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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.

EthnicMinority
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1 Answers1

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

goldenratio
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  • 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. – EthnicMinority Apr 08 '15 at 05:20
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    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. – goldenratio Apr 08 '15 at 05:44