A hidden assumption

Doron, you've misunderstood the D2 group---it's not "really" points on a plane, that's just a convenient way to explain it.

As you seem to be immune to explanations, I'll stop trying. Goodbye and good luck.
 
jsfisher said:
You are using terminology that you think has meaning, but does not. Information does not flow between ZFC axioms. (By the way, did you notice that you used another verb form to describe something?) The axioms simply exist. { {}, {{}} } is a set withing the ZFC framework simply because it is consistent with the axioms, not because of any flow of information.

The best way for you to get others to understand your theory is for you to describe it using defined terms. You continue to not define things.
Click to expand...

Let us take this part:
jsfisher said:
The axioms simply exist.
Click to expand...
Now please do this simple thought experiment:

Your memory enables you to get one and only one thing.

If another axiom is examined the previous one is forgotten.

In that case the multitude is not a property of your realm.

In other words, you get only locality.

Is it understood?
 
Last edited:
doronshadmi said:
Let us take this part:

Now please do this simple thought experiment:

Your memory enables you to get one and only one thing.

If another axiom is examined the previous one is forgotten.

In that case the multitude is not a property of your realm.

In other words, you get only locality.

Is it understood?
Click to expand...

No.

You continue to not define your terms.
 
jsfisher said:
No.

You continue to not define your terms.
Click to expand...

Ok, let's try this version of the simple thought experiment:

Your memory enables you to get one and only one thing, in such a way
that if you get another thing, than the previous thing is forgotten.

In that case your realm is no more than a one thing (a one thing of many things, but your memory does not enable you to know that) and you are unable to determine:"The things simply exist".

I call this state of realm Locality.

Is it understood?
 
Last edited:
Since we are not making any progress with these asides, let's go all the way back to something you said in your first post:

doronshadmi said:
Cantor is wrong because no non-finite collection has the magnitude of the non-local ur-element ( en.wikipedia.org/wiki/Urelement ) real-line, and as a result any given non-finite collection is open and incomplete when compared with the non-local ur-element real-line's magnitude.
Click to expand...

I have bolded words you are using in a non-standard or undefined way. (And even though you cited Wikipedia for the meaning of 'ur-element', you are using it differently.)

The onus is on you to give these words meaning if you expect to communicate.
 
Last edited:
jsfisher said:
No, the set is not a pair, and it is not a pair for exactly the same reason it is not an orange.

Is this going someplace? Why won't you define your terms?
Click to expand...

http://mathworld.wolfram.com/Pair.html does not agree with you.

Also http://en.wikipedia.org/wiki/Ordered_pair does not agree with you (if we ignore order then a pair is a collection of two distinguishable objects, and so is {a,b} or {b,a}).

|{a,b}| = 2 . In that case a collection of two distinguishable objects does not have the cardinality of a one thing
(for example |{{a,b}}|=1).

In other words, a pair is not simply a one thing (as you claim).

Furthermore, {} is the empty set and {{}} is a set that its member is the empty set.

The same holds in the case of {a,b} and {{a,b}}.

{a,b} is a collection of two distinguishable objects (known also as pair) and {{a,b}} is a set that its member is a pair.
 
Last edited:
doronshadmi said:
http://mathworld.wolfram.com/Pair.html does not agree with you.

Also http://en.wikipedia.org/wiki/Ordered_pair does not agree with you (if we ignore order then a pair is a collection of two distinguishable objects, and so is {a,b} or {b,a}).
Click to expand...

Check again. There is a requirement the two elements be linked in some way. You did not establish any linkage between a and b. Also, the conventional notation for a pair in mathematics is (a,b), not {a,b}. You may not misuse standard notation if you expect to be understood, just like you need to define your terms.

You also may note that Wolfram is using the word, set, in describing pair a bit loosely. Wolfram correctly points out that pairs are generally ordered which is not generally a set property. Wolfram should have been more precise and avoided the word, set, entirely.

So, no, the set you presented, {a,b}, is not a pair.

...<irrelevant things in which pair and set notations are conflated>...
Click to expand...

Ignoring the pair vs. set dichotomy, why to you frequently point out things like

| {a,b} | = 2 and
| {{a,b}} | = 1 ?

