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A proof that |R| < C

  1. Sep 2, 2003 #1
    Because by Conventional-Mathematics, every R member is a point in the Real-line, then:

    {.} = any non-empty R member

    |{}| = The cardinality of the empty set = 0

    |{.}| = The smallest catdinality of any non-empty set = 1

    0 or 1 are members of W.

    Between 0 to 1 there is {} or in other words, the transition from
    0 to 1 and vice versa, is a phase transition or a quantum leap.

    The transition's type from {} to {.} = the transition's type from 0 to 1 but,
    because it is a phase transition, and we cannot use {} or {.}
    as an element between {} to {.}, we have no choice but to
    define a new set's content.

    {} = Emptiness
    {.}= Localized element = Point
    {_}= Non-localized element = Line

    Therefore between {} to {.} there is {_}.

    Now we can conclude that between any two non-empty R members there
    exist a non-localized element.

    Therefore |R| does not have the power of the Continuum.
     
    Last edited by a moderator: Sep 3, 2003
  2. jcsd
  3. Sep 2, 2003 #2

    Integral

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    There lies your trouble, as far as the real numbers go the only difference between 1 and 0 is location. You seem to be implying that 0 is somehow a "special" spot in the real line. It is only special in that it is defined to be the additive idenity element. So if (in your notation
    |{.}| = 1

    is a point on the real line then we must also have

    |{.}| = 0

    Since 0 is simply a point on the real line like every other point on the real line.

    If you can get a hold of that fact perhaps you can quit wasting your time with these nonsense "proofs"
     
    Last edited: Sep 2, 2003
  4. Sep 2, 2003 #3

    HallsofIvy

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    As long as you insist upon changing the definitions of the words, you can "prove" anything you like but it will still be meaningless.

    I could easily prove that C< |R| by C to be the number of tables in my house and |R| to the number of chairs! Based on MY definitions, C< |R| but it is as meaningless as your post.
     
  5. Sep 3, 2003 #4
    Hi Integral,

    How can the cardinality of a non-empty R member can be less than 1 ?

    |{}| = the cardinality of the empty set = 0

    The cardinality of any non-empty set ( |{.}| ) never can be less then 1 !

    So, |{.}| = 0 simply does not hold.

    --------------------------------------------------------------------------

    Hi HallsofIvy,

    A table or a chair or any other element that is not nothingness, cannot have a cardinality, which is less than 1 .

    So, your argument is based only on the non-empty word, but my proof is based on both empty and the non-empty words.
     
    Last edited by a moderator: Sep 3, 2003
  6. Sep 3, 2003 #5

    Integral

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    Not only do you make up your own definitions, you change them at the whim of the winds.

    It would be time well spent for you to find a good book on Real Analysis. You need to make an effort to learn what how to communicate your ideas. The best way to do this is within the frame work which already exists. It is a waste of time to reinvent the wheel. Espesially since you seem to want a square one.

    Edit:
    Just where is this emptiness,or gap< you continue to speak of? Is this gap unique to zero? Why? Why does the gap not exist between any 2 integers? What happens if I compute {gap} + 1? or 10? Why are you so intent on finding this gap at zero? Why not at 100?

    I, and other, mathematicains will point out that a gap does not exist, since we can place a number in the middle of any gap you name. So where is this gap? How can a gap, which is filled with numbers be a gap?
     
    Last edited: Sep 3, 2003
  7. Sep 3, 2003 #6
    Sorry Integral,


    But you did not answer my argument.

    All what I did is to tune my proof, after I realized that you don't understand it.

    Please read the proof (carefully) again, and after you understand it, then and only then please write your remarks.

    Thank you for your reply.


    Yours,

    Doron
     
    Last edited by a moderator: Sep 3, 2003
  8. Sep 3, 2003 #7

    Integral

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    You have not answered any of my questions either.
    Please address my questions.
     
  9. Sep 3, 2003 #8
    Integral,

    It is my mistake, I forgot to write that 0 or 1 are the members of W.

    So, now you will understand why I put {} between 0 to 1, in the first stage of my proof.

    So, please read it again, and thank you.




