What a wonderful thread. Are we talking real or complex numbers here?
I think Richard is confusing logic and common sense. The common sense square root of 16 is 4, the logical square roots are -4 and 4.
You thought someone with his avatar would understand logic…
What do you think of quantum physics Richard ? That’s completely logical, but makes no sense, how can something be in 2 places at once ?
I think Richardm has an evil twin :s
Apparently we’re talking playskool math. Mommy, what is a function?
[quote=“Notsu”]I think Richardm has an evil twin :s[/quote]Yes, a negative Richardm to go with the positive Richardm, they are both square roots of Richardm squared.
[quote=“Richardm”]Matthew, if you had a brain you’d take it out and play with it.[/quote]Mods, he’s picking on me ! Personal insults are against the rules, you pointy eared nob.
I just love teaching mathematics to dimwits.
[quote=“Big Fluffy Matthew”]
What do you think of quantum physics Richard ? That’s completely logical, but makes no sense, how can something be in 2 places at once ?[/quote]
I think wave/particle duality is a little too complex for our buddy here. Perhaps we should teach quadratic equations first, to ease him into the idea that there can be two solutions for x (or three, or four, for that matter)
when solving for x in the following equation:
A(x)^2+B(x)+C=0
use the following formula,
(-B + and - (B^2 - 4(A)©)^(1/2))/(2(A))
you’ll see that the (+ and -) part allows for two solutions for (X), which, when graphing the equation, will be obvious to the naked eye.
I’m no math whiz, but. . .
Assume X = 4
X squared = 16
the square root of X squared = 4
Therefore, the square root of X squared = X
But, isn’t Mathew correct that. . .
If X = -4
X squared = 16
the square root of x-squared = 4
Therefore, the square root of X squared = -X
So the correct answer is X or -X, right?
There’s the understatement of the year.
Wrong!
It’s the absolute value of x. End of story. See you later. Bye bye.
it should be duely noted to Richards defense, that when graphed, the function (x^2)^(1/2) is an exact replica of the absolute value of X graph.
online graphing utility
In searching for the truth, and thinking really hard about why a graph would represent it as the absolute value of x, it seems there might be an explaination.
order of operations
in that function (x^2)^(1/2), you are first squaring x, which, no matter what, produces a positive number…
x * x will always be an absolute value, never negative
then, taking the square root of an absolute value is, indeed, an absolute value.
Sorry for doubting you Richard, but I can admit when I’m wrong
There’s the understatement of the year.
Wrong!
It’s the absolute value of x. End of story. See you later. Bye bye.[/quote]
Give me a break teacher, I’m an English major. Can you please show me where I went wrong in my answer.
Edit: oh, maybe I’m starting to understand.
If X = -4, then apparently 4 does not = -X (but is only the absolute value of X). Is that true?
If so, then I’ll give you credit for your answer spock.
[quote=“axiom”]it should be duely noted to Richards defense, that when graphed, the function (x^2)^(1/2) is an exact replica of the absolute value of X graph.
online graphing utility
In searching for the truth, and thinking really hard about why a graph would represent it as the absolute value of x, it seems there might be an explaination.
order of operations
in that function (x^2)^(1/2), you are first squaring x, which, no matter what, produces a positive number x * x will always be the absolute value of x
then, taking the square root of a the absolute value of x squared is, indeed, the absolute value of x.
Sorry for doubting you Richard, but I can admit when I’m wrong[/quote]
Sometimes an extra chromosome can come in handy.
The reasoning is totally incorrect, but the answer is right.
then, please, do enlighten me with the correct reasoning.
[quote=“Mother Theresa”]
Edit: oh, maybe I’m starting to understand.[/quote]
From understatement to overstatement.
It is the absolute value of x by definition. It cannot be proved. (Or is that proven?)
A function cannot result in two values.
[quote=“Richardm”]
A function cannot result in two values.[/quote]
I don’t know about that
take: (3x^3)+(10x^2)+(5x)…when x=0, y has three values.
furthermore, I’m not too sure the absolute value thing make all that much sense anymore
[quote=“RichardM”]
It cannot be proved.[/quote]
No, but it can be proven wrong
the “function” you have given us is, f(x)=(x^2)^(1/2), which can be simplifed to simply f(x)=x…that’s simple mathmatical laws.
Graphing utility or not.
[quote=“axiom”]take: (3x^3)+(10x^2)+(5x)…when x=0, y has three values.
[/quote]It’s the other way around, when y=0, x can one of 3 values
can have 1,2 or zero solutions
[quote=“Big Fluffy Matthew”]It’s the other way around, when y=0, x can one of 3 values
[/quote]
my bad
The emphasis on simple.
Lord, you give them eyes but they cannot see the difference between a function and an equation. Please smite them.
The emphasis on simple.
Lord, you give them eyes but they cannot see the difference between a function and an equation. Please smite them.[/quote]
you offer alot of insults, but no real explanation…other than “it can’t be explained”…yeah, that’ll hold up in a scientific and mathmatical society
and the emphasis on “simple” was put in to add bewillderment to the fact that you can’t understand it.
http://en.wikipedia.org/wiki/Square_root#Properties Points 2 and 3 (Which I presume was written by someone with more mathetical knowledge than all of us put together) Explains the difference between a square root (with 2 results) and a principle square root (with one value).
Point 5 clearly says 
which proves that Richard was right all along, :eh:
Look Richard, you can’t say “just because it is”, this is the International Politics forum, you have to give some proof or a link or something.