If I am correct, it's stating to prove for all n $\ge$ 1, where n is a real number. However, I have only been shown induction proofs for integers. Is it acceptable to prove by assuming a k exists such that a(k) is false, using the well-ordering principle, and discovering a contradiction?
(where a(x) is the second statement.)
Thank you-- hints would be appreciated.
Note that $n$ is used in the subscript of $a_n$, and we are told that we are given only numbers $a_1,a_2,a_3,\ldots$. So you are to assume that $n$ is a natural number.
Therefore regular induction is appropriate here.