Algebraic Field Extension over Algebraic Field Extension

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In this video we prove that an algebraic extension of an algebraic extension is algebraic over the smallest field.
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5:30 every time you say s omethinh not instantly apparent and might have to ponder a liitle, I go for a coffee cause I know it's going to be hours.

debendragurung
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Why not using tower law to conclude the finite dimension of the new extension, and therefore algebraic.

therensdns