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- Without_loss_of_generality abstract "Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used before an assumption in a proof which narrows the premise to some special case; it implies that the proof for that case can be easily applied to all others, or that all other cases are equivalent or similar. Thus, given a proof of the conclusion in the special case, it is trivial to adapt it to prove the conclusion in all other cases.This is often enabled by the presence of symmetry. For example, if some property P(x,y) of real numbers is known to be symmetrical in x and y, namely that P(x,y) is equivalent to P(y,x), then in proving that P(x,y) holds for every x and y, we may assume "without loss of generality" that x ≤ y. There is then no loss of generality in that assumption: once the case x ≤ y ⇒ P(x,y) has been proved, the other case follows by y ≤ x ⇒ P(y,x) ⇒ P(x,y); hence, P(x,y) holds in all cases.".
- Without_loss_of_generality wikiPageExternalLink wlog.pdf.
- Without_loss_of_generality wikiPageID "296000".
- Without_loss_of_generality wikiPageLength "2664".
- Without_loss_of_generality wikiPageOutDegree "10".
- Without_loss_of_generality wikiPageRevisionID "662845616".
- Without_loss_of_generality wikiPageWikiLink Category:Mathematical_terminology.
- Without_loss_of_generality wikiPageWikiLink List_of_mathematical_jargon.
- Without_loss_of_generality wikiPageWikiLink Material_conditional.
- Without_loss_of_generality wikiPageWikiLink Mathematical_jargon.
- Without_loss_of_generality wikiPageWikiLink Mathematics.
- Without_loss_of_generality wikiPageWikiLink Pigeonhole_principle.
- Without_loss_of_generality wikiPageWikiLink Real_number.
- Without_loss_of_generality wikiPageWikiLink Symmetry.
- Without_loss_of_generality wikiPageWikiLink Theorem.
- Without_loss_of_generality wikiPageWikiLink Trivial_(mathematics).
- Without_loss_of_generality wikiPageWikiLink Triviality_(mathematics).
- Without_loss_of_generality wikiPageWikiLink Up_to.
- Without_loss_of_generality wikiPageWikiLinkText "No generality is lost".
- Without_loss_of_generality wikiPageWikiLinkText "WLOG".
- Without_loss_of_generality wikiPageWikiLinkText "Without loss of generality".
- Without_loss_of_generality wikiPageWikiLinkText "no loss of generality".
- Without_loss_of_generality wikiPageWikiLinkText "no loss".
- Without_loss_of_generality wikiPageWikiLinkText "without (any) loss of generality".
- Without_loss_of_generality wikiPageWikiLinkText "without loss of generality".
- Without_loss_of_generality hasPhotoCollection Without_loss_of_generality.
- Without_loss_of_generality id "2946".
- Without_loss_of_generality title "WLOG".
- Without_loss_of_generality wikiPageUsesTemplate Template:Planetmath_reference.
- Without_loss_of_generality wikiPageUsesTemplate Template:Quote.
- Without_loss_of_generality wikiPageUsesTemplate Template:Redirect.
- Without_loss_of_generality wikiPageUsesTemplate Template:Reflist.
- Without_loss_of_generality subject Category:Mathematical_terminology.
- Without_loss_of_generality comment "Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used before an assumption in a proof which narrows the premise to some special case; it implies that the proof for that case can be easily applied to all others, or that all other cases are equivalent or similar.".
- Without_loss_of_generality label "Without loss of generality".
- Without_loss_of_generality sameAs Без_ограничения_на_общността.
- Without_loss_of_generality sameAs Bez_gubitka_opštosti.
- Without_loss_of_generality sameAs Sense_pèrdua_de_generalitat.
- Without_loss_of_generality sameAs Ohne_Beschränkung_der_Allgemeinheit.
- Without_loss_of_generality sameAs Sin_pérdida_de_generalidad.
- Without_loss_of_generality sameAs Sans_perte_de_généralité.
- Without_loss_of_generality sameAs ללא_הגבלת_הכלליות.
- Without_loss_of_generality sameAs 一般性を失わない.
- Without_loss_of_generality sameAs Zonder_verlies_van_algemeenheid.
- Without_loss_of_generality sameAs m.01r7vl.
- Without_loss_of_generality sameAs โดยไม่สูญเสียคุณลักษณะทั่วไป.
- Without_loss_of_generality sameAs Genelliği_kaybetmeden.
- Without_loss_of_generality sameAs Q162252.
- Without_loss_of_generality sameAs Q162252.
- Without_loss_of_generality sameAs 不失一般性.
- Without_loss_of_generality wasDerivedFrom Without_loss_of_generality?oldid=662845616.
- Without_loss_of_generality isPrimaryTopicOf Without_loss_of_generality.