Math = God. .. actually, it's 2 and -2 inb4 red thumbs Math = God actually it's 2 and -2 inb4 red thumbs
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> hey anon, wanna give your opinion?
asd
#3 - potatophucker
Reply +143 123456789123345869
(07/12/2013) [-]
**potatophucker rolls 22**
User avatar #8 to #3 - prosusliks
Reply -14 123456789123345869
(07/12/2013) [-]
**prosusliks rolls 15**
Check 'em
User avatar #121 to #3 - tenday
Reply -2 123456789123345869
(07/13/2013) [-]
**tenday rolls 52**
#5 to #3 - potatophucker
Reply +11 123456789123345869
(07/12/2013) [-]
**** yes
#4 to #3 - fireyvoidence [OP]
Reply +12 123456789123345869
(07/12/2013) [-]
Comment Picture
#7 - tazze
Reply +127 123456789123345869
(07/12/2013) [-]
actually, it's 2 and -2   
inb4 red thumbs
actually, it's 2 and -2
inb4 red thumbs
User avatar #74 to #7 - rothingham
Reply -1 123456789123345869
(07/12/2013) [-]
2 OR -2, not AND, OR.
#14 to #7 - anon id: 2ca21213
Reply 0 123456789123345869
(07/12/2013) [-]
Wut.. square root of 4 is 2, not -2
#20 to #14 - yunablade
Reply 0 123456789123345869
(07/12/2013) [-]
You might want to reconsider
You might want to reconsider
User avatar #15 to #14 - palewolf
Reply 0 123456789123345869
(07/12/2013) [-]
No, he's correct, -2 multiplied by -2 is 4. That's basic maths.
User avatar #24 to #14 - nazrix
Reply -2 123456789123345869
(07/12/2013) [-]
x² = 4
√x² = √4
│x│= 2
±x = 2
so,
x = ±2
User avatar #25 to #24 - pooplol
Reply 0 123456789123345869
(07/12/2013) [-]
thats only if you bring in the square root yourself
User avatar #36 to #24 - bronybox
Reply -1 123456789123345869
(07/12/2013) [-]
You are 100% correct, there are two solutions to x^2 = 4, ±2
HOWEVER.

You are wrong in the fact that √x² = √4
It should be ±√x² = ±√4

Because √x is a function (let's denote it f(x) = √x)
f(x) can never equal both 2 and -2 when x = 4 by the definition of a function.
User avatar #192 to #36 - nazrix
Reply 0 123456789123345869
(07/13/2013) [-]
ever heard of an injective function?
f(x) = f(y) => x=y

there are, however, functions that are not injective. quite many.
User avatar #196 to #192 - bronybox
Reply 0 123456789123345869
(07/13/2013) [-]
An injective function is the basic function we always think of, I don't understand what you mean. The square root of x does happen to be an injective function by it's definition.
#191 to #36 - nazrix
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#190 to #36 - nazrix
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User avatar #42 to #36 - metaldrone
Reply -1 123456789123345869
(07/12/2013) [-]
STOP IT!!! I'm learning.
User avatar #37 to #36 - bronybox
Reply -1 123456789123345869
(07/12/2013) [-]
Or rather, you aren't wrong that √x² = √4 , it is simply an incomplete statement.
#17 to #7 - anon id: d605668e
Reply 0 123456789123345869
(07/12/2013) [-]
but thats only if you bring in the square root yourself.
User avatar #23 to #7 - Kelsenial
Reply 0 123456789123345869
(07/12/2013) [-]
Good god that's terrifying
User avatar #53 to #7 - warbob
Reply 0 123456789123345869
(07/12/2013) [-]
square root is a function that is always equal or above 0.
mathematically put : sqrt(x) >= 0
User avatar #75 to #7 - kaxu
Reply 0 123456789123345869
(07/13/2013) [-]
Depends if you are on R or on C
#135 to #75 - anon id: 3d49123d
Reply 0 123456789123345869
(07/13/2013) [-]
It depends on whether one considers the principal square root function or the multivalued relation. Choosing between R and C is irrelevant (for what anyway? domain? codomain?). You can map from reals to reals with a real image and still have both the positives and negatives. It just won't be a function. R vs C is irrelevant.
#112 to #7 - anon id: f7f5f2ea
Reply 0 123456789123345869
(07/13/2013) [-]
That square root sign means only the positive square root. 2 is the right answer.
#130 to #7 - usaisnotamerica
Reply 0 123456789123345869
(07/13/2013) [-]
But still its =2.
#136 to #7 - anon id: 3d49123d
Reply 0 123456789123345869
(07/13/2013) [-]
Nope. This is why notation is critically important.

