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Math Help - I Need a Binary Operation

  1. #1
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    I Need a Binary Operation

    Define a binary operation on the rationals so that the map defined by is an isomorphism between sets with binary operations. Prove that is an isomorphism.

    By Isomorphism i mean i need to find a binary operation such that for all u, v in ,
    \phi(u \bullet v) = \phi(u) + \phi(v)
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  2. #2
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    Quote Originally Posted by kbartlett View Post
    Define a binary operation on the rationals so that the map defined by is an isomorphism between sets with binary operations. Prove that is an isomorphism.

    By Isomorphism i mean i need to find a binary operation such that for all u, v in ,
    \phi(u \bullet v) = \phi(u) + \phi(v)
    You want \phi (u\bullet v) = \phi (u) + \phi (v) to hold for all u,v.
    Therefore, 7(u\bullet v) + 1 = (7u + 1) + (7v+1).
    Thus, u\bullet v = u + v + \tfrac{1}{7}
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  3. #3
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    thankyou, it seems so obvious now. The big words just confussed me .

    Do u know how i could go about Proving that \phi is an isomorphism.
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