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I'm currently working through Wendell Motter's Foundations for Higher Mathematics and there's an exercise at the end of the chapter on induction that I'm stumped on. The question asks to prove that the First Principle of Mathematical Induction follows from the Second Principle of Mathematical Induction, specifically using that fact that all inductive sets are weakly inductive sets.

I've seen proofs online that show how the Second Principle follows from the First (the book also includes this), but not the other way around. If this was answered in a similar question, sorry for the redundancy.

Thanks so much!

1junkt3st1
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  • This should be helpful https://math.stackexchange.com/questions/1184541/what-exactly-is-the-difference-between-weak-and-strong-induction – Irving Rabin Oct 10 '21 at 18:53
  • @eng2math This link was incredibly helpful. Thanks so much. I think there's also certain intuitions that come for a novice like me when it comes to which definition you use for weak induction. Just random thoughts. Anyways, thanks again, this cleared a lot up. – 1junkt3st1 Oct 10 '21 at 19:29
  • Of course @ 1junkt3st1 – Irving Rabin Oct 11 '21 at 01:39

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