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Math Help - Isomorphic binary structures

  1. #1
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    Isomorphic binary structures

    Problem: Determine whether the given map \phi is an isomorphism of the first binary structure with the second.

    <F,+> with <F,+> where \phi(f)(x) = \frac{d}{dx}[\int_0^x d(t) dt]

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    Well, \phi(f)(x) = \frac{d}{dx}[\int_0^x d(t) dt] is simply f(x), so does that fact make this problem trivial? Since \phi(f(x)) = f(x), it appears that \phi doesn't do anything at all, it just returns what you put into it. Since both binary structures are the same, and the mapping function just spits out what you put into it, is this trivially isomorphic?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Isomorphic binary structures

    Quote Originally Posted by tangibleLime View Post
    Problem: Determine whether the given map \phi is an isomorphism of the first binary structure with the second.
    <F,+> with <F,+> where \phi(f)(x) = \frac{d}{dx}[\int_0^x d(t) dt]
    What is F?. What is d(t)?. The problem is not completely defined.
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