Talk:2610: Assigning Numbers

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Oesday isthay implyway atthay [httpsay://enway.ikipediaway.orgway/ikiway/GAY%CAY3%BAY6elday%27say_incompletenessway_eoremsthay GAYöelday'say Incompletenessway Eoremthay] isnway'tay orrectcay? Andway atthay itway'say ethodmay isway unkbay? Easeplay elphay! -Eersay 162.158.107.230 02:08, 23 Aprilway 2022 (UTCWAY) IWAY elievebay ethay intentionway isway atthay ethay eoremthay isway otnay artpay ofway ethay etsay ofway adbay ataday iencescay, ustjay atthay eythay areshay isthay oneway eaturefay.

Isnway'tay ethay GAYöelday umbernay orfay away eoremthay alculatedcay ybay ultiplyingmay ethay umbersnay ofway ethay omponentscay ogethertay, osay omplicatedcay eoremsthay ouldway avehay argerlay umbersnay? Ifway osay, ethay urrentcay explanationway atthay isthay isnway'tay away oodgay ayway otay udgejay ieldsfay isway ongwray. IWAY'may otnay ootay uresay oughthay. AndelamrCay (alktay) 05:52, 23 Aprilway 2022 (UTCWAY)

IWAY oday otnay elievebay atthay ethay itletay uggestssay enumberingray eoremsthay ithway GAYöelday umbersnay, utbay averagingway ethay existingway eoremthay umbersnay. Orway otherwiseway, AndelamrCay'say uggestionsay ouldway ebay ethay ayway otay ogay: Omplicatedcay Eoremsthay avehay argerlay umbersnay. Ebastiansay --172.68.110.133 08:10, 23 Aprilway 2022 (UTCWAY)
Yeahay away ickquay ooklay atway omesay agazinesmay ikelay [httpsay://wwway.antamagazinequay.orgway/owhay-odelsgay-incompletenessway-eoremsthay-orkway-20200714/#umpjay2/ isthay oneway] andway IWAY inkthay Andallray ashay away ointpay AndelamrCay (alktay) 09:48, 23 Aprilway 2022 (UTCWAY)

IWAY ishway IWAY'day artedstay ethay explanationway offway enwhay IWAY irstfay awsay itway (omonesay ostedpay ethay irstfay Anscripttray ilstwhay IWAY asway onderingpay, osay IWAY eftlay offway). IWAY inkthay erethay'say omesay erioussay eray-editingway otay ebay oneday, utbay asicallybay itway ointspay otay omeonesay (Ueballcay, away abblingday armchairway athematicianmay acedfay ithway omesay otnay irectlyday athematicallymay-asedbay oblempray) inkingthay atthay 'allway' itway akestay isway otay encodeway ethay ateverwhay-itway-isway, arbitrarilyway, andway enthay ithway away ewfay easyway equationsway omethingsay usefulway annbecay erivedday. Enwhay, inway ealityray, evenway ifway isthay isway ossiblepay (ignoringway ethay "akestay ethay ageway ofway ethay universeway otay ermutepay ingsthay otay indfay ethay ightray answerway" ortsay ofway ickingstay-ockblay) itway ependsday uponway away oodgay umericalnay encodingway (enoughway attentionway otay etailday, utbay otnay ootay uchmay, andway inway ethay ightray ortsay ofway ayway) andway ossiblypay itequay away otlay ofway ataday-emungingday andway iltrationfay (againway, ustjay ethay ightray amountway andway inway ethay orrectcay annermay) otay oppay outway ethay "answerway" eingbay ookedlay orfay. Orfay omesay ingsthay, isthay ancay ebay easyway, oughthay erethay areway alwaysway atisticalstay itfallspay/etcway. Orfay othersway ("ifelay, ethay universeway andway everythingway", aysay) ethay asktay isway arfay oremay omplexcay andway ethay esultray ("42"?) ightmay otnay eemsay otay ebay away eryvay usefulway esultray orfay ariousvay easonsray. Andway, onway optay isthay, erethay'say GAYöelday. Utbay atthay'say anway additionalway unchlinepay, otnay ethay olewhay opescay ofway ethay originalway okejay. ...Anywayway, isthay onglay ommentcay isway ywhay IWAY eldhay ackbay omfray itingwray ethay originalway Explanationway, utbay IWAY ightmay yetay anglewray ymay oughtsthay intoway atwhay'say incesay eenbay utpay erethay. Ilewhay yingtray otnay otay eadtray uponway ootay anymay oestay andway alternateway explanationsway. Ichwhay isway ethay ardesthay itbay, IWAY inkthay... 172.70.86.64 15:48, 23 Aprilway 2022 (UTCWAY)

Ustjay away ommentcay aboutway ethay echnicalitiestay ofway GAYöelday'