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Old 01-29-2008   #11 (permalink)
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Re: Arithmatic expression vs. set description connotation of the square root

Why doesn't it matter? I mean it should be astated in a definition if it is not unique (would have saved me half an hour), so to me it would have matered very much!

But I agree in practictal things it doesn't seem to matter...usually


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Old 01-29-2008   #12 (permalink)
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Re: Arithmatic expression vs. set description connotation of the square root

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Originally Posted by sanctus View Post
Why doesn't it matter?
In the strictest sense there is only one imaginary unit and the other is its additive inverse.

However, because the constructive definition of the unit doesn't distinguish between them, it's true that you could exchange them; this is an automorphism of \mathbb{C} and, unlike changing sign in \mathbb{R}, not just of the additive group but of the actual field. This automorphism is, of course, complex conjugation.

In any case, good question.


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