.

It is not as easy task but I am not going to give up easily.

Time and again you've shown that you can't even articulate your "notions" in plain English. Time and again, you've also shown to have no eff-ing clue about standard math notions. Small wonder it's no easy task. You've also shown time and again an unwillingness to learn standard math practice. You'll never get there, and only waste your and others' time in the process.

Thank you for your patience.

I'm really only posting here to expose your writings for the crackpottery they are, and to mock them.

 

[Apathia]

I am trying to build a bridge from my notions to the currently agreed notions.

It is not as easy task but I am not going to give up easily.

Yes, Doron, I realize you are in rough water and haven't have time to answer my posts.
I don't think you catch the difficulty I'm in with what you seem to be presenting about sets and non-local elements.
It seems to me (I confess I'm like the mad gardener.) that you are presenting sets as containers of always indefinite quantity and number. The set contaning the square root of 144, for example. Conventionaly we'd say it was {12}. But it seems as if you are saying that by virtue if non-locality, 12 is not its complete and definite content.

What I've been hoping for all along, but not getting, is some clarification and/or qualification on what is complete and what is incomplete about a set, and how your ONNs are reckoned but not counted.

It seems to me your disallowance of definite quantity doesn't provide a new paradigm of Mathematics but guts mathematics and leaves its intestines for the vultures.

 

[doronshadmi]

Do the formulae, X = Y and X ≠ Y, not carry their conventional meanings?

No, they do not.

In this case I try to use the minimal must have terms in order to research pre-conditions (x,y in this case) according to some rules (definitions) in order to conclude something about x.

If a line segment or a point are not made of sub-elements and we wish to research the relations =, <, > , ≠ between them without using an external point of view of another object, we have no choice but to use one of them w.r.t the other.

In that case x is the observer that has the point of view and y is the observed that helps us to conclude something about x.

Only by using these minimal terms, you can get my notion of xRy (which is not the same as yRx)

 

[jsfisher]

No, they do not.

Then what meaning would you like them to have?

Start with equal and not-equal.

 

[doronshadmi]

What I've been hoping for all along, but not getting, is some clarification and/or qualification on what is complete and what is incomplete about a set,

What I say is this:

Any researchable thing cannot be complete (total).

By my notion, a set is the result of an interaction between two totalities, which are Isolation and Connectivity.

Objects are a non-total version of Isolation where Relations are a non-total version of Connectivity where a set is the result of Relation\Object Interaction, and therefore non-total (or incomplete).

EDIT:

It seems to me your disallowance of definite quantity doesn't provide a new paradigm of Mathematics but guts mathematics and leaves its intestines for the vultures.

One of my aims is to show that in addition to, so called, objective and external point of view w.r.t researched mathematical subjects, there can be many other points of view that may change our understanding of these subjects.

In other words, the observer's point of view must not be ignored and by using it we can improve (by training) our abilities to use observation in more fruitful ways.

 

[doronshadmi]

Then what meaning would you like them to have?

Start with equal and not-equal.

= is a single relation from x to itsef.

≠ is a single relation from x not to itself.

 

[jsfisher]

= is a single relation from x to itsef.

≠ is a single relation from x not to itself.

Ok, fine. I'm pleased you left out references to > and <.

Now back to your twice-revised definition #4. It makes everything local.

 

[ddt]

= is a single relation from x to itsef.

≠ is a single relation from x not to itself.

Apart from the clumsy formulation: what's different with standard equality in math?

 

[doronshadmi]

Ok, fine. I'm pleased you left out references to > and <.

x=x (a single relation from x to itself)

x≠y (a single relation from x not to itself)

x<y (a single relation from x not to itself)

x>y (a single relation from x not to itself)

In all cases x is local, where there is no conclusion about y because y is observed through x, and not vice versa.

 

[doronshadmi]

Apart from the clumsy formulation: what's different with standard equality in math?

In this case, any observation is only from x, and any conclusion is only about x.

Please look also at http://www.internationalskeptics.com/forums/showpost.php?p=4221149&postcount=734 .

 

[jsfisher]

In all cases x is local, where there is no conclusion about y because y is observed through x, and not vice versa.

In X = Y, either they are the same or they are not. The equal relation is symmetric. X = Y implies Y = X. Nothing "is observed through" anything else.

If you need such a concept, then you need to express it in your definitions. You also need to pick some new symbols; the equal sign has a well-established meaning already.