Graduate Thesis Or Dissertation
 

Indirect proofs in elementary mathematics

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  • Proving mathematical theorems usually involves the proof of an implication, p --> q. Often it is convenient to prove the implication by proving one which is equivalent to or "stronger" than the original theorem. Proofs of this type are called indirect proofs. In Chapter I five forms of indirect proofs are considered. An outline of the rules of inference is also presented. This outline is not a rigorous development of the fundamentals of logic. Rather, it is a sketch of the laws referred to in later parts of the thesis. These rules are used to study the logical structures of the five forms of indirect proofs. In Chapter II examples from elementary mathematics are used to further expose the structures of the different forms of indirect proofs.
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