The radical √n denotes only the principal value. The content only shows the principal root, therefore we should only see positive 2's.
User avatar #148 to #7 - animedudej
Reply 0 123456789123345869
(07/13/2013) [-]
inb4 trip thumbs
#16 to #7 - drfaust
Reply +1 123456789123345869
(07/12/2013) [-]
Actually by definition it's only positive 2. Even though -2 squared is 4, the square root of 4 is 2.
User avatar #21 to #16 - yunablade
Reply +1 123456789123345869
(07/12/2013) [-]
both results are valid, the correct answer is: +/− 2
#29 to #21 - anon id: b408037e
Reply 0 123456789123345869
(07/12/2013) [-]
Both x=+2 and x=-2 are solutions to x^2=4. HOWEVER, sqrt(x) is defined as the POSITIVE solution to x^2=4. Hence sqrt(4)=2 and not +/-2.
User avatar #30 to #29 - yunablade
Reply -2 123456789123345869
(07/12/2013) [-]
Maybe it's a cultural thing, when I took math I was required to express the results to a square root always as +/- (unless imaginary number) and if the root was part of a bigger operation record both results (when the value is negative and when positive)
User avatar #45 to #30 - kabuthefox
Reply +1 123456789123345869
(07/12/2013) [-]
math is "universal"
User avatar #144 to #30 - shredheadxd
Reply 0 123456789123345869
(07/13/2013) [-]
Don't say these things.
User avatar #26 to #16 - deathstare
Reply -2 123456789123345869
(07/12/2013) [-]
-2 * -2 = 4
2 * 2 = 4

(sqrt) 4 = +/- 2
User avatar #60 to #7 - shredheadxd
Reply +1 123456789123345869
(07/12/2013) [-]
If you start with 4, then take the square root, then you are right. The answers are 2, and -2.

But if you start with the square root of 4, then you are wrong. The only answer is 2.

Sincerely,
A 4th year math major, not that anybody cares.
#137 to #60 - anon id: 3d49123d
Reply 0 123456789123345869
(07/13/2013) [-]
Not really. In this case, it's not really clear whether or not we're talking about the just the principal value or not. Unlike written out mathematical notation, words can be ambiguous on this matter. So we clarify,

You start with 4, take the (principal) square root, and you will only have 2. Likewise, if you start with the (principal) square root of 4, then you will still only have 2.
User avatar #143 to #137 - shredheadxd
Reply +1 123456789123345869
(07/13/2013) [-]
On the contrary,
When you do the action of square rooting, you must consider the positive and negative cases. Since you do not know whether the square root was principal or not, you must consider both cases. The positive case is the one shown in the content - the principal square root. The negative case will give you -2.

If you start with simply "square root of 4", you have skipped the action of square rooting, and jump right to evaluating the positive case (the principal square root).

It is quite extremely crystal clear.
User avatar #202 to #143 - bronybox
Reply 0 123456789123345869
(07/13/2013) [-]
Then would you (should you?) not write in the notation "±√4" as opposed to simply writing the notation for the principal square root?
User avatar #204 to #202 - shredheadxd
Reply 0 123456789123345869
(07/14/2013) [-]
Lemme break it down.

±√4 = +√4 AND -√4 (it's "AND" or "OR" depending on the situation)
+√4 = √4 = 2
-√4 = -2

So if you just look at the above statements, you can see that √4 = 2. Not -2. Math don't lie!
User avatar #205 to #204 - bronybox
Reply 0 123456789123345869
(07/14/2013) [-]
Isn't that what I've been saying?
√4 = 2 and only 2
-√4 = -2 and only -2

That's been my point throughout this entire discussion.
User avatar #206 to #205 - shredheadxd
Reply 0 123456789123345869
(07/15/2013) [-]
that's correct! I wasn't sure what you were talking about, but the math wasn't ambiguous so I just reiterated it.
#207 to #206 - ambiguous **User deleted account**
Reply 0 123456789123345869
(07/15/2013) [-]
I stopped looking at porn for this?
I stopped looking at porn for this?
User avatar #208 to #207 - shredheadxd
Reply 0 123456789123345869
(07/15/2013) [-]
I usually get off to my own comments too!
#100 to #60 - anon id: 920f3d4c
Reply 0 123456789123345869
(07/13/2013) [-]
I was going to say this. The difference is subtle, but it's surely there and will affect some problems.
#33 to #7 - bronybox
Reply +4 123456789123345869
(07/12/2013) [-]
Get ready to learn ************(s).

