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Conservapedia:Critical Thinking in Math (view source)
Revision as of 21:53, August 9, 2008
, 21:53, August 9, 2008→Draft Curriculum: reply re: rigor of different types of proof
:::::::::: Googly's original question was simply "What's the controversy?" Is this it? Proof by contradiction, Hilbert's program and Gödel's incompleteness theorems are all already on the draft curriculum. Whether elementary proofs are better or not isn't really a controversy. Is there something else? [[User:AdrianDelmar|AdrianDelmar]] 09:57, 9 August 2008 (EDT)
:::::::::: Googly's original question was simply "What's the controversy?" Is this it? Proof by contradiction, Hilbert's program and Gödel's incompleteness theorems are all already on the draft curriculum. Whether elementary proofs are better or not isn't really a controversy. Is there something else? [[User:AdrianDelmar|AdrianDelmar]] 09:57, 9 August 2008 (EDT)
::::::::::: So you seem to agree that not all types of proofs are absolutely identical in rigor. Or do you? [[Elementary proof]]s are plainly preferred and more rigorous than, say, proofs that rely on the [[Axiom of Choice]]. If it is possible to prove something without relying on the [[Axiom of Choice]], then that approach is preferred. Surely you don't doubt that [[Paul Erdos]] would have confirmed as much.
::::::::::: You haven't rebutted the criticism of proofs by contradiction. As I said, it is impossible to know as a matter of logic whether the contradiction is due to the math or the falsity of the proposition.--[[User:Aschlafly|Aschlafly]] 17:53, 9 August 2008 (EDT)
*You say: "No tools beyond about 9th grade math are required, and motivated students younger than 9th grade will not have difficulty with the concepts." I think 9th-graders will struggle with Goldbach, Wiles, Hilbert... [[User:Googly|Googly]] 21:09, 6 August 2008 (EDT)
*You say: "No tools beyond about 9th grade math are required, and motivated students younger than 9th grade will not have difficulty with the concepts." I think 9th-graders will struggle with Goldbach, Wiles, Hilbert... [[User:Googly|Googly]] 21:09, 6 August 2008 (EDT)