Proving (x^2)>0: A Simple Guide

[cacosomoza]

Pretty simple, how do I prove (x^2)>0 ?

 

[jegues]

Pretty simple, how do I prove (x^2)>0 ?

Why not use induction and try to prove it?

 

[cacosomoza]

x belongs to R, not N, so I cannot apply induction

 

[fluxions]

Assuming you meant to indicate that x is not equal to zero, then either x < 0 or x > 0.
Try using this property: If x < y and z > 0, then xz < yz, examining each case separately.

 

[JonF]

Pretty simple, how do I prove (x^2)>0 ?

Well how you wrote it, it isn’t true since 0^2 = 0. You probably meant x^2 ≥ 0.

Since this is in the calculus and beyond forum do you know how to find minima for a function?

EDIT:
Or you could use the properties: that a positive real times a positive real is greater than 0, a negative real times a negative real is greater than 0.

 

[HallsofIvy]

Part of the requirements for any "ordered field" (which includes the field of real numbers but not the field of complex numbers) is that "if a< b and c> 0, then ac< bc". Take a= 0, b= x, c= x.

 

[JonF]

Part of the requirements for any "ordered field" (which includes the field of real numbers but not the field of complex numbers) is that "if a< b and c> 0, then ac< bc". Take a= 0, b= x, c= x.

slick