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 \geq b \geq c}</math> without loss of generality because the inequality is symmetric in <math>\displaystyle a</math>, <math>\displaystyle b</math> and <math>\displaystyle c</math>. Without loss of generality is often abbreviated "WLOG." Be sure not to write WLOG when you mean "with 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 <math>{a \geq b \geq c}</math> without loss of generality because the inequality is symmetric in <math>\displaystyle a</math>, <math>\displaystyle b</math> and <math>\displaystyle c</math>. Without loss of generality is often abbreviated "WLOG." Be sure not to write WLOG when you mean "with loss of generality"! | ||
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| + | == Example Problems == | ||
| + | === Introductory Level === | ||
| + | * [[2006_AMC_10B_Problems/Problem_17 | 2006 AMC 10B Problem 17]] | ||
Revision as of 23:44, 13 July 2006
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." Be sure not to write WLOG when you mean "with loss of generality"!
