0
$\begingroup$

I am a university student and I was self-teaching myself induction methods.

I did question (3)(b). The answer to (3)(a) is g n = 2^n + 1 for n is a positive natural number.

My solution differs from the given solution by the university.

Mine has 2 base cases. I see that the given solution has 1 base case but it splits its inductive step into two cases (while I don't).

I've taken screenshots below for quick reference.

Question: enter image description here

Given solution: enter image description here

My solution (please mind my poor handwriting): enter image description here

The question is, is my solution perfectly okay -i.e. is a perfectly valid strong induction proof? Is there something I have done wrong or something I have done badly against convention.

Which solution is better or preferred - and why? (i.e. which style can be more easily applied to other questions)

Thank you in advance.

$\endgroup$
1
$\begingroup$

You practically did the same thing. Your solution is completely fine.

$\endgroup$
  • $\begingroup$ Yeah I did, but if the question asked for strong induction specifically, do you think my solution is perfect? Which solution do you think is more intuitive, better or common? I am new to strong induction so I don't know if my solution is "set out" correctly. Thank you. $\endgroup$ – EthnicMinority Apr 8 '15 at 5:20
  • 1
    $\begingroup$ It is really doing the same thing. Instead of bothering with a minor case in the inductive step, you decided to get rid of it from the first. Which is perfectly fine. I can't tell which one is better for you. I would suggest you ask your professor because he/she might be sensitive towards certain syntax and etc. $\endgroup$ – goldenratio Apr 8 '15 at 5:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.