Right. A simple example to show that induction does not work to infinity:

    0 < 1
    For any natural n, if n-1 < n, then n < n+1
    (proof: add 1 to both sides of the given inequality)
    By induction, for all natural n, n < n+1

But clearly this does not work for infinity, because ∞-1 = ∞ = ∞+1. So induction proves something about all natural numbers, but ∞ is not a natural number.