Inductive step assumption for all numbers up to $n$

Question

I know that the inductive step should be "for all $n$ (if $P(n)$ then $P(n+1)$)" and NOT "if (for all $n$ $(P(n)$)) then (for all $n$ ($P(n+1)$))" - see this answer.

But can it be like "if (for all $i$, where $i = 1, \ldots, n$, ($P(i)$)) then $P(n+1)$)"?

You might want to search for the difference between strong induction and weak induction. — Raj, May 11 '14 at 15:32

score 0 · Accepted Answer · edited Apr 13 '17 at 12:20

0

Yes, it can. It is called strong induction.

Thanks to Raj, I found answer to my question here: difference between simple induction and strong induction.

edited Apr 13 '17 at 12:20

Community

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answered May 11 '14 at 23:52

betatester07

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Inductive step assumption for all numbers up to $n$

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