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If ##v## is an element of a vector space ##V## and for example ##\mathcal{B}=\{e_1,e_2,e_3\}## is a basis of ##V##, then, at least, there should be another basis for ##V## in which the vectors of ##\mathcal{B}## can be expressed, but at the same time, the vectors of this other basis must also be expressed using ##\mathcal{B}##'s vectors.
Why is there no problem here?
Why is there no problem here?