Let f be a group homomorphism from G into H. We define the kernel of f as kerf = {x in G | f(x) = e_H} where e_H is the identity in H. Thus is x is in kerf then we have f(x) = e_H. We prove that if the kernel of f contains only the identity element of G, then f must be an injective function. This is a simple but fun proof. I hope this helps someone learning abstract algebra!
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