Writing Computations Clearly In Proofs

1. Jun 23, 2012

jmjlt88

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. Jun 23, 2012

micromass

Staff Emeritus
I like (2) better in this case.