1. ## Compare-numbers

x real number
compare this numbers :

2. Consider different cases:

Case 1: If $\displaystyle x>1$, (eg: 3)
$\displaystyle x^3>x^2>x$

Case 2: If $\displaystyle x=1$,
$\displaystyle x^3=x^2=x$

Case 3: If $\displaystyle 0<x<1$, (eg: 0.5)
$\displaystyle x>x^2>x^3$

Case 4: If $\displaystyle x=0$,
$\displaystyle x^3=x^2=x$

Case 5: If $\displaystyle -1<x<0$, (eg: -0.5)
$\displaystyle x^2>x^3>x$

Case 6: If $\displaystyle x=-1$,
$\displaystyle x^2>x^3=x$

Case 7: If $\displaystyle x<-1$, (eg: -3)
$\displaystyle x^2>x>x^3$

3. Hello : - What is the methodology used to compare the two numbers?
Thanks

4. Originally Posted by dhiab
Hello : - What is the methodology used to compare the two numbers?
Thanks
I edited my previous post. Now does it make sense?

5. Originally Posted by alexmahone
I edited my previous post. Now does it make sense?
Hello : Thank you
that is they are every time to make to study the sign of difference between this nombers two
graphically :

6. Originally Posted by dhiab
Hello : Thank you
that is they are every time to make to study the sign of difference between this nombers two
graphically :
Yes.

It is easier to compare graphically.