Difference between revisions of "Talk:Fermat's Last Theorem"
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Also, the profoundly intuitive [http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29 trichotomy] is equivalent to AC, so be careful what you call controversial. [[User:BenjB|BenjB]] 20:29, 27 January 2008 (EST) | Also, the profoundly intuitive [http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29 trichotomy] is equivalent to AC, so be careful what you call controversial. [[User:BenjB|BenjB]] 20:29, 27 January 2008 (EST) | ||
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| + | "Any proof which uses the axiom of choice can be transformed into one that doesn't"?! Lol. If C is the axiom of choice, then C (vacuously) proves C. By your assertion, that proof can be 'transformed' into a proof not using C, which means you can prove C from ZF, which is a contradiction. Really, lol. [[User:Tomkup32|Tomkup32]] 09:26, 9 December 2009 (EST) | ||
Revision as of 14:26, December 9, 2009
The first computer program I wrote - between high school and college - generated solutions to the Pythagorean Theorem. I guess I should have programmed it to count them, too. --Ed Poor Talk 21:25, 20 December 2007 (EST)
Axiom of choice
Any proof which uses the axiom of choice can be transformed into a proof that doesn't. Granted, it will be a somewhat more complicated proof, but it always works, and that's a fact. That is the reason that AC is much less controversial these days than it was, in the early 1900s.
There is a complete explanation of the process and the proof that it's reliable here.
Also, the profoundly intuitive trichotomy is equivalent to AC, so be careful what you call controversial. BenjB 20:29, 27 January 2008 (EST)
"Any proof which uses the axiom of choice can be transformed into one that doesn't"?! Lol. If C is the axiom of choice, then C (vacuously) proves C. By your assertion, that proof can be 'transformed' into a proof not using C, which means you can prove C from ZF, which is a contradiction. Really, lol. Tomkup32 09:26, 9 December 2009 (EST)
