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And why would R be "entitled" to an algebraic closure?

(I have a math degree, so I don't have any issues with C, but this is the kind of question that would have troubled me in high school.)

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> And why would R be "entitled" to an algebraic closure?

It's the birthright of every field.

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When it doesn't, we yearn for something that will fill the void so that it does. It's like that note you yearn for in a musical piece that the composer seems to avoid. One yearns for a resolution of the tension.

Complex numbers offers that resolution.

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The good news is that Q is not really entitled to a closure either.
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