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 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 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 \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 WLOG when you mean "''with'' loss of generality"! | ||
| − | + | 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 | |
== Example Problems == | == Example Problems == | ||
=== Introductory Level === | === Introductory Level === | ||
Revision as of 15:59, 22 July 2020
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 or WOLOG. Be sure not to write WLOG when you mean "with loss of generality"!
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
