$$\\

\mathbb{R}\textup{ is the set of real numbers. For any number }x\textup{ in }\mathbb{R:}\\

x^2\geq 0\\

(x^2)^{1/2}\geq 0^{1/2}\\

x^{2\times1/2}\geq 0\\

x^1\geq 0\\

x\geq 0$$

Are all these calculations correct ? Or is there some form of miscalculation ?

EinsteinJr
May 2, 2015

#3**+5 **

Thanks EinstienJr,

did you already know the problem with the question?

If you did you really should say so up front because otherwise, one day you will ask a 'real' question and I will think,

I won't answer that because I am buy and I expect that he/she already knows the answer. :)

Melody
May 3, 2015

#1**+5 **

There is a bit of a problem here Einstein,

I have been struggling with exactly the same problem on complex number questions lately.

$$\\(x^2)^{1/2}>0\qquad true\\\\$$

consider

$$\\x^2=36\\

\sqrt{x^2}=\pm 6\\

$I put the square root in so both answers are valid$\\$$

so

$$\\(x^2)^{1/2}\ge0\\

\pm x \ge0\\

$either $x\ge0\;\;or\;\;-x\ge 0\\

$either $x\ge0\;\;or\;\;x\le 0\\

$Hence x is any real number $$$

Melody
May 2, 2015

#3**+5 **

Best Answer

Thanks EinstienJr,

did you already know the problem with the question?

If you did you really should say so up front because otherwise, one day you will ask a 'real' question and I will think,

I won't answer that because I am buy and I expect that he/she already knows the answer. :)

Melody
May 3, 2015