As displayed by the graph of a square root function (shown on the left), there are no negative y values, and thus f(x) can never be negative [ sqrt(2) can never equal - 2 ]. This is because the square root operation IS A function, and thus their can only be 1 y value for every x value (but not necessarily the other way around).

You are stating one of the most common misconceptions people have once they are taught to solve quadratic equations, observe.

1. x^2 = 4
2. x = sqrt (4)
3. x = ± 2

You make the assumption that the square root of 4 is equal to +/- 2, however, by actual mathematical definition, line 2 holds a mistake. This is because x DOES NOT equal sqrt(4). The correct solution is:

1. x^2 = 4
2. x = ± sqrt(4)
3. x = ± 2

Just as you cannot take the square root of a negative number, the square root of a positive number can never be negative. The radical symbol by definition is only the principal square root, i.e., always positive.
User avatar #154 to #33 - kikisu
Reply 0 123456789123345869
(07/13/2013) [-]
Wait wait, you're totally wrong. If the square root of a positive number can never be negative, why is -2 squared 4? That one you have up is only the positive, not negative roots.
User avatar #169 to #154 - bronybox
Reply -1 123456789123345869
(07/13/2013) [-]
You're not understanding the definition of a square root. I even put a graph there and everything.
User avatar #195 to #169 - kikisu
Reply 0 123456789123345869
(07/13/2013) [-]
I am. If you take the root of 4, its both -2 and 2. But if you already have the square root of four, its just two. I do understand the definition of a square root, with is a number that when multiplied by itself gives you the original. -2 times -2 is 4.
User avatar #197 to #195 - bronybox
Reply 0 123456789123345869
(07/13/2013) [-]
I'm saying the square root operation signified by the radix will only yield the positive roots of a number by definition.
User avatar #198 to #197 - kikisu
Reply 0 123456789123345869
(07/13/2013) [-]
If you start with a square root yeah. But if I take a square root it will be both.
User avatar #199 to #198 - bronybox
Reply 0 123456789123345869
(07/13/2013) [-]
But when you take the square root, you are taking the positive and negative root, and you SHOULD technically be using the notation "±sqrt (a)", otherwise what you are writing is simply incorrect by means of notation. You may be doing the right thing in your head, but you're not writing down what you should be.
User avatar #200 to #199 - kikisu
Reply 0 123456789123345869
(07/13/2013) [-]
I never said anything about not having the plus or minus sign. But yeah I see what you mean.
#126 to #33 - anon id: 1ead4bf7
Reply 0 123456789123345869
(07/13/2013) [-]
you sure can take a square root of an imaginary number; you just have to use complex numbers.
[url deleted]
[url deleted]
#128 to #126 - anon id: 1ead4bf7
Reply 0 123456789123345869
(07/13/2013) [-]
forgot about the stupid url deleting
[url deleted] [url deleted] /wiki/Squar e_root
[url deleted] [url deleted] omplex.htm
#125 to #33 - anon id: 454c0a4b
Reply 0 123456789123345869
(07/13/2013) [-]
Math'd. Good job.
#119 to #33 - ningyoaijin
Reply 0 123456789123345869
(07/13/2013) [-]
>using a badly coded graphing software to demonstrate an incorrect point
#201 to #119 - bronybox
Reply 0 123456789123345869
(07/13/2013) [-]
Type the square root of x into any graphing software and I assure you it will either give you that exact graph (might also include the imaginary part as well, a reflection along the y-axis)

Here's an example from Wolfram|Alpha
#134 to #119 - anon id: 3d49123d
Reply 0 123456789123345869
(07/13/2013) [-]
The only bad part I see is "the square root of a positive number can never be negative". However, given the context one can easily tell that he's still referring to the principal square root.

Besides this, how is he incorrect? (unless this is what you meant)
User avatar #59 to #33 - kjelli
Reply 0 123456789123345869
(07/12/2013) [-]
why are you thumbed down, this is correct
User avatar #54 to #7 - mrloverlover
Reply +15 123456789123345869
(07/12/2013) [-]
everyone is replying to this with math equations etc.

