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User avatar #81 - aliethecakeis (07/13/2013) [-]
Could also be -2
User avatar #203 to #81 - aliethecakeis (07/14/2013) [-]
I enjoy when my comments spark debates about math.
User avatar #107 to #81 - pebar ONLINE (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 (07/13/2013) [-]
This. caret.
User avatar #117 to #108 - cormy (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 ONLINE (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 (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 (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 ONLINE (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.

#165 to #163 - pebar ONLINE (07/13/2013) [-]
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 (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 (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 ONLINE (07/13/2013) [-]
well, actually it's an operator..... same difference
#106 to #81 - danruaul (07/13/2013) [-]
nice. square root of 4 is also -2. this is nice.
#103 to #81 - articulate (07/13/2013) [-]
It is only positive 2 in principal.

#84 to #81 - trickytrickster has deleted their comment [-]
User avatar #86 to #84 - Harkonnen (07/13/2013) [-]
yes it can... (-2)(-2) is what?
User avatar #101 to #86 - Wtfisthatshit (07/13/2013) [-]
+4...you mean (-2)(+2)
#88 to #86 - trickytrickster has deleted their comment [-]
#85 to #84 - sellatio (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 has deleted their comment [-]
#95 to #87 - sellatio (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 has deleted their comment [-]
User avatar #92 to #87 - Harkonnen (07/13/2013) [-]
- sq 4 is 2 or -2.
#96 to #92 - trickytrickster (07/13/2013) [-]
I'm just gonna go now.
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