Math help (3 Viewers)

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Well it was a joke about the rep, if rep was still back, my motivation for posting would be because Im bored, I want to benefit my own understanding by teaching someone else, and I want to help. Rep is as it always should be, a positive side-effect of being what I presume to be helpful.

Looking at wikipedia Fundemental Theroem Of Algebra says:


Where k is a complex number, kx has at least one complex root?

That is not the FTA. Just a specific (and rather trivial) case of it.

 

[Sy123]

Re: Math help (Because Carrot made me do this)

Oh yes hang on I read it wrong...oops.
So:


Where the a's can be any number (real, complex), so this polynomial must have at least 1 complex root?
Thanks for clarification

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

but srsly, i dont understand why someone just tutors fawun in person

seriously.

i appreciate the very long explanations, Sy, but... i dunno. i just see all these WoTs, nicely written, but... i'm just thinking in the back of my mind "all this effort, and he doesn't need it!"

arguably more time consuming, but i think she'd also get more out of it

but if you feel you're getting something from them too - then don't worry about it.



And, I'm just remembering things by mentioning it. It's a method.

So... Gauss proved the FTA in his doctoral thesis - which we'll assume is very long and laborious, and apparently it took him three years. Alternatively, we can use complex analysis methods - so you have a non-zero polynomial, p, in the complex plane, therefore its reciprocal 1/p is an entire function... *three lines of handwaving*, contradiction. FTA proved.


Also, FTA is basically every polynomial has at least one complex root

 

[deswa1]

Re: Math help (Because Carrot made me do this)

^I don't get how Gauss' proof of FTA versus modern proof techniques has anything to do with Fawun's situation... Explain?

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

^I don't get how Gauss' proof of FTA versus modern proof techniques has anything to do with Fawun's situation... Explain?

metaphorical


if i want to prove FTA, i use modern techniques - because it's easier and less laborious

i argue that helping fawun in person is easier and less laborious than numerous posts


It's like teaching people how to paint by writing a book on it with no pictures.

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

metaphorical


if i want to prove FTA, i use modern techniques - because it's easier and less laborious

i argue that helping fawun in person is easier and less laborious than numerous posts


It's like teaching people how to paint by writing a book on it with no pictures.

To establish the validity of these "modern techniques" one has to write considerably more than 5 lines. There are proofs that do not require so much machinery.

Eg Gauss' doctoral proof of FTA wasn't completely justified, he appealed a bit to geometric intuition and it was quite some time until his assumptions were justified. But D'Alembert's original attempt at a proof (whilst not entirely rigorous at the time) can be justified now...and if we were to write every line of the proof from axioms to FTA then D'Alembert's would be considerably shorter / easier than using Liouville's / some equivalent complex analytic result.

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

guys, come on - it's metaphorical


you're not going to reply to someone who said "the assignment was easy as pie": "lolwat we didn't eat the assignment - how is pie even easy lolololololol u so silly"


the metaphors purpose is to highlight two equivalent ways of doing something, one easy and one difficult - and one choosing the difficult option.

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

How about we stop going off on tangents, and stick to answering Fawun's questions for now. The issue of her having a private vs. class tutor is something you can PM her about, or talk about in the Chit Chat thread.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Hi.

I need help in graphing again (Yes I know what you're thinking).

How would you sketch this:



All I have so far are the intercepts for which when you sub x=0 and y=0, my intercepts for x and y are both 0.
I also know that it's a hyperbola because it has an x as the denominator.

:s

 

[RealiseNothing]

Re: Math help (Because Carrot made me do this)

Hi.

I need help in graphing again (Yes I know what you're thinking).

How would you sketch this:



All I have so far are the intercepts for which when you sub x=0 and y=0, my intercepts for x and y are both 0.
I also know that it's a hyperbola because it has an x as the denominator.

:s

It approaches 1 as x goes to plus and minus infinity.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

It approaches 1 as x goes to plus and minus infinity.

wat

 

[RealiseNothing]

Re: Math help (Because Carrot made me do this)

wat

You done limits yet?

 

[Fawun]

Re: Math help (Because Carrot made me do this)

You done limits yet?

The ones where you factorise and sub in the thing? yeah. I've also done discontinuity thing and that's about it.

I just don't get the whole infinity stuff.

 

[RealiseNothing]

Re: Math help (Because Carrot made me do this)

The ones where you factorise and sub in the thing? yeah. I've also done discontinuity thing and that's about it.

I just don't get the whole infinity stuff.

How about dividing the top and bottom by the highest power of the denominator?

 

[Fawun]

Re: Math help (Because Carrot made me do this)

How about dividing the top and bottom by the highest power of the denominator?

I can't tell if this is a question on if I have done it before or if it's like suggestion on what I should do to solve the question :s

 

[deswa1]

Re: Math help (Because Carrot made me do this)

How about dividing the top and bottom by the highest power of the denominator?

Or cheat- pick a very big number on your calc (like 10^30) and sub it in- you'll get one so the curve approaches one as x approaches infinity (yes this is not rigorous but it'll defs work for your questions)

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Or cheat- pick a very big number on your calc (like 10^30) and sub it in- you'll get one so the curve approaches one as x approaches infinity (yes this is not rigorous but it'll defs work for your questions)

??

So I sub the big number like 10^30 into the function as the x?

so it will be like:



Am I doing it right?

 

[RivalryofTroll]

Re: Math help (Because Carrot made me do this)

??

So I sub the big number like 10^30 into the function as the x?

so it will be like:



Am I doing it right?

Yep and what do you notice?

y approaches 1 as x approaches infinity.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Yep and what do you notice?

y approaches 1 as x approaches infinity.

So how are you suppose to graph that? :s

 

[RealiseNothing]

Re: Math help (Because Carrot made me do this)

Or cheat- pick a very big number on your calc (like 10^30) and sub it in- you'll get one so the curve approaches one as x approaches infinity (yes this is not rigorous but it'll defs work for your questions)

or L'Hopital the fuck out of the fraction.