Show that the vector space of polynomials R[x] is isomorphic to a proper subspace of itself:
Vector Space Isomorphism exists when there exists a bijective (one-to-one and onto) linear mapping F:V $\rightarrow$U. the coefficient of the polynomials can be written as $(a_0,a_1,a_2...)$. But how to find the subspace?
What about instead to prove the dimension of the the two vector spaces is the same, which means isomorphic? But how to do it?