Is the basis of a vector space unique? Justify your answer.
I know that the answer is 'No'. I can justify the answer by providing two different basis of the same vector space. Is there any other way to defend the answer by giving logic and arguments.
Why don't you formulate your statement precisely, using quantifiers "for all" and "there exists"? I would say that the answer to "Is it possible to have more than one basis of a vector space?" also depends on the vector space.