- #1
Saladsamurai
- 3,020
- 7
Homework Statement
Prove that if 0≤x<y then xn < yn
Homework Equations
12 properties of numbers.
The Attempt at a Solution
For the case: 0 =x < y is trivial.
So now we just need y > x > 0 :
Now, I am having a bit of trouble with this. Take the case where n=2:
x < y
so x*x < x*y AND x*y < y*y and so by transitivity x*x < y*y.
But when I upgrade to being arbitrary:
x < y
x*xa < y*xa AND x*ya < y*ya
but I cannot make the connection by transitivity.
Is there a completely different approach for this that I am overlooking?