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Math Help - Well ordered set

  1. #1
    Super Member Deadstar's Avatar
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    Oct 2007
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    722

    Well ordered set

    Suppose (A,\leq) is a well-ordered set. Let B = \mathbb{R}^A. Find an explicit linear order on B.

    So I have to prove reflexivity, antisymmetry, transitivity and that B is linear. Thing is I cant really get my head around what B = \mathbb{R}^A actually is... Set of functions from A to \mathbb{R}. But A is well ordered... So how does that change things?

    Does this involve creating an in/bijection between B and some well ordered set?
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  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
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    clic-clac explained how to form the linear order pretty well for me:

    http://www.mathhelpforum.com/math-he...order-set.html

    proving the rest is a bit easier.

    Now, know anything about question 4? http://www.mathhelpforum.com/math-help/discrete-mathematics-set-theory-logic/111677-ordinal-arithmetic.html
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