Do high school students possess any evidence in support of the fundamental theorem of algebra?

[Boojatta]

[msongs]

1. you betcha! nt

[DeadManInc]

2. I'd like to use a life line!

[Uben]

3. I was asked why we needed to study algebra.....

....by my teen-aged daughter. I replied, "So when you grow up and have kids, you will be able to explain it to them."

Ha! That was the best I could come up with!

[eppur_se_muova]

4. No, they accept it on faith.

Because some grownup said so.

[HamdenRice]

5. There is no theorem

Only Zuul.

[Indenturedebtor]

6. I know it's not the classic definition fof a proof

but geometry pretty much convinced me that algebra was "real" :D

[TechBear_Seattle]

10. There are several proofs, actually

All of them (that I know) use induction, ie it can easily be proven for the case where n=1, and we can establish through rigorous logic that it is also true for the case where n=(n+1). Therefore, it must be true for all cases where n is a positive integer because it can be proven for any value n-1.

With induction, the proof of the fundamental theorem of algebra is pretty simple. The problem is that it requires theorems that need limits and group theory to prove, and that sort of stuff is upper division college level material. But then, the proof of the Associative Property of Addition -- that (5+1)+3 = 5+(1+3) -- requires group theory and mathematical field theory, even though most kids understand how the associative property works by second grade.

[Dr. Strange]

7. Sure: why do you think they spend so much time talking about Liouville's theorem in junior high?

[Dead_Parrot]

8. In what respect, Charlie? nt

[caraher]

12. HAHAHA!!!

That's one thing I'll miss about the demise of Palin - cheap laughs!

[TechBear_Seattle]

9. Do you even know the fundamental theorem of algebra?

Can you explain it without quoting the Wikipedia?

[Boojatta]

13. Can I explain it in detail without consulting my own handwritten notes?

No.

Did I create my handwritten notes purely by analyzing the words "fundamental", "theorem", and "algebra" and without attending lectures, reading textbooks, consulting Wikipedia (god forbid!), or otherwise connecting with external sources? No.

However, one would have to demonstrate that whatever inadequacy plagues the author of the poll also makes the poll itself inherently tainted. Otherwise, you haven't demonstrated that there's any problem with the poll itself.

[Random_Australian]

11. Oh wow! Wow! I know what you are talking about because you're on about one of my posts!

I recognise that!

Cool!

Hey, way to use a different (ie. the common) meaning of evidence as well.

In your next post, you should mention that you saw this lady who looked sick buying apples, and your theory was she thought her diet was poor.

You can then ask if you think fruit is a vital part of a healthy diet.

If people talk about fruit and use the definition of 'theory' you've implied and talk about the problem at hand, then you can turn around and say scientists use this definition of theory.

Spot on intellectual honesty there!

In answer to your question, they either know the proof or they don't. This means they are either certain that it is true within the given framework, or completely reliant on trusting other people. No such thing as half a proof in mathematics. ;) Sort of.

P.S. This sprung up from http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=214&topic_id=183020&mesg_id=186394 or GOD strike me dead!

[Boojatta]

14. "way to use a different (ie. the common) meaning of evidence"

How do you extract, from the poll question, what meaning of the word "evidence" is being used?

"Spot on intellectual honesty there!"
I find it troubling that there is some notion of "intellectual honesty" that needs to be distinguished from ordinary, garden variety honesty. Are ordinary people neglecting some important rules of honest discourse that are recognized only by intellectuals?

[Random_Australian]

15. Not being used. eing implied. You can think whatever you want when you write it,

hell, you can even declare the fundamental theorem of calculus to be associativity in addition, but what I am talking about is the way it will be interpreted.

Putting the focus on high school student abilities means everyone who reads it will just use the meaning most likely to be applicable to what you are saying, just like in my example I could mean 'theory' to mean the exact scientific one, but people reading it would skip that meaning as inconsistent with context and go for the normal one.

As for intellectual honesty, who ever said it was not a subset of honesty?