Recent content by dabokey

That's an excellent hint and I wish that I would have seen it a little earlier. I appreciate your help!

Thank you, your proof seems so simple. I honestly appreciate your help and feel humbled. :) Regarding your question as to why I started with what I was trying to prove: The answer is that I'm new to proofs and am trying to learn how to do them. I've been out of school for about 4 years...

Ok, I've heard of rings and your answer makes sense. I believe that I've proved f(0) = 0 as follows: f(x + y) = f(x) + f(y) Take y = 0 f(x + 0) = f(x) + f(0) f(x) = f(x) + f(0) f(x) - f(x) = f(x) - f(x) + f(0) 0 = f(0), which is what I was trying to prove. But to prove -f(x) = f(-x), I'm at...

Ok, so I am working under the operation of addition because I'm given that f(x+y) = f(x) + f(y) for f: G-->H. Thanks to your clarification, I now understand the difference in identity elements between the additional and multiplication operations. Now, I'm working with addition and am...

Hurkyl, I am at the beginning of learning group theory on my own, so my questions may seem a bit basic. Why doesn't f(-1 * x) make sense? Does f(-x) actually mean the f(inverse of x)? With regards to '*' and '-1', I meant to factor '-x' into two separate parts so that I can somehow apply the...

I'm not sure that f(n) = n. That isn't given in the problem statement. Verifying that f(1) = 1 isn't difficult, but I do appreciate your proof. For a homomorphism, f(x+y) = f(x) + f(y) because f maps G → H How do I show that f(-x) = -f(x)? For that matter, is it true that f(-1) = -1? Thank...

Homework Statement Let f : G → H be a homomorphism of Abelian groups. 1. Show that f (0) = 0. 2. Show that f (−x) = −f (x) for each x ∈ G. Homework Equations The Attempt at a Solution My background in topology / group theory is next to nothing. 1. Show that f(0) = 0. My attempt is as...