Editing Without loss of generality (section)

== Example ==

Consider the following [[theorem]] (which is a case of the [[pigeonhole principle]]):

{{quote|If three objects are each painted either red or blue, then there must be at least two objects of the same color.}} 

A proof: 
{{quote|Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished.|sign=|source=}}

The above argument works because the exact same reasoning could be applied if the alternative assumption, namely, that the first object is blue, were made, or, similarly, that the words 'red' and 'blue' can be freely exchanged in the wording of the proof. As a result, the use of "without loss of generality" is valid in this case.