These facts are not in controversy, so why bring them up as if they were?
 
ben_m said:
By focusing on the words "Symmetry" and "non-local atom" and whatnot, you've overlooked the fact that this set of subgroups has exactly the same properties as your preferred "XX vs XY" version.
Click to expand...

XX is not a case of reflection ,and XY is not a case of rotation in my framework.

XX is the invariant, which is the fundamental property of any symmetrical state.

I reduced XX representation to X in order to represent better the notion of the invariant.

XY is the variant, which is the fundamental property of any asymmetrical state.

My framework is not "X vs XY" but "X\XY association".

So the exact system is not less than the organic one:

Code: 
Y   Z
 \ /
  X

which gives the exact answer to this question:

What is the minimal term that enables different things to interact with each other?
 
Last edited:
jsfisher said:
Check again. There is a requirement the two elements be linked in some way.
Click to expand...

The same requirement holds if |{a,b}|=2

In both cases (a set or a pair) we are talking about a collection of more than a one distinct object.
 
Last edited:
Here is the current list of terms you need to define:

magnitude
non-local
ur-element
real-line
open
incomplete​
 
Some correction of http://www.internationalskeptics.com/forums/showpost.php?p=3555287&postcount=153

ben_m said:
By focusing on the words "Symmetry" and "non-local atom" and whatnot, you've overlooked the fact that this set of subgroups has exactly the same properties as your preferred "XX vs XY" version.
Click to expand...

XX is not a case of reflection ,and XY is not a case of rotation in my framework.

XX is the invariant, which is the fundamental property of any symmetrical state.

I reduced XX representation to X in order to represent better the notion of the invariant.

XY is the variant, which is the fundamental property of any asymmetrical state.

In order to avoid confusion between symmetry and asymmetry, let us use "YZ" for the variant instead of "XY".

My framework is not "X vs YZ" but "X\YZ association".

So the exact system is not less than the organic one:

Code: 
Y   Z
 \ /
  X

which gives the exact answer to this question:

What is the minimal term that enables different things to interact with each other?
 
Last edited:
doronshadmi said:
Ok, let's try this version of the simple thought experiment:

Your memory enables you to get one and only one thing, in such a way
that if you get another thing, than the previous thing is forgotten.

In that case your realm is no more than a one thing (a one thing of many things, but your memory does not enable you to know that) and you are unable to determine:"The things simply exist".
Click to expand...

Hi Doron,

Again, you're mentioning (in your own vague terms) things that are familiar to mathematicians and computer scientists. The symmetry that allows TT, TF, FT, and FF "reducing to" XX and XY is the same as the familiar group-theory symmetry that allows D2 to "reduce to" D1. You rejected this casually, but the way you did it makes me suspect that you'd never heard of dihedral groups, and spent less than a few minutes thinking about them. Is this true?

Processes which "cannot look at more than one thing" are familiar in formal computer-science proofs; the property you describe is that of a one-state Turing machine. If you're going to try to make some argument about behaviors which are or are not possible in your theory, perhaps it'd be worth your while to learn about Turing machines and try to utilize some of the language, existing proofs, etc., which have been developed for these machines. Maybe there's some property which is important to your system, for which an analogous property exists which has been subjected to theory-of-computation proofs. If you can find those analogies, that's important.

That would be how a mathematician would approach it: most theorems are valid across many related domains. Many theorems that are true on the real number line are also true on the unit circle; theorems that are true in 2-D Euclidean space are also true on the complex plane; theorems that are true in dihedral D2 are also true on the Klein 4-group; theorems that are true in position-space are also true in Fourier-space.

You seem to be unwilling to think outside of your pre-thought-out box, and to look at nearby areas of math for inspiration; this gives the strong that you are a crackpot. You could try to dispel this impression by actually taking some of our suggestions seriously ...
 
Last edited:
MattusMaximus said:
Have you tried to submit this to any professional math journals? If so, what was the result? If not, why haven't you done so?
Click to expand...

Because hes apparently a masochist and would rather have a gaggle of cynical laymen on a web forum question his sanity.
 
You must log in or register to reply here.

Share this page

ISF - Join now!

Every member here is approved by hand. No bots, no spam, just people who care about evidence and honest debate.

Membership is free!

Create your free account

Back
Top Bottom