Favorite Equation: Quadratic Formula - Solving for X

[Gib Z]

First Point- I don't get you d_leet...
Second Point - Z being the set of integers in an american thing isn't it? I've always seen it like that from the internet and stuff, but when my teacher did it he said it was J, i put my hand up and said it was noramlly Z wasn't it? He said its an american thing, so i wasn't totally incorrect, but that didn't stop my stupid class for laughing at me. They seem to think I am a pompus bigot who thinks I know everything, and they love to see me get something wrong. Hate it!

 

[ssd]

http://www.doug-long.com/einstein.htm

That is Einstein to me.

 

[d_leet]

First Point- I don't get you d_leet...

My point was more or less that there are algebraic system/structures(I'm not sure which would be the correct term) where 1+1 does not necessarily equal 2, well even this might be incorrect because in the group Z₂ 1+1 does at least belong to the equivalence class of 2.. namely [1]+[1]=[2]=[0], where [a] represents the equivalence class of a, and a relates b if and only if 2 divides a-b. I'm not completely sure of the correctness of any this at the moment because I'm tired and it still is fairly new to me so if anyone would care to make a correction please feel free, however, I believe my point still stands that there are algebraic systems where 1+1 is not necessarily equal to 2.

Second Point - Z being the set of integers in an american thing isn't it? I've always seen it like that from the internet and stuff, but when my teacher did it he said it was J, i put my hand up and said it was noramlly Z wasn't it? He said its an american thing, so i wasn't totally incorrect, but that didn't stop my stupid class for laughing at me. They seem to think I am a pompus bigot who thinks I know everything, and they love to see me get something wrong. Hate it!

I'm not sure about this, I've always seen it in textbooks as Z, but then again I live in America, and all the textbooks I have seen were written here as well, so i don't think I can really answer this one way or another.

 

[theperthvan]

I'm an Aussie and have only seen Z for the set of integers.

 

[Gib Z]

My teacher said all schools in New South Wales had J in the syllabuss and not Z.

Im guessing that you live in Western Australian, thePERTHvan, so maybe that's why.

 

[theperthvan]

Indeed I do

 

[Gib Z]

That post is 9 characters long! I thought PF has a minimum of 10 and that spaces don't count.

EDIT: I tried posting 10 spaces, didnt work.

 

[murshid_islam]

< 10

 

[uart]

My teacher said all schools in New South Wales had J in the syllabuss and not Z..

That's quite interesting GibZ. Personally I've only ever seen Z used but I have to admit that J seems a bit more intuitive. Still I'd prefer to have a standard (world wide) convention for it, whatever that standard happened to be.

 

[CRGreathouse]

I'm in the US and have seen J for integers, but only once and then only in high school. I've never read a paper from Australia that used anything other than Z for integers, and I've read maybe a dozen number theory papers from Australian authors.

 

[quasar987]

Z being the integers is certainly not just an american thing. And in fact it's primarily a german thing as Z is for 'Zahlen' (numbers). Before english, german was the official language of science and many words have their origin in german. For instance, what we call fields in english are 'Körper' in german, meaning "body" and the french word for field is 'corp', meaning "body" as well. 'Ring' is the litteral german translation of 'Zalhring', a term first coined by Hilbert according to Wiki.

An example from physics: the partition function, conventionally noted Z, stands for 'Zugstansum' (probably spelt wrong) meaning 'sum over all states'.

 

[Gib Z]

I want a stand world wide one too! I don't care, Z or J, though i think Z looks better in BlackBold :)

 

[PhilosophyofPhysics]

- \frac{\hbar^2}{2m}\nabla^2\Psi +V\Psi = i\hbar\frac{\partial\Psi}{\partial t}<br />

 

[Gib Z]

Nice. Very nice. You do Schrodinger proud.

 

[theperthvan]

Nice. Very nice. You do Schrodinger proud.

How can he be proud if he is dead?

