# How to understand math Unboundedness

1. Oct 11, 2005

### pinki82

Max (x_1)
x_1 - x_2 <= 1
x_1, x_2 >= 0

is obviously 'Unbounded'.

But i dont really understand this.. How do we know that it is
Unbounded??
what does it mean by Unboundedness?

2. Oct 12, 2005

### HallsofIvy

Staff Emeritus
"Unbounded" means precisely that! It has no bounds. In this case it is the fact that x1 and x2 are required to be non-negative but there is no "bound" on how large they can be. If we were given:
x1>= 0, x2>= 0 and x1+ x2<= 1, then that last inequality would bound x1 and x2- since they are non-negative and their sum[\b] can't be larger than 1, neither can be larger than 1.

However, because the condition is that x1- x2<= 1, there is no "bound", x1= 10000000, x2= 9999999 fit all conditions as does x1= A, x2= A-1 for any positive number A.