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>.
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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."

Revision as of 21:52, 23 June 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 ${a \geq b \geq c}$ without loss of generality because the inequality is symmetric in $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$. Without loss of generality is often abbreviated "WLOG."

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