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Is this true?

An algebraic extension is a finite extension

No — it is false.

The counterexample

The field of all algebraic numbers Q̄ over

Every element is algebraic, but the extension has infinite degree (it contains for every n).

The kind of mistake this is

Base field or ring

The answer changes with the field or ring you are working over.

Drill statements like this
fields

Others that fail the same way

From Rings and Fields › Field extensions, splitting fields, finite fields

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