Prove that for every positive integer n, one can find n + 1 linearly independent vectors in F(−[infinity], [infinity]). [Hint: Look for polynomials.] b. Use the result in part (a) to prove that F(−[infinity], [infinity]) is infinite-dimensional. c. Prove that C(−[infinity], [infinity]), Cm(−[infinity], [infinity]), and C [infinity](−[infinity], [infinity]) are infinite-dimensional.