and i'm just sat here thinking what the **** is wrong with that dog
#10 - anon id: 7e9a8556
Reply 0 123456789123345869
(07/12/2013) [-]
I don't get it.
User avatar #51 to #10 - intexuz
Reply -10 123456789123345869
(07/12/2013) [-]
found the 12 year old
User avatar #11 to #10 - superpats
Reply +61 123456789123345869
(07/12/2013) [-]
the man on the pedestal is claiming to be something greater, better, or more important than those around him. The man being led away is speaking out and trying to show them that he's not anything more than they are, because the square root of 4 is 2.
#138 to #11 - anon id: 3d49123d
Reply 0 123456789123345869
(07/13/2013) [-]
Reminds me of the film 10,000 BC. "He is not a god!" Whilst prior everyone trembled before him. Yeah, it wasn't a very good movie. I thought it was okay.
#19 - trazyntheinfinite
Reply 0 123456789123345869
(07/12/2013) [-]
Square root of 4 is 2.
Half of 2 is 1.
1+2=3
Half Life 3 Confirmed.
#22 to #19 - sonofawitch
Reply -7 123456789123345869
(07/12/2013) [-]
User avatar #41 to #22 - epicalania
Reply +40 123456789123345869
(07/12/2013) [-]
**epicalania rolls 3**
Three
User avatar #62 to #41 - resbiansrock
Reply +2 123456789123345869
(07/12/2013) [-]
You are my √4 now.
User avatar #44 to #41 - LookinHereWhy
Reply 0 123456789123345869
(07/12/2013) [-]
WELP
User avatar #127 to #22 - pioneermhm
Reply -1 123456789123345869
(07/13/2013) [-]
Yes, it's as easy as 1,2,4
User avatar #39 to #19 - bothemastaofall
Reply +19 123456789123345869
(07/12/2013) [-]
shut up
User avatar #57 - jingleforth
Reply +19 123456789123345869
(07/12/2013) [-]
**jingleforth rolls 44**
#76 to #57 - fireyvoidence [OP]
Reply +3 123456789123345869
(07/13/2013) [-]
Comment Picture
#61 - evilwheatleycore
Reply +14 123456789123345869
(07/12/2013) [-]
**evilwheatleycore rolls 22**
#9 - nexu
Reply +11 123456789123345869
(07/12/2013) [-]
Here's a little trick: Use the windows calculator, get the sqrt of 4 then subtract 2 and see what you get.
User avatar #18 to #9 - pooplol
Reply -1 123456789123345869
(07/12/2013) [-]
the amount of ***** i dont give?
User avatar #31 to #18 - nexu
Reply -1 123456789123345869
(07/12/2013) [-]
That sure is an interesting amount of ***** you don't give. (It's not 0)
User avatar #34 to #31 - pooplol
Reply -2 123456789123345869
(07/12/2013) [-]
i know, but its still less than 0. But it might as well be since its something like .0000000000000000000000000000000008146
#158 to #34 - hopdiggity **User deleted account**
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User avatar #194 to #158 - pooplol
Reply 0 123456789123345869
(07/13/2013) [-]
it was a negative number. I just forgot to put the "-"
User avatar #122 to #9 - ningyoaijin
Reply 0 123456789123345869
(07/13/2013) [-]
The code in the program is only made to recognize a certain number of significant figures. The algorithm they use to calculate square roots must therefore produce very slightly incorrect results.
#151 to #122 - nexu
Reply 0 123456789123345869
(07/13/2013) [-]
Yeah, I know a little bit about how it works. It's just fun to show people things like that, pic related
#149 to #9 - creamcorn
Reply 0 123456789123345869
(07/13/2013) [-]
squirt 4, wut
#40 to #9 - ctfacrylic
Reply +1 123456789123345869
(07/12/2013) [-]
What?? How
#102 - ybigballz
Reply 0 123456789123345869
(07/13/2013) [-]
wait there are 6 2s kneeling then 6/2 is three well do you see where this is going?
#114 to #102 - oxan
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(07/13/2013) [-]
User avatar #131 to #114 - jaknik
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(07/13/2013) [-]
I now wonder what it would be like if a presidential candidate ignored political platforms and just promised the voters game sequels... "America, we have waited too long, elect me president, and WE WILL have Half-life 3!"
User avatar #142 to #131 - sketchE
Reply 0 123456789123345869
(07/13/2013) [-]
most of gamers dont vote anyways
User avatar #146 to #142 - jaknik
Reply 0 123456789123345869
(07/13/2013) [-]
Oh they will.......they WILL....
User avatar #147 to #146 - sketchE
Reply 0 123456789123345869
(07/13/2013) [-]
while more people voted in the 2008 election we still didnt break 65% and millions of black people sat at home
#80 - pearfield
Reply +6 123456789123345869
(07/13/2013) [-]
**pearfield rolls 01**
M = 13
A = 1
T = 20
H = 8

