I have the following question in my textbook, it appears at the end of a section that talks about Mathematical Induction:

Use aninduction argumentto show that for each natural number n, the interval (n, n+1) fails to contain any natural number.

Not exactly sure how to structure the proof.

Since this is induction, I think I'm going to have to deal with two consecutive intervals. Intervalkand intervalk+1.

I show that (1, 2) intersected with N is empty then I assume the intervalkcontains no natural numbers and show that intervalk+1also contains no natural numbers? I don't know if this makes sense to me.

Maybe I'm looking at this from the wrong angle. Are only the end points the inductive ingredients in the proof?

Thanks