Changes

I would suggest deleting the second paragraph until you get something that is mathematically correct. The axiom of choice is needed for well-orderings, not ordinary linear orderings. A theorem that characterizes the real numbers might be more appropriate on the Real Numbers article. [[User:RSchlafly|RSchlafly]] 14:15, 16 February 2009 (EST)

I would suggest deleting the second paragraph until you get something that is mathematically correct. The axiom of choice is needed for well-orderings, not ordinary linear orderings. A theorem that characterizes the real numbers might be more appropriate on the Real Numbers article. [[User:RSchlafly|RSchlafly]] 14:15, 16 February 2009 (EST)

:Deleted it, at least until I can sort the concepts out better. I know there is some theorem that you can't order the complex numbers (I guess as an ordered ring) because ''i'' causes violations of the ordering. I had thought there was something more basic than that, but I guess that unless you can talk about the algebra of the complex numbers (and thus, talk about "numbers" rather than topological "points"), the complex numbers won't look any different than the long line or other topological spaces that look like continua. -[[User:Foxtrot|Foxtrot]] 14:39, 16 February 2009 (EST)

:Deleted it, at least until I can sort the concepts out better. I know there is some theorem that you can't order the complex numbers (I guess as an ordered ring) because ''i'' causes violations of the ordering. I had thought there was something more basic than that, but I guess that unless you can talk about the algebra of the complex numbers (and thus, talk about "numbers" rather than topological "points"), the complex numbers won't look any different than the long line or other topological spaces that look like continua. I'll look into this more. -[[User:Foxtrot|Foxtrot]] 14:39, 16 February 2009 (EST)