    A proof that |R| < C
    --------------------

    Because by Conventional-Mathematics, every R member is a point in the Real-line, then:

    {.} = any non-empty R member

    |{}| = The cardinality of the empty set = 0

    |{.}| = The smallest catdinality of any non-empty set = 1

    0 or 1 are members of W.

    Between 0 to 1 there is {} or in other words, the transition from
    0 to 1 and vice versa, is a phase transition or a quantum leap.

    The transition's type from {} to {.} = the transition's type from 0 to 1 but,
    because it is a phase transition, and we cannot use {} or {.}
    as an element between {} to {.}, we have no choice but to
    define a new set's content.

    {} = Emptiness
    {.}= Localized element = Point
    {_}= Non-localized element = Line

    Therefore between {} to {.} there is {_}.

    Now we can conclude that between any two non-empty R members there
    exist a non-localized element.

    Therefore |R| does not have the power of the Continuum.
     
    Last edited by a moderator: Sep 3, 2003
  10. Sep 3, 2003 #9

    Integral

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    What is W?
    What proof? No, I do not understand what {} is.

    What is a non-empty R member?

    What is W?
    This is what you are trying to prove. Where is the proof? All you do is state it. Where is your definition of phase transition or Quantum leap?

    I see, you define it to be so. You have not defined "line element" what is that?
    Quite a leap, How did you make it? You have not given me any proof, only claims. You apparently have defined it to be true.

    Now please address even one of my questions.

    Where is this gap? Why is it only near zero?
     
  11. Sep 3, 2003 #10
    W is the set of the Whole numbers.

    N = The set of all positive integers, whitout 0.
    W = The set of all positive integers, include 0.
    Z = The set of all integers.
    Q = The set of all rational numbers.
    R = The set of all irational numbers.
    C = The set of all complex numbers.

    Any memeber of the sets above, is a point = {.} in the real-line.
    {} = The Empty set (Set's content does not exist)
    {.} = Some set's member (content exists)

    |{}| = The cardinality of the Empty set = 0
    |{.}| = The smallest catdinality of any non-empty set = 1

    Between any two W members there is nothing(={}),and if there is, thay are not N,W,or Z members, but R or C members.

    Therefore, there is a phase transition between |{}|(=0) to |{.}|(=1) and vice versa.

    Between {}(= no content) to {.}{= a content) there is also a phase transition between {} to {.}, and vice versa.

    We cannot use {} or {.} as an element between {} to {.}, so we have no choice but to define a new set's content.

    {} = Emptiness
    {.}= Localized element = Point
    {_}= Non-localized element = Line

    Therefore between {} to {.} there is {_}.

    Now we can conclude that between any two non-empty R members there
    exist a non-localized element.

    Therefore |R| does not have the power of the Continuum.
     
    Last edited by a moderator: Sep 3, 2003
  12. Sep 3, 2003 #11

    Integral

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    This needs to be proven.
    This needs to be proven.
    This needs to be proven.
    Prove it.
    You still have not provided a meaningful definition of "Non-localized element = Line" What is a line?
    You have proven nothing, you can conclude nothing.
     
  13. Sep 3, 2003 #12
    Hi Integral,

    Please give me more detailed information on one of the parts that you say
    that it is has to be proven.

    Thank you.
     
  14. Sep 3, 2003 #13

    Integral

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    What do you mean, more detail? What you say cannot be concluded from the infromation you have provided. Pleade proof these statements. A proof is not a series of unspported statements. It is a logical development where a fact follows from fact. What you present is a series of unsupported statement which do not follow from what goes before. Your terms are undefined, your conclusions are predetermined and by definition, not proof. You define a gap and call that proof. Not the case.

    When will you answer a single question I ask. What do you mean by a line?
     
  15. Sep 3, 2003 #14
    OK Integral,

    I think I have got the idea, which is, when one does not understand something, then he wants it to be proven.

    A line is a non-localized element, the opposite of a point, which is a localized element.

    For example: an X-axis with no Y data is a line, or a non-localized element.

    Any localized element (some point) needs at least x,y data.
     
