TheoremProving: Difference between revisions
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Larry_Sanger (talk) See /Talk |
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Mathematicians, logicians, and others who prove [[theorem]s seek to establish chains of [[LoGic|reasoning]] that are convincing to others. |
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A [[mathematical theorem]] begins with a [[mathematical hypothesis]], proceeds through [[mathematical reasoning]] to reach a [[mathematical conclusion]]. |
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Mathematicians seek to establish chains of [[LoGic|reasoning]] that are convincing to other mathematicians. The main differences between mathematical argument and ordinary logical [[LoGic|argument]] are in the [[Mathematics/Schemes|topics]] of mathematical discourse. |
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The following diagram displays the relations among the terms: |
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*<font size=+2 color=red>Theorem = Hypothesis--->Proof--->Conclusion</font> |
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I don't follow this. In my mind a theorem consists of a statement of the theorem followed by a proof of its truth. See, for example, the theorems in [[ElementaryGroupTheory]] |
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One may seek to prove a new theorem by hypothesis->investigation->conclusion, but that isn't the theorem. |
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There are many ways of proving a theorem correct, including: |
There are many ways of proving a theorem correct, including: |
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* [[Reductio ad absurdum]]: If we can show that the assumption that our hypothesis is false leads to a contradiction, it follows that the hypothesis must be true. |
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''By mathematical hypothesis, are we meaning the result to be proven or [[axioms]]? |
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/Talk |
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Revision as of 19:35, 12 March 2001
Mathematicians, logicians, and others who prove [[theorem]s seek to establish chains of reasoning that are convincing to others.
There are many ways of proving a theorem correct, including:
- Reductio ad absurdum: If we can show that the assumption that our hypothesis is false leads to a contradiction, it follows that the hypothesis must be true.
/Talk