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Conservapedia:Critical Thinking in Math (view source)
Revision as of 00:43, August 9, 2008
, 00:43, August 9, 2008reply to Googly
:::On an unrelated note, is this class still supposed to happen? It's been over a year since it was announced. -[[User:CSGuy|CSGuy]] 20:46, 6 August 2008 (EDT)
:::On an unrelated note, is this class still supposed to happen? It's been over a year since it was announced. -[[User:CSGuy|CSGuy]] 20:46, 6 August 2008 (EDT)
:::::: Sorry Aschafly, but your second sentence is just not correct. Are you teaching this Critical Thinking in Maths course yourself? If so, I'd say you've got some pretty muddled ideas which you need to straighten out before you let yourself loose on students. There's nothing at all second-rate about a proof by contradiction. [[User:Googly|Googly]] 20:47, 6 August 2008 (EDT)
:::::: Sorry Aschafly, but your second sentence is just not correct. Are you teaching this Critical Thinking in Maths course yourself? If so, I'd say you've got some pretty muddled ideas which you need to straighten out before you let yourself loose on students. There's nothing at all second-rate about a proof by contradiction. [[User:Googly|Googly]] 20:47, 6 August 2008 (EDT)
::::::: Proof by contradiction can be unsatisfying because often it leads to unconstructive proofs of important statements. For example, [[Euclid]] used proof by contradiction to show there are infinitely many prime numbers, but that doesn't tell us what they are, or even give an infinite set of them with some formula like <math>2^n -1</math>. Another example: there is a [[transcendental number]] in the [[reals]]. If you prove this as suggested in the transcendental number article by using [[cardinality]], you'd never actually have a transcendental number to work with. It's far more useful to actually show a number like <math>pi</math> or ''e'' is transcendental and not use contradiction to do it. -[[User:Foxtrot|Foxtrot]] 20:43, 8 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)