11
edits
Changes
Jump to navigation
Jump to search
Line 93:
Line 93: + + + + + +
Conservapedia:Critical Thinking in Math (view source)
Revision as of 22:29, August 9, 2008
, 22:29, August 9, 2008Proof by contradiction cont.
::::::::::: 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 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)
:::::::::::: If a proof isn't rigorous then it's not really a proof, and there is nothing not rigorous about proof by contradiction. A proof that uses contradiction might not be rigorous, but any kind of proof can fail to be rigorous. The axiom of choice is irrelevant.
:::::::::::: Take a look at this [http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php proof by contradiction] that <math>\sqrt{2}</math> is irrational. Where is the unseen underlying contradiction? That something times two is an even number? That the product of two even numbers (and therefore the square of an even number) is an even number? That a fraction consisting of two even terms is not simplified to its lowest terms?
:::::::::::: Are you thinking of [http://mathworld.wolfram.com/IntuitionisticLogic.html Intuitionistic Logic]? [[User:AdrianDelmar|AdrianDelmar]] 18:29, 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)