Without loss of generality

Without loss of generality, abbreviated wlog, is occurring in mathematical proofs formulation. Furthermore, the formulation is without loss of generality ( o E. A. d ) used or short, without limitation, ( oE or ligature Œ).

With these formulations is expressed that a restriction is required (eg, the range of values ​​of a variable ) only to simplify the proof ( in particular to reduce paperwork ) without the validity of the measures taken following statements with respect to the public suffers. The proof is carried out for only one of several possible cases. This occurs under the condition that the other cases can be proved in a similar manner ( for example, in symmetry).

By wlog also trivial special cases can be excluded.

Example

Intermediate value theorem of Bolzano

Sentence: A continuous function in the interval with the · property possesses at least one zero.

It can be seen that the other case, and also covered in this argument by simply replaced. The fact that the general public is not limited thereby, it follows from three properties: