Suppose a,b e G, where G is an abelian group under +. Show -(a + b) = (-a) + (-b). Thanks for any help.
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Originally Posted by jzellt Suppose a,b e G, where G is an abelian group under +. Show -(a + b) = (-a) + (-b). Thanks for any help. By a property of inverses, . Since and G is Abelian, then
How do we know that -(a + b) = (-b) + (-a)? Isn't that something I would have to show while giving a solid proof?
Originally Posted by jzellt How do we know that -(a + b) = (-b) + (-a)? Isn't that something I would have to show while giving a solid proof? You need to keep in mind that if is a group , then . In additive notation, this would be the same as , where is a binary operation. In this case, that binary operation is . Does this clarify things?
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