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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 property|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 WOLOG when you mean "''with'' loss of generality"!
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| − | WLOG means that it is ok to assume a value for a variable, or other such unknown, in order to solve the problem. This is often done in problems concerning ratios, or any other value that remains constant regardless of what is assumed
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| − | == Example Problems ==
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| − | === Introductory Level ===
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| − | * [[2006_AMC_10B_Problems/Problem_14 | 2006 AMC 10B Problem 14]]
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| − | * [[2006_AMC_10B_Problems/Problem_17 | 2006 AMC 10B Problem 17]]
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| − | * [[2006_AMC_12A_Problems/Problem_20 | 2006 AMC 12A Problem 20]]
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| − | * [[2007_AMC_10A_Problems/Problem_19 | 2007 AMC 10A Problem 19]]
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| − | * [[2012_AMC_10A_Problems/Problem_23 | 2012 AMC 10A Problem 23]]
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| − | * [[2021_AMC_10A_Problems/Problem_25 | 2021 AMC 10A Problem 25]]
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| − | [[Category:Definition]]
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| | === Advanced Level === | | === Advanced Level === |
| | * [[2017_USAJMO_Problems/Problem_3 | 2017 USAJMO Problem 3]] | | * [[2017_USAJMO_Problems/Problem_3 | 2017 USAJMO Problem 3]] |
