Precalculus (6th Edition) Blitzer

We know that in the method of mathematical induction one assumes that ${{S}_{k}}$ is true and one has to prove that ${{S}_{k-1}}$ is true using ${{S}_{k}}$. If one can prove ${{S}_{k-1}}$ is true, then one can say that ${{S}_{n}}$ is true for all real numbers. Thus, the above statement does not make sense.