I have the following question in my textbook, it appears at the end of a section that talks about Mathematical Induction:
Use an induction argument to 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. Interval k and interval k+1.
I show that (1, 2) intersected with N is empty then I assume the interval k contains no natural numbers and show that interval k+1 also 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?