ATAR Notes: Forum
VCE Stuff => VCE University of Melbourne Extension Program => VCE University Enhancement Programs => VCE Subjects + Help => VCE Mathematics => Topic started by: Jeggz on February 05, 2013, 10:23:16 pm
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Can someone please, briefly yet very clearly explain to me what Induction is all about?
I am so very confused!
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http://en.wikipedia.org/wiki/Mathematical_induction
wiki (most of the time) is your best friend when it comes to maths :P
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bahaha!
i will take your word for it, thanks alot :)
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De moivre's theorem is proven with this as far as I know
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it is basically a way of doing a PROOF
so you basically have to start of with one integer, most likely it would be 1 and then put into the left hand side of the original equation, if it matches with the right hand side then it is said to be true.
then after you make your induction hypothesis. you now have to prove for any integer + 1
so basically (k+1) while k being an integer
and then so either left or right hand side and it equal the other.
DONE
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http://en.wikipedia.org/wiki/Mathematical_induction
wiki (most of the time) is your best friend when it comes to maths :P
very true, TT
The quality of Maths on Wiki is very high and puts a lot of other academic sources to shame.
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yup in fact alot of my current research is all referenced from wiki (more specifically the references they put up), it's a great way to start off learning the basics and then you can always dig up their references to read deeper
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Can someone please, briefly yet very clearly explain to me what Induction is all about?
I am so very confused!
Hey, so this might come a bit late but this was the way I was taught it:
Mathematical Induction (which actually used to be in the methods course a while ago) is like a set of dominoes. The set, usually natural numbers, goes 1,2,3,.... So you have your first domino, second domino, third domino, etc etc.
For the theorem to work, the first domino has to fall, which is why you test for n=1, P(1). Now, lets assume a domino, say at k place, falls and knocks over the (k+1) domino. So you want to prove the k+1 domino does fall iff the domino before it, k, falls. This is why we prove P(k+1) using P(k).
And then, since we all know how dominoes work, we have proved the first one falls, knocks over the next one, which knocks over the one after that and so on and so forth hence proving the theory with mathematical induction.
Just do a lot of practise questions and you'll be fine!! It's just the inequality proofs that require a bit more thought..