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New definitions to the continuum and the discreteness concepts

  1. Sep 25, 2003 #1
    p and q are real numbers.

    If p < q then

    [p,q] = {x : p <= x <= q} or
    (p,q] = {x : p < x <= q} or
    [p,q) = {x : p <= x < q} or
    (p,q) = {x : p < x < q} .

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

    Double-simultaneous-connection is a connection between any two real numbers
    included in p,q ( = C = Continuum = a non-localized element = {.___.} ).

    Therefore, x is . XOR .___.

    Please tell me what do you think ?
    Last edited by a moderator: Sep 25, 2003
  2. jcsd
  3. Sep 25, 2003 #2


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    Science Advisor

    Okay, you asked:

    The first point I would make is that your very first statement:

    is not true. It's only true if p<q and you only said "p is not equal to q".

    It's a minor point but symptomatic of your tendency to say things sloppily and without precision. All you are really doing is using big words in non-standard ways without bothering to give precise definitions.

    Basically, you do not understand what mathematics IS, and, in particular, the difference between mathematics and physics.
  4. Sep 25, 2003 #3
    Hi HallsofIvy,

    Thank you for your correction, I am learning from you "on the fly" therefore
    I am going to fix my definition and write p>q instead of "p is not equal to q".

    Now, after I fix it, please show me by using a formal mathematical way, why my definitions to . XOR ___ are not precise.

    Thank you.

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