TheoremProving: Difference between revisions

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Revision as of 18:31, 12 March 2001

A mathematical theorem begins with a mathematical hypothesis, proceeds through mathematical reasoning to reach a mathematical conclusion.

Mathematicians seek to establish chains of reasoning that are convincing to other mathematicians. The main differences between mathematical argument and ordinary logical argument are in the topics of mathematical discourse.

The following diagram displays the relations among the terms:

Theorem = Hypothesis--->Proof--->Conclusion

There are many ways of proving a theorem correct, including:

Contradiction - If we can show that the assumption that our hypothesis is false leads to a logical contradiction, it follows that the hypothesis must be true. Also known as reductio ad absurdum.

mathematical induction

By mathematical hypothesis, are we meaning the result to be proven or axioms?

@@ Line 15: / Line 15: @@
-There are ? basic ways of proving a theorem correct:
+There are many ways of proving a theorem correct, including:
-* Contradiction - Assuming the theorem is always false and proving that the assumption is never true
+* [[reductio ad absurdum|Contradiction]] - If we can show that the assumption that our hypothesis is false leads to a logical contradiction, it follows that the hypothesis must be true.  Also known as [[reductio ad absurdum]].
+* [[mathematical induction]]
-* [[Inductance]] (do you mean [[mathematical induction]]?)
-* ?