Talk:Logic for Computer Scientists/Induction

induction also means a kind of inference, this chapter should present just inductive definitions
It is fine that this part talks about inductive definitions, and inductive proofs. But induction is also a kind of inference, the opposite to deduction it may cause some confusion later.

Although there is a relation in the meaning of induction in both uses of the word, I think that this part should only explain inductive definitions simplifying the content. To talk about structural induction, seems more important in the context of programming languages and data types. If this book intend to be an elementary introduction to logic, I think that it may be too complex for the new, then confusing.

I think it is enough to explain inductive definitions, but there is no need to dispose the article, just to modify it as an introduction to other topics. When there is a need to present an inductive proof in some logic, it is the time to present inductive proofs. One thing that is hard to grasp for earlier semesters students is what is the induction hypothesis $$p(n)$$ and why one wants to prove $$p(n)\to p(Succ(n))$$. I think that one problem is previous exposure to induction proofs with examples like the Gauss sum formula $$\sum_{i=0}^n i=\frac{n(n+1)}{2}$$. Using $$n+1$$ in place of $$Succ(n)$$ makes them forget that naturals are defined inductively. Something that is important when they need to prove thinks about inductively defined data types like lists or trees.

An elementary book, should only have the material needed to understand the topics presented later.

In my experience in mathematics course for beginners, It is hard for them to grasp, inductive proofs, and inductive definitions at the same time is too much for them. I should say that this is the situation in Mexico, because unfortunately the elementary school system have been deliberately and gradually destroyed by the corrupt governments since the 70s.