HSC Stuff > HSC Mathematics Extension 2
Interesting induction questions
Mahan:
--- Quote from: RuiAce on November 01, 2016, 09:54:53 am ---Whilst I don't deny the course has been made easier, neither of the proofs provided are to within reasonable bounds of the current Extension 2 level, especially with how the inductive hypothesis must be applied more than once.
Because expecting an Extension 2 student to think that deeply into pure mathematics is stretching too far. The necessity of considering the elements in such a way, despite being one of the easiest things to teach, is not something that one is expected to know.
As for simplicity though, I'd say that your answer is indeed simpler
(We could really add a beyond 4U section of this forum but I didn't bring it up cause I didn't see enough value in it yet - forum still needs popularity for that.)
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Also, I still wish to ask for my friend. What is the source of this question?
--- End quote ---
I agree that the level of the question is higher than what we should expect from an average Extension2 student but I think by exposing students to these simple but interesting ideas, we will open their minds and will give them some problem solving skills that might be useful in different types of questions.
But I agree with you. :)
About the repeated elements, Although you are right about undefined cardinality of the sets if we choose multiple elements, This is a restriction you imposed on the question by using set theory. In my proof I avoided using set theory, although I used the word set, I should've used collection instead. In the question there is no mention of distinct elements.
the book is an introduction to IMO competition but unfortunately it is in another language, I chose that question carefully to make sure the question is easy and doable for ext2 students and at the same time it uses a new idea that most students have not seen before.
If you are interested I can cite the book, but I don't think it is gonna be useful.
RuiAce:
--- Quote from: Mahan on November 01, 2016, 10:25:00 am ---I agree that the level of the question is higher than what we should expect from an average Extension2 student but I think by exposing students to these simple but interesting ideas, we will open their minds and will give them some problem solving skills that might be useful in different types of questions.
But I agree with you. :)
About the repeated elements, Although you are right about undefined cardinality of the sets if we choose multiple elements, This is a restriction you imposed on the question by using set theory. In my proof I avoided using set theory, although I used the word set, I should've used collection instead. In the question there is no mention of distinct elements.
the book is an introduction to IMO competition but unfortunately it is in another language, I chose that question carefully to make sure the question is easy and doable for ext2 students and at the same time it uses a new idea that most students have not seen before.
If you are interested I can cite the book, but I don't think it is gonna be useful.
--- End quote ---
Was all necessary, cheers (y) @source
Whilst it's a shame that most people are just there in 4U because they're good at maths and don't necessarily have a passion for it, it's still something to consider. It's quite unfortunate how these things are often glanced at and then ignored.
Mahan:
Well, it's been a while since I have posted an induction question. A few days ago I came across another interesting induction question.
Suppose and for we have
then prove by induction, for every
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