Difference between revisions of "Talk:Fermat's Last Theorem"
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== Axiom of choice == | == 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. | + | 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 [http://web.unicam.it/matinf/aila/Scuola%20AILA/sulla%20varieta%20dei%20metodiAC_sem02.pdf here]. | There is a complete explanation of the process and the proof that it's reliable [http://web.unicam.it/matinf/aila/Scuola%20AILA/sulla%20varieta%20dei%20metodiAC_sem02.pdf here]. | ||
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) | ||
Revision as of 01:31, January 28, 2008
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)
