Difference between revisions of "Without loss of generality"

(Introductory Level)
(Introductory Level)
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* [[2012_AMC_10A_Problems/Problem_23 | 2012 AMC 12A Problem 23]]
 
* [[2012_AMC_10A_Problems/Problem_23 | 2012 AMC 12A Problem 23]]
 
[[Category:Definition]]
 
[[Category:Definition]]
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=== Advanced Level ===
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* [[2017_USAJMO_Problems/Problem_3 | 2017 USAJMO Problem 3]]

Revision as of 13:01, 27 June 2019

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 $a \ge b \ge c$ without loss of generality because the inequality is symmetric in $a$, $b$ and $c$. 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

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