In the derivation of the generalized uncertainty principle (as pgs 1-2 of here), there is an anticommutator term that is dropped at the end, leaving just the commutator part...this is said to "strengthen" the relation, as both terms are positive. I don't understand this. So we basically have C>A+B, and we are dropping B. Then we are lowering the lower limit of the uncertainty, which I interpret as making the relation 'looser' rather than 'stronger'. Can anyone try convincing me otherwise? Thanks!