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 without loss of generality because the inequality is symmetric in , and . Without loss of generality is often abbreviated WLOG or WOLOG. Be sure not to write WLOG when you mean "with loss of generality"!

Example Problems

Introductory Level

• 2006 AMC 10B Problem 17
• 2007 AMC 10A Problem 19
• 2006 AMC 12A Problem 20
• 2012 AMC 12A Problem 23

Advanced Level

• 2017 USAJMO Problem 3