Recent content by clone

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    Proof that the images of parallel lines under an isometry are parallel

    Thanks! I see now that I was looking at what actually needed to be proved from completely the wrong way
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    Proof that the images of parallel lines under an isometry are parallel

    I don't really understand what any of that means to be honest. I guess I should have been more specific about the context. This is from Serge Lang's basic mathematics, and in the section titled "Intuitive Geometry". We are just doing 2d geometry, drawing diagrams on paper. The definition of...
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    Proof that the images of parallel lines under an isometry are parallel

    The proof in the solutions was done much differently then mine (much simpler), so I would like feedback on whether my proof is valid or not. Assume that F(L) and F(K) are not parallel, then they necessarily intersect. Let X' be the point of intersection. Then X' lies on both F(L) and F(K). Let...
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    Addition problem in Serge Lang Basic Mathematics

    Relevant Rules: N5: -(a+b) = - a - b N4: a = -(-a) N2: a + (-a) = 0 and -a + a = 0 I tried just manipulating -(a - b) with the rules to get the answer: -(a - b) = -(a + (-b)) With N5: = - a + (-(-b)) With N4: = - a + b Commutativity: b - a The provided solution in the book used N2 to prove it...