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Unformatted text preview: M 333 L Suggestions for Writing Proofs Suggestion 1: Write a Direct Proof by defining an arbitrary generic object and proving the assertion is true about that arbitrarily chosen object. Suggestion 2: Write a proof by dividing the proof into cases and proving the assertion is true in all possible cases with individual arguments for each case. Suggestion 3: Write a ProofbyContradiction These suggestions are illustrated in the following two proof solutions to Exercise #3 from Section 1.2. The first is a direct proof illustrating suggestions 1 and 2 above. The second is a proofbycontradiction illustrating suggestion 3. Before the proofs are presented, the suggestions above are explained in greater detail. In a direct proof, we prove that an assertion is true about every particular OBJECT of a certain type (as in Exercise #3, we need to prove that something is true about every particular pair of Fe's in the system). The technique is to let an arbitrary one of such objects be given by saying, for instance, "Let OBJECT 1 be a given arbitrary suchandsuch object." be a given arbitrary suchandsuch object....
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This note was uploaded on 11/02/2010 for the course MATH modern geo taught by Professor Shirley during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Shirley
 Indirect Proof

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