Question

What is similarity and difference between first principle induction and second principle induction ?

When to use each principle? are there characteristics that distinguish the issue to be solved by the first or second principle?!

Answer 1

Similarity: Both of the principles are induction over (Set of Natural Numbers) to prove certain assertion of the form is true.

For both cases we have to assume some truth to prove the ultimate result.

Difference: In second principle of mathematical induction we don't need to do that initial steps like first principle induction.

Here (2nd principle) we just assume is true to prove the truth of for all instead to assume only .

Rule of use that induction are not specific. We select one procedure in order to make the problem simple and this has no specific rule. By doing some exercises you can get a nice idea to select which would be best for that problem.

No. There is no such official distinguish of characteristics between them. But as I said before you can easily choose the best one to approach any induction based problem by doing several exercises.

Thank You.

Still if you need any clarification feel free to leave a comment.

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