Inductive Proof:
We wish to show for all n∈Z,n≥1,P(n):n=n+1.
Let k be a particular but arbitrarily chosen integer such that P(k) is true. That is, k=k+1, which is our inductive hypothesis. We must show that P(k+1) is true. That is, k+1=(k+1)+1. Note that k+1=(k+1)+1 by the inductive hypothesis
So P(k+1) is true. Thus, by PMI we have shown ∀n≥1,n∈Z,n=n+1.
If the student is correct, then fill in the needed to
- make the proof completely correct
- make sure each assertion made is fully justified
- make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true.
If the student is incorrect, then
- Identify any errors in the proof above.
- Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect.
