Induction Steps
What is step 2 in the template for proofs by mathetmatical induction
2. Write out the words "Basis Step." Then show that P(b) is true, taking care that the correct value of b is used. This completes the first part of the proof.
What is step 3 in the template for proofs by mathematical induction
3. Write out the words "Inductive Step."
What is step 4 in the template for proofs by mathematical induction
4. State, and clearly identify, the inductive hypothesis, in the form "assume that P(k) is true for an arbitrary fixed integer k ≥ b."
What is step 5 in the template for proofs by mathematical induction
5. State what needs to be proved under the assumption that the inductive hypothesis is true. That is, write out what P(k + 1) says.
What is step 6 in the template for proofs by mathematical induction
6. Prove the statement P(k + 1) making use the assumption P(k). Be sure that your proof is valid for all integers k with k ≥ b, taking care that the proof works for small values of k, including k = b.
What is step 7 in the template for proofs by mathematical induction
7. Clearly identify the conclusion of the inductive step, such as by saying "this completes the inductive step."
What is step 8 in the template for proofs by mathematical induction
8. After completing the basis step and the inductive step, state the conclusion, namely that by mathematical induction, P(n) is true for all integers n with n ≥ b.
What is step 1 in the template for proofs by Mathetmatical induction
Template for Proofs by Mathematical Induction 1. Express the statement that is to be proved in the form "for all n ≥ b, P(n)" for a fixed integer b.