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Again, the idea behind this 
slide is meant to be sort of a

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timestamp thing if you
want to try to find this,

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you can go to this 
approximate minute stamp.

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What are we going to 
talk about in this video?

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We're going to talk about the Principle
Mathematical Induction, that was the

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main topic of 
the week.

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We'll see an example and 
we'll highlight the base case,

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the inductive hypothesis, 
and the inductive step.

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We're going to talk about when induction 
isn't enough, so a situation where… 

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what do I 
want to say…

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the usual 
or the

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typical induction statement’s 
not going to work,

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and that's where we would like to use 
something called strong induction,

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which will help us out so 
we'll talk with that in slide 7.

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I'm going suppress from this video 
an example of strong induction,

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You can go on the Math 
135 Resources Page

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and check out an example 
of strong induction there.

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Then we're going to talk about the
Fibonacci sequence. We'll just

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or just remind ourselves what it is, 
and that's all we'll say about that,

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and then the last four
bullets, so this is where

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my course might differ 
from your course substantially.

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I decided to do the
Fundamental Theorem of Arithmetic

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as the last lecture 
of the induction week.

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t turns out that we
can't actually do it. We

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actually need something called Euclid's 
Lemma that we don't have yet,

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but we will prove 
that next week,

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but assuming that we can actually do 
the Fundamental Theorem of Arithmetic,

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particularly see the proof. 
I think it's one of the

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most difficult proofs in 
this course to do formally,

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so in class I did it formally. 
Here I'm going to…

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well okay I should say 
in class in January 2016,

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I did it 
formally.

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But in this video, I’m 
going to do it informally.

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I'm going to do an existence proof 
formally, and I'm going to do

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an informal uniqueness proof 
just to kind of get the idea down.

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The formal proof kind 
of takes away from

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what's really going on, and I
think the informal proof

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is good to 
see once.

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So this is the 
outline for this week.