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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)