13+1+20+8 = 42
#111 to #80 - anon id: ac252b5a
Reply 0 123456789123345869
(07/13/2013) [-]
I'll give you an A
User avatar #81 - aliethecakeis
Reply +3 123456789123345869
(07/13/2013) [-]
Could also be -2
#84 to #81 - trickytrickster
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#85 to #84 - sellatio
Reply +1 123456789123345869
(07/13/2013) [-]
But every square number has both a positive and negative root, whether or not a sign appears before the root operator.
#87 to #85 - trickytrickster
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#95 to #87 - sellatio
Reply 0 123456789123345869
(07/13/2013) [-]
Length is a scalar, thinking in negative terms confuses calculations, so convention says to work with the positive root. But many times in mathematics, and physics, it is important to consider the negative root also.
#97 to #95 - trickytrickster
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User avatar #92 to #87 - Harkonnen
Reply 0 123456789123345869
(07/13/2013) [-]
- sq 4 is 2 or -2.
#96 to #92 - trickytrickster
Reply -1 123456789123345869
(07/13/2013) [-]
I'm just gonna go now.
User avatar #86 to #84 - Harkonnen
Reply 0 123456789123345869
(07/13/2013) [-]
yes it can... (-2)(-2) is what?
User avatar #101 to #86 - Wtfisthatshit
Reply 0 123456789123345869
(07/13/2013) [-]
+4...you mean (-2)(+2)
#88 to #86 - trickytrickster
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#91 to #88 - mericaisgreat
Reply +4 123456789123345869
(07/13/2013) [-]
Comment Picture
#106 to #81 - danruaul
Reply 0 123456789123345869
(07/13/2013) [-]
nice. square root of 4 is also -2. this is nice.
User avatar #203 to #81 - aliethecakeis
Reply 0 123456789123345869
(07/14/2013) [-]
I enjoy when my comments spark debates about math.
#103 to #81 - articulate
Reply +1 123456789123345869
(07/13/2013) [-]
It is only positive 2 in principal.

User avatar #107 to #81 - pebar
Reply +4 123456789123345869
(07/13/2013) [-]
actually it's not
if x²=4, then x could be -2
but the function itself cannot be negative
User avatar #110 to #107 - articulate
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(07/13/2013) [-]
This. caret.
User avatar #108 to #107 - pebar
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User avatar #117 to #108 - cormy
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(07/13/2013) [-]
I'm confused, where in your back up did it state that the function itself could not be negative? It said it COULD be, but we disregard it for the sake of simplicity.
#118 to #117 - pebar
Reply 0 123456789123345869
(07/13/2013) [-]
It said it could be DEFINED as such, but it is not currently because that wouldn't be as simple.
A function by definition cannot produce multiple outcomes so the range is restricted.
User avatar #210 to #118 - demandred
Reply 0 123456789123345869
(07/17/2013) [-]
f(x)=sqrt(x) is (in this case) a function that takes on the positive value of the sqrt of x. This bechause what you said, for a given x, f(x) can only have one value, so we forget about the negative one. It's still a solution to f(x) tho.
User avatar #163 to #118 - AeroChic
Reply 0 123456789123345869
(07/13/2013) [-]
I'm also confused. Since this picture is not stating whether it's a function or not, wouldn't the negative still be considered?
User avatar #176 to #163 - pebar
Reply 0 123456789123345869
(07/13/2013) [-]
this should explain it better

Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign.

en.wikipedia.org/wiki/Nth_root#Square_roots
#165 to #163 - pebar
Reply 0 123456789123345869
(07/13/2013) [-]
No.
The radical sign is itself a function (the f(x)= means it's a function too). If you want to include the negative half, you have to write it like so.

User avatar #211 to #165 - demandred
Reply 0 123456789123345869
(07/17/2013) [-]
plus/minus sign indicates two solutions. The square root of a number has two real solutions. What you wrote has therefore 2*2=4 solutions, it's just that (in the case of x=4) the solutions ++2 and --2 are identical, just as -+2 and +-2. therefore, in the case you wrote, the plus/minus sign adds no information, it merely reminds us that square roots do indeed have two real solutions - one positive and one negative.
User avatar #178 to #165 - AeroChic
Reply 0 123456789123345869
(07/13/2013) [-]
I know that the plus or minus is used to demonstrate that's it's both solutions, but when we first learned about square roots in middle school or whenever, we were taught that they always had two solutions without the plus or minus. However, once into harder math courses, the plus or minus sign was used for clarification. I thought that technically it still had two solutions, but you just used the principal value.
User avatar #171 to #165 - pebar
Reply 0 123456789123345869
(07/13/2013) [-]
well, actually it's an operator..... same difference