Without loss of generality

Without loss of generality is a term used in proofs to indicate that an assumption is being made that does not introduce new restrictions to the problem. For example, in the proof of Schur's Inequality, one can assume that ${a \geq b \geq c}$ without loss of generality because the inequality is symmetric in $\displaystyle a$ , $\displaystyle b$ and $\displaystyle c$ .