1. The problem statement, all variables and given/known data Let S be a set of nonzero polynomials. Prove that if no two have the same degree, then S is linearly independent. 2. Relevant equations 3. The attempt at a solution We will proceed by contraposition. Assume that S is a linearly dependent set. Thus there exists a linear dependence relation ##a_1p_1 + \cdots + a_np_n = 0## such that ##a_1,...,a_n## are not all zero. Now, the RHS of the relation has degree -1. Hence, the LHS must have degree -1 also. In this case, assume that no two polynomials have the same degree. Then the LHS would have the degree of the polynomial with largest degree, which is other than -1 since there are no zero polynomials in the set S. This is a contradiction, because the LHS must have degree -1. Hence, there must exist at least two polynomials with the same degree. In this correct? Am I begging the question if I claim that the LHS must have degree -1 also?