Order relation question

1. Feb 6, 2004

Ed Quanta

How do you go about proving a statement like n^3>n^2 for n is equal to or greater than 2? I can prove this using mathematical induction, but I am unsure how to show n^3-n^2 is an element of the set of natural numbers without just saying in general that this must always yield a number equal to or greater than 1.

2. Feb 6, 2004

suyver

Can't you just say that because

$$\forall\alpha>1:\alpha n^2 > n^2$$

we must conclude that

$$\forall n>1: n^3 > n^2$$

3. Feb 6, 2004

HallsofIvy

Staff Emeritus
Why not just note that n3- n2= n2(n-1)? As long as n> 1, this will be a positive integer.

4. Feb 6, 2004

Ed Quanta

Yeah, Halls of Ivy, thats what I was thinking. It just looked like too short a proof so I thought I was missing something. Thanks dudes.