 

[Gib Z]

>.<"

Have you observed him dead? Hes in a superposition of many states, one of them in which he is alive and proud! :P

 

[murshid_islam]

great answer, Gib Z.

 

[PhilosophyofPhysics]

e^{i\theta}=\cos\theta + i \sin\theta

This has already been mentioned but I thought it was the coolest thing ever when using series to show it.

 

[Plastic Photon]

Laplace L(f)=integral(e^(-sx))(f)dx

 

[Thrice]

Us physics guys chiming in

G_{\mu \nu}=T_{\mu\nu}

(screw the 8pi)

 

[Sir]

\int_{-\infty}^{+\infty} e^{-x^{2}} = \sqrt{\pi}

 

[robert Ihnot]

\frac{\pi^2}{6} = \sum_{n=1}^{\infty} \frac{1}{n^2}

\frac{\pi^4}{90} = \sum_{n=1}^{\infty} \frac{1}{n^4}

Discovered by Euler, who continued to study the Riemann Zeta-function,


\varsigma(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}

And, as uart tells us on page 1: \prod_{n=1}^\infty \frac{1}{1-(1/p_n)^a} = \sum_{n=1}^\infty 1/n^a

 

[AKG]

My point was more or less that there are algebraic system/structures(I'm not sure which would be the correct term) where 1+1 does not necessarily equal 2, well even this might be incorrect because in the group Z₂ 1+1 does at least belong to the equivalence class of 2.. namely [1]+[1]=[2]=[0], where [a] represents the equivalence class of a, and a relates b if and only if 2 divides a-b. I'm not completely sure of the correctness of any this at the moment because I'm tired and it still is fairly new to me so if anyone would care to make a correction please feel free, however, I believe my point still stands that there are algebraic systems where 1+1 is not necessarily equal to 2.

There are algebraic systems where there is a 1 and a + but no 2, and hence in such systems "1 + 1 = 2" is not true (but only because it has no meaning; there is no use for a symbol '2' and hence there is none). But any algebraic system with a 1, a +, and a 2 will have 1 + 1 = 2. [Unless someone purposefully makes a senseless interpretation of the symbols]

 

[AKG]

Yeah, it obviously does. But WHAT if it didn't?

Are you calling Hilbert an "it"? :) No listen, the guy said "we defined 1 + 1 to be 2" so we did it, not an "it". So what if we didn't define it that way? Then everything would be the same as it is today, we'd just be using different symbols.

 

[theperthvan]

Not too sure what you're saying.
If you mean that we, mathematicians, human beings, whatever, decided that we will make 1+1=2, then good. Have a lolly.
Even if it is defined differently, the fact still remains that if Bob has an apple and Sally gives him another apple, Bob now has two (whatever two means) apples, which is what I meant. Not really talking about how it is written or what base is being used or any definition stuff, just the concept.

 

[davidpetertuc]

If this were one of the physics forums, I'd probably cite Maxwell's Equations. But since this is the world of math, I'm definitely going to have to go with the Fundamental Theorem of Calculs. But Uart's example was also interesting...



This, I must admit, is pretty awesome. I wonder how it's derived, especially since there's no obvious formula for calculating the nth prime.

This formula is even better. If n=2 then is equals PI^2/6

 

[Mike_Bson]

lim Re(zeta(1 + ix)) = gamma
x to 0

It's awesome because it involves the coolest function ever, and the coolest constant ever.

I tried to write it with Latex, how do I make it appear in my post?

 

[zgozvrm]

I would have to say "I = 1,000,000,000"

where I represents me, and 1,000,000,000 represents the amount of money in my bank account.

 

[n1person]

\int_\Omega \mathrm {d}\omega = \oint_{\partial \Omega} \omega

Stokes Theorem, so useful all the time...

 

[hgfalling]

The story about L'Hopital's rule being work for hire done by Bernoulli because L'Hopital wanted to have something named after him, which now all first year calculus students hear about, is awesome.