    Last edited by a moderator: Sep 3, 2003
  16. Sep 3, 2003 #15

    Integral

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    Is there something wrong with that? If the connction was clear, and what you said was obvious then it would not need proof.
    That is not the case for your statements.
    I will not permit you define you line in terms of real numbers, you have already said that it is an absence of real numbers so how can it be complsed of point on the line. If it is not points WHAT IS IT!
    I still do not know what you are talking about. PLEASE SHOW ME WHERE A GAP IS
     
  17. Sep 3, 2003 #16
    This is the Continuum itself, and it does not need any POINTS to exist.

    We can use it as a connector (not a conteiner) between any two points.

    In Conventional Math 0^0 is not well defined, because each number is a point (a localized element).

    Let us say that power 0 is the simplest level of existence of some set's content.

    Because there are no points in the Continuum, its base value = 0, but because it is exist (unlike the emptiness), its cardinality = 0^0 = 1.

    |{}| = 0
    |{_}| = 0^0 = 1
    |{.}| = 1^0 = 1
     
    Last edited by a moderator: Sep 3, 2003
  18. Sep 3, 2003 #17

    Integral

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    Once again, you are changing the topic.

    What is your continum, I do not understand this out of the context of the real numbers.

    Please specify, WHERE IS THE 'liNE' Or GAP, are they the same thing or different.

    You have steadfastly refused to answer this question. If you cannot show me where it is, IT DOES NOT EXIST.
     
  19. Sep 3, 2003 #18
    Integral,

    In Quantum mechanics there exist two opposite forms: a Particle and a Wave.

    A Particle is a localized element, and a Wave is a non-localized element.

    As you know, there is an information's XOR ratio between a Particle and a Wave.

    I discoverd that the same information's XOR ratio exists between a Point and a Line.

    So, you cannot noticed the Continuum, if you try to understand it in terms of its
    opposite, which is a Point.

    XOR ratio between LINES to POINTS
    ---------------------------------
    0(LINE) 0(POINT) -> 0-(No information) -> no conclusion.
    0(LINE) 1(POINT) -> 1-(Clear Particle-like information) -> conclusions on points.
    1(LINE) 0(POINT) -> 1-(Clear Wave-like information) -> conclusions on lines.
    1(LINE) 1(POINT) -> 0-(No clear information) -> no conclusion.
     
    Last edited by a moderator: Sep 3, 2003
  20. Sep 3, 2003 #19

    Integral

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    The entire point of a proof is to prove something. You only make claims. Please provide some proof and some definitions which will give your claims some meaning.


    When did we jump from real analysis to Quantum Mechanics. Please stick to a single topic. Seems to me you are dancing around avioding the questions I ask. You have not been able to prove the existance of this thing you call a line element, whatever that is, you have not been able to prove the existance of a gap or quantum leap in the real line, you have proven nothing only made wild unsubstainicated claims. The entire point of a proof is to prove something, you do not have a clue what that means.

    I am being to think you should not be allowed to post this nonsense in the math forum. Were it within my powers, I would move this thread to the Theory Development. Since you refuse to adhear to the known priciples of mathematics, this is not math. It is a thing of your own construction. You have not been able to demonstrate that it is either consistent or meaningful so what is the purpose?

    Until you have done me the curtsy of making some effort to learn the universal language, I can see no real benifit in continuing this conversation.
     
  21. Sep 3, 2003 #20
    Dear Integral,


    Let us say that I have a new fundamental Idea, which is out of the conventional formal editing tools, and let us say that you are an editor.

    First you have to understand the new fundamental idea.

    After you understand it, you can accept or reject it.

    If you accept it, you can try to edit it but, because it is a new fundamental idea (and you understand it), you realize that you have to develop a new editing tools that are out of the conventional formal editing tools.

    You can't understand the new fundamental idea, if you try to understand it through the conventional formal system.

    I gave you all what you need to do the step and see something new, but you did not want to do this step, which is OK, but than you can say nothing on my new idea, because you don’t understand it.


    Have a good time.

    Yours,

    Doron





    The convitional editing tools
     
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