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Noncommotative structural numbers

  1. Oct 16, 2003 #1
    Noncommutative structural numbers


    In the attached address (at the end of the web page) there is a short paper (a pdf file) on noncommutative structural numbers:


    I'll be glad to get your remarks.

    Thank you (and special thanks to Hurkyl that gave the formal definition, which is written in the first 7 sentences of the paper).

    Last edited: Oct 17, 2003
  2. jcsd
  3. Oct 17, 2003 #2


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    I don't see any formal definition- certainly not in the first 7 sentences. I don't actually see any definition at all. I see a lot of general vagueness and use of undefined symbols.

    You say "A single-simultaneous-connection is any single real number included in p, q
    ( = D = Discreteness = a localized element = {.} )."

    What do you mean by "included in p,q"? In particular, what do you mean by "p, q"? I would tend to assume you mean "any of [p,q], [p,q), (p,q], (p,q) which you had given above. I take it then that "A single-simultaneous connection" is a singleton set?

    "Double-simultaneous-connection is a connection between any two different real numbers
    included in p, q , where any connection has exactly 1 D as a common element with some
    other connection ( = C = Continuum = a non-localized element = {.___.} )."

    Okay, so a "double-simultaneous-connection" is a pair of numbers?
    "where any connection has exactly 1 D as a common element with some other connection" is not clear. You appear to be saying that two "connections" (I take you mean "double-simultaneous-connection") that have both elements the same are not considered to be different. That's actually part of the definition of set.

    I have absolutely no idea what " = C = Continuum = a non-localized element = {.___.} )" could possibly mean.

    "Therefore, x is . XOR .___."
    This makes no sense. The only use of "x" before this was as a bound variable in the (standard) definition of [a,b], [a,b), etc.
    In any case, you have been told repeatedly that your use of "XOR" has no relation to the standard use. Please don't use a standard notation for a non-standard use.

    You seem to be still agonizing over the difference between the discrete integers and the continuous real numbers. I can only suggest again that you take a good course in basic mathematical analysis. (And it might be a good idea to learn what a "definition" really is.)

    By the way, what does "non-commotative" mean? Did you mean "non-commutative"? I didn't see any reference to that in you post.
  4. Oct 17, 2003 #3
    Hi HallsofIvy,

    I wrote:
    First, thank you for the correction. it is noncommutative.

    Please after you open the web page, go to the end of it (as I wrote above) and then open the pdf file, which is under the title:

    Noncommutative structural numbers

    I'll be glad to get your remarks.

    By the way, please reply to my answer to you, that exists at the end of this thread:


    Thank you.
    Last edited: Oct 17, 2003
  5. Oct 19, 2003 #4


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