(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that weak induction is equivalent to strong induction.

2. Relevant equations

To prove this...we assume weak induction. That is

(i) 1 [itex]\in[/itex] S

(ii) n[itex]\in[/itex] S [itex]\Rightarrow[/itex] n+1 [itex]\in[/itex] S for all n in N

3. The attempt at a solution

So to prove strong induction we need to prove the following:

(i) 1 [itex]\in[/itex] S

This is given by our assumption of weak induction.

(ii) {1....n} [itex]\in[/itex] is a subset of S.

SInce we know 1 is in S, we can make 2...n by 1+1, 1+1+1, 1+....+1 (n times)

(iii) if (ii) is true than n+1 is in S.

I think this is true because our assumption guaranteed this.

This is a rough sketch of what I wan to say. Am I on the right track.

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# Homework Help: Weak induction is equivalent to strong induction

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