[adwight]

Well, in my Precalculus class we just got to the most confusing math concept I've ever seen, Mathematical Induction.  It involes series, and proving those series are true for all real positive integers.  Does anyone have notes or could walk me through on how to do this?  Its so bleeping confusing I have no idea where to begin.

[Goober5000]

Induction is fun, but presented in the wrong way it can be confusing.  Try starting here:
http://en.wikipedia.org/wiki/Mathematical_induction

[adwight]

That helped a little but I still don't get the part past
"This is that statement for n = m + 1. Note that it has not been proved as true: we made the assumption that P( m ) is true, and from that assumption we derived P( m + 1 ). Symbolically, we have shown that:"

They don't look equal to me, unless im totally stupid.  Also, how can you think this stuff is fun?

[phreak]

isn't it a bit early to be starting math induction in precalculus?

[Goober5000]

I would think so.  And it's only fun when you understand it.

Say you have two statements:
(a) X is true
(b) Y is true when X is true
You have no way of proving that Y is true directly, but if you can prove both (a) and (b), then "by induction" Y must also be true.

Now substitue X + 1 for Y in the above argument:
(a) X is true
(b) X + 1 is true when X is true
Since you can always count one number higher, you prove X is true for all counting numbers.

[adwight]

Well this is "Honors Precalculus".(AP Calc next year, yuck).  I think I sort of understand it, but if someone could take me step by step, over a messenger service or something, it would be quite helpful.

[Goober5000]

ICQ.  Number in profile.

[Stealth]

goober's a good man *thumbs up*

[adwight]

Sorry man, I don't have ICQ.  I have MSN and Aim.

MSN is [email protected]
AIM is tsthor07

[Goober5000]

And you don't seem to be on.

[adwight]

Well I'm on my AIM now.  I've been on MSN for quite a while.
I'm stupid, its TSThor7 my bad.

[mikhael]

*heh* Induction is fun--when you're dealing with it in Calculus.

It stops being fun when you start using it in set theory and counting and all those other discrete maths topics.

Where's a vomit smiley when you need one?

[phreak]

i'm taking discrete math in the fall, my linear algebra prof said were going to do a lot of induction.

theres a few vomit smilies here
http://www.mysmilies.com/?cat=obscene&page=1

[adwight]

Goober is a stud, he just spent the last hour helping me understand how to do it, and I actually know how.  Thank you so much Goober.

[Goober5000]

You're welcome.

[mikhael]

Originally posted by PhReAk
i'm taking discrete math in the fall, my linear algebra prof said were going to do a lot of induction.

You poor, poor bastard. I've got an A so far, but I'll be honest: I make it up as I go along and the teacher just slaps an A on it.

[phreak]

luckily for me my Discrete Math prof speaks english as opposed to something else.  My data structures prof wasn't a native speaker and when you get into technical subjects it can be difficult to convey ideas

You know sorting? no?  Well all you do is put all the skilled laborers over here and all the unskilled laborers over there

[Setekh]

Ah, I'm too late! And induction is actually something I'm good at. Mega props to you, Goober, for stepping in there.

[Goober5000]

Thanks. I'd have contacted you about your math assignment except I was asleep at the time.

[kode]

I did some induction in two of my previous math courses. proving the fibonacci numbers and other simple stuff. my fav part was when the professor proved that there are as many even natural numbers as there are natural numbers...