SOLUTION: Discuss in detail why the dimension of a finite dimensional vector space is well-defined.

Question 1204482: Discuss in detail why the dimension of a finite dimensional vector space is well-defined.
Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
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Open your Algebra textbook and read / learn from there . . .

It is WHY your textbooks do exist and why you should learn from them.

Alternatively (if you are not satisfied as your textbook treats this issue), read from this source

https://www.quora.com/Why-is-the-dimension-of-a-vector-space-well-defined-How-do-I-know-that-all-such-bases-must-have-the-same-number-of-elements

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