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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
the field extension  is not finite
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(Corollary)
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Proof. [Proof of the Corollary] If the extension was finite, it would be an algebraic extension. However, the extension $\Reals/\Rats$ is clearly not algebraic. For example, $e\in\Reals$ is transcendental over $\Rats$ (see e is transcendental). 
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"the field extension  is not finite" is owned by alozano.
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See Also: pi, algebraic, finite extension
| Other names: |
the reals is not a finite extension of the rationals |
| Keywords: |
pi, transcendental, reals, rationals |
This object's parent.
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Cross-references: e is transcendental, transcendental, algebraic, fields, extension, algebraic extension, finite field extension
There is 1 reference to this entry.
This is version 3 of the field extension  is not finite, born on 2003-09-11, modified 2005-05-02.
Object id is 4726, canonical name is ExtensionMathbbRmathbbQIsNotFinite.
Accessed 3283 times total.
Classification:
| AMS MSC: | 12F05 (Field theory and polynomials :: Field extensions :: Algebraic extensions) |
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Pending Errata and Addenda
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