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Writing Computations Clearly In Proofs

  1. Jun 23, 2012 #1
    Here's a quick question concerning writing clearly in proofs. I am revising and refining some of my proofs [this is for a self-study], and I across a problem where I had to prove that f: G->G defined by f(x)=axa-1 is a automorphism. To show it has the homomorphism property, I had to do some calculations. Which of the following would be more accepted?

    METHOD 1

    Evaulating f(xy), we get,

    (1) f(xy)=axya-1
    (2) =axeya-1 [property of e]
    (3) =axa-1aya-1 [property of inverses]
    (4) =f(x)f(y).
    Hence, f(xy)=f(x)f(y).

    METHOD 2

    We have that f(xy)=axya-1. Then f(x)f(y)=axa-1aya-1=axya-1. Hence, f(xy)=f(x)f(y).

    Thanks!!! :)
  2. jcsd
  3. Jun 23, 2012 #2
    I like (2) better in this case.
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