“WLOG” (or “WOLOG”) is an acronym which stands for “without loss of generality.”

WLOG is invoked in situations where some property of a model or system is invariant under the particular choice of instance attributes, but for the sake of demonstration, these attributes must be fixed.

For example, we might want to prove something about open intervals (a,b) of the real number line. But the proof might become too tedious if a and b were arbitrary real numbers, so in the proof we simply assume that a=0 and b=1, and without loss of generality, the same arguments apply to general intervals (a,b). Depending on the proof, the loss of generality might be accomplished by translating and scalingMathworldPlanetmath the interval to (0,1) before carrying out the argument, and then translating and rescaling back to (a,b) afterwards.

WLOG can also be invoked to shorten proofs where there are a number of choices of configurationPlanetmathPlanetmath, but the proof is “the same” for each of them. We need only walk through the proof for one of these configurations, and “WLOG” serves as a note that we haven’t weakened the argument. For example, the proof of the fundamental theorem of arithmeticMathworldPlanetmath uses this notion, in essence settling on a “canonical form” for prime factorizationsMathworldPlanetmath to simplify the argument.

For more examples, see http://planetmath.org/?op=search&term=WLOG+without+loss+generalityapproximate index of PM entries invoking WLOG.

Title WLOG
Canonical name WLOG
Date of creation 2013-03-22 12:40:17
Last modified on 2013-03-22 12:40:17
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 6
Author akrowne (2)
Entry type Definition
Classification msc 00A99
Synonym WOLOG
Synonym without loss of generality