Answer:
Proof
Step-by-step explanation:
Given:
- If you run 1 or 2 miles
- You can always run 2 miles more after running specified number of miles
Find:
- Prove that you can run any number of miles
Solution:
- Let M ( n ) be " You can run the nth mile"
Basis step: n = 1 and n = 2
- M(1) and M(2) are True, because you can run one or two miles as given in statement.
Inductive Step:
- We assume that M(1) , M(2), ......, M( k ) are all true, thus you can run the first k miles.
- We then need to prove that M ( k+ 1 ) is also true.
- Since M ( k - 1 ) is true then M ( k + 1 ) is true. ( You can always run 2 miles more after running specified number of miles )
Conclusion:
- By the principle of strong induction, M ( n ) is true for all positive n integers.
