Heisenberg's Uncertainty Principle

Last night in physics, we were diving further and further into Quantum Mechanics, and my professor gave us a simple derivation of Heisenberg's Uncertainty Principle. However, there is something I don't get. Maybe you guys can help me out. I get all the stuff at the beginning, but its pretty much the last bit where I'm lost...

http://img.photobucket.com/albums/v4...heisenberg.jpg

Due to Taylor Approximations, for small values of

Thus,

From deBroiglie's Equation, we discover that .

Therefore, .

Using the idea that , We can see that .

Thus,

I understand numerically that , but why is it that we say in the Uncertainty Principle that ???

I'd appreciate any input.

--Chris