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Ohda!: Definition of Order in Baby Rudin

  1. Mar 21, 2012 #1

    Bacle2

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    Hi, All:

    Just curious:

    Rudin defines order in his "Baby Rudin" book ; an order relation < in a set S, as a relation* satisfying, for any x,y,z on S:

    1) Either x<y , y<x , or y=x

    2)If x<y and y<z , then x<z , i.e., transitivity.

    Just curious: why is Rudin only considering only total orders in his book? Isn't the partial-order relation of "is a subset of" (among others) important-enough to allow for partial orders?


    * Rudin never formally-defined relation, just in case, tho let's assume a relation

    on S is a subset of SxS with the above properties.
     
  2. jcsd
  3. Mar 21, 2012 #2

    micromass

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    I suppose that it is sufficient for his goals. Certainly the subset relation is very interesting, but he probably doesn't need it anywhere in his book.

    I guess he wants to stay close to the intuition of the order relation on the reals...
     
  4. Mar 21, 2012 #3

    Bacle2

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    You may be right. Still, AFAIK, you need to work with set containment to prove, e.g., Hahn-Banach. Maybe he does that in his "Non-Baby" book.
     
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