Abstract
One deficiency of the real numbers is that the equation \(x^2 = - 1\ {\rm has\ no\ solution}\ x \in {\rm \mathbf R}\) (Corollary 11.23). In this chapter, we will extend R to overcome this deficiency; the price that we will have to pay is that this extension does not have a useful ordering relation.
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© 2010 Matthias Beck and Ross Geoghegan
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Beck, M., Geoghegan, R. (2010). Complex Numbers. In: The Art of Proof. Undergraduate Texts in Mathematics, vol 0. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7023-7_17
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DOI: https://doi.org/10.1007/978-1-4419-7023-7_17
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