Question: Every linear space has a basis. [Let P be the set of all linearly independent subsets of a linear space X. P is partially ordered

Every linear space has a basis. [Let P be the set of all linearly independent subsets of a linear space X. P is partially ordered by inclusion. Use Zorn's lemma (remark 1.5) to show that P has a maximal element B. Show that B is a basis of X.]

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