Difference between revisions of "Without loss of generality"

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'''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 <math>a \ge b \ge c</math> without loss of generality because the inequality is [[symmetric]] in <math>a</math>, <math>b</math> and <math>c</math>.  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 ===
=== Advanced Level ===
* [[2006_AMC_10B_Problems/Problem_17 | 2006 AMC 10B Problem 17]]
* [[2017_USAJMO_Problems/Problem_3 | 2017 USAJMO Problem 3]]
* [[2007_AMC_10A_Problems/Problem_19 | 2007 AMC 10A Problem 19]]
* [[2006_AMC_12A_Problems/Problem_20 | 2006 AMC 12A Problem 20]]

Latest revision as of 12:47, 30 July 2021

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