Inductions!!!

For the discussion of math. Duh.

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smileyfaces147
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Inductions!!!

Postby smileyfaces147 » Mon Dec 03, 2007 2:36 am UTC

My math term paper is due soon and i originally picked mathematical inductions as my topic and its too late to change it now...but i am freaking out b/c i don't know what to do in relation to math inductions!!
If anyone has any specific topic ideas, how i could get started (it has to be original)

Thank you :) I'd appreciate it

TemperedMartensite
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Re: Inductions!!!

Postby TemperedMartensite » Mon Dec 03, 2007 3:04 am UTC

You could do something like other applications of induction outside of purely abstract math proofs. Nothing so obscene as "Induction in Everyday Life" but more along the lines of how it has been used in other disciplines...

Herman
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Re: Inductions!!!

Postby Herman » Mon Dec 03, 2007 3:15 am UTC

Some topic ideas:

- "Regular" induction versus strong induction.
- Proving something by induction and by a "traditional" proof; one example in which each is easier than the other.
- A few inductive "proofs" that are subtly false; and the reason they're false. (There are some non-mathematical "proofs" like this).
- The history of induction.
- Induction on more than one parameter, and for the reals instead of the naturals.
- Rigorous, logical basis of induction (well-ordering principle, etc.)
- Modern significant research that uses induction.
- Induction as used in logic and computer science (structural induction). Compare and contrast to numerical induction.

This is presumably in addition to an intro on the basics of what induction is.

I don't know the specifics of your paper, so maybe one or some or none of these is good. Anyway, good luck!

smileyfaces147
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Re: Inductions!!!

Postby smileyfaces147 » Tue Dec 04, 2007 2:22 am UTC

what original work could i do in relation to "weak" and "strong" induction?? it's due this week so i'm desperate

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Owehn
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Re: Inductions!!!

Postby Owehn » Tue Dec 04, 2007 2:36 am UTC

You could also compare strong induction to transfinite induction, but I'm not sure what you mean by "original work".
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btilly
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Re: Inductions!!!

Postby btilly » Tue Dec 04, 2007 3:36 am UTC

Another topic is relating induction to recursion. Also you could spend some time discussing the Peano axioms.
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glup.up
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Re: Inductions!!!

Postby glup.up » Tue Dec 04, 2007 8:26 am UTC

reverse induction
flawed induction argument
while moronic idle do something (stupid).

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Elenion
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Re: Inductions!!!

Postby Elenion » Tue Dec 04, 2007 12:36 pm UTC

god, i hate induction. i just dont get it - and i know i need to cause it seems to be important in my study (computers). it seems simple when i get it explained but if i try to do it myself i fail every time..hehe. oh well, good luck on your paper:)
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mike-l
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Re: Inductions!!!

Postby mike-l » Tue Dec 04, 2007 5:30 pm UTC

I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2m by induction, and then showing that the nth case implied the n-1th case. Anyone know of a problem that needs to be proved as such?

It has occurred to me in the occasionally that we should teach Well Ordering instead of Induction, since Well Ordering is more 'obvious', and induction proofs easily become well ordering proofs. Plus we get to use contradiction.

Cheers,
Mike
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Torn Apart By Dingos
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Re: Inductions!!!

Postby Torn Apart By Dingos » Tue Dec 04, 2007 5:53 pm UTC

mike-l wrote:I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2m by induction, and then showing that the nth case implied the n-1th case. Anyone know of a problem that needs to be proved as such?

That's how my book proved the AM-GM inequality.

mike-l
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Re: Inductions!!!

Postby mike-l » Tue Dec 04, 2007 7:53 pm UTC

Torn Apart By Dingos wrote:
mike-l wrote:I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2m by induction, and then showing that the nth case implied the n-1th case. Anyone know of a problem that needs to be proved as such?

That's how my book proved the AM-GM inequality.


Sweet, thanks!

Mike
addams wrote:This forum has some very well educated people typing away in loops with Sourmilk. He is a lucky Sourmilk.


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