/sci/ - Science & Math

its been bugging me too

http://tinyurl.com/4lwblno

With a sage

>inb4 thousands of mathematicians

2

+/-2

Rain or shine, I'll root for you

>>2505044

±2

It's just 2. The square root of 4 refers only to the principal root, ie. the positive root of x^2 = 4. So x^2 = 4 has two solutions, ±√(4) where √(4) = 2 and ≠ – 2.

everyone who says "+-2" is a retarded piece of shit.

The symbol displayed in the op is a bijection from the positive reals into the positive reals (in particular, it's function, so it can only have one value).

There's a difference between the square root function and the set of solutions to some quadratic equation.

inb4 the children go fuck fulltard on this

>>2505046
>mfw slaanesh is on this board
>mfw 40k fags are on this board

>>2505084
>>2505087
I disagree

>>2505092

Look it up on Wolfram Mathworld. Come on this is grade ten math, probably even in West Virginia.

>>2505092
I care.

to everyone who says +/-2, what is <span class="math">\sqrt[3]{8}[/spoiler]?

>>2505087

Dumbfuck. Rainbow means ±.

>>2505121
2

>>2505025
I don't see a question

>>2505131
But the equation x^3 = 8 has three distinct solutions.

Why do you include both solutions for quadratic equations but throw away two solutions for a cubic?
WHAT THE HELL, MAN?

I can still remember when I learned about roots in school. I just couldn't accept <span class="math">\sqrt4=+2[/spoiler] for just the same reasonst most people here want to have a <span class="math">\pm[/spoiler] here.
On the other hand, I wasn't trying to talk about math to others. (For a reason. Please follow my example.)

>>2505121
+/-2

>>2505142

i thought we were talking about real solutions

>>2505150

But (–2)^3 = (–2)(–2)(–2) = (4)(–2) = –8 so it's not a solution.

Looks like /sci/'s having more trouble with this than integrating 1/x dx.

>>2505142
Solutions are undefined unless some algebra is given.
Consider an anticommutative whatever; <span class="math">x^n=y[/spoiler] has no solutions there for <span class="math">y\neq 0, n>1[/spoiler]. ;)

>>2505121
³√8={2, -1+i√3,-1-i√3}

>>2505164

>implying the cube root of 8 is a set

sort your fucking notation out bitch

>>2505156
wat? The term "algebra" has a very precise meaning, and I doubt you're talking about that.

Perhaps you mean talking about the solution set of an algebraic equation is meaningless without saying what ring the solutions are supposed to lie in?

I would be inclined to agree, though I can say for certain that by context one could have concluded I was talking about the complex numbers.

>>2505168
he got it right, you need to shut your cornhole

If we take this question into the complex imaginary plane...
Z^2=4
Z = sqrt(4)
Z = sqrt(4cis0) or sqrt(4cis2Pi)
Z = 2cis(0pi) and 2cis(Pi)

2cis0 = 2
2cis(pi)= -2

Your argument is invalid.

the rainbow of the square root of 4?

not sure. Ask an engineer.

sure is high school in here

http://en.wikipedia.org/wiki/Fundamental_Theorem_of_Algebra

>>2505173

fuck no i won't. fix that fucking notation or i'll stay here yelling all fucking night. this isn't high school, it isn't enough that i "know what he meant."

>>2505168
This guy knows what he's talking about.

All you fools, if √(4) = ±2, how do I denote only the positive or only the negative square root of 5? It's a definition issue. The only way that I can distinguish between the positive and negative square roots of 5 is if √(5) is either only positive or only negative.

End of thread.

>>2505181
you're right, this isn't high school, this is 4chan. lol yell all day bro.

>>2505168
>implying that everything in mathematics isn't defined as a set.

Amateur Mathfags lookie here.

|4^½| = 2
4^½= ±2

Now wheres the Dinosaurs at?

if x^2=4, then x=±2
but √4 = 2, as √ only indicates the positive root

>>2505181

fn:C->C:z|->z^n
The inverse image of the singleton set is the set of nth roots of that element which in itself is a set
Thus f3^-1({8})={2, -1+i√3,-1-i√3}

>>2505025
It looks like a sort-of-nerdy romantic card:
"Rainbow over two".

>>2505248
I thought it meant the answer could go both ways.

>>2505168
>>2505181

[Spoiler] it is a set
>http://en.wikipedia.org/wiki/Fiber_%28mathematics%29

yeah the cube root function is NOT taking the preimage of the complex function z mapsto z^3, fucktard. Never has been, never will be.

inb4 hurf

>>2505256
Hmmm, I think I see what you did there.

you guys are stupid...

...im pretty sure this is a refrence to

DOUBLE RAINBOW(ya know, 2 x raindbow is double the raindbow)

>yeah the cube root function is NOT taking the preimage of the complex function z mapsto z^3, fucktard. Never has been, never will be.

The cube root function can't have more than one output. To find all z such that f(z)=z^3=8 you need to take the preimage of 8 for f.

>>2505305
I'm surprised and somewhat disappoint a chan board didn't jump at that. Then again, I hail from [a/ so I get bewildered when it doesn't rain liquid gay.