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...analysis, we could next show that <math>\mathbb{C}</math> has no finite [[field extension|extension]] and must therefore be [[algebraic closure|algebraically closed]

*12Fxx [[Field extension]]s

...tain (real) roots for those polynomials. Now, the Galois group of a normal field extension (roughly, one that arises through adjunction of all roots of a set of polyn ...in this analysis, we discover that <math>\mathbb{C}</math> has no finite [[field extension|extension]] and must therefore be [[algebraic closure|algebraically closed]