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for K>or equal to 1 let P

_{k}denote the the vector space of all real polynomials of degree at most k. For which value of n is P

_{k}isomorphic to R

^{n}. Give a brief reason for your answer.

Now from what i have found on two vector spaces being isomorphic they need to have equal dimensions (dimu=dimv) so knowing that we have dimR

^{n})=n is as far as i have got. Not really understanding this one, surely they would be isomorphic at any value of n as long as it's between 1 and k????