>>A general isomorphism cannot exist since R is an ordered field but C is not...
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>Why isn't C ordered?
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The order axioms aren't satisfied. For example, is i greater than -i?

>>(I'm sure this info will be useful to all UT folks!) :~)
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>Well, I like to remember all this things I never used. :)
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Yes, you never know when a bit of theoretical math might come in handy. Maybe you're on 'Jeopardy' and Alex says: 'This number field is not ordered'...Now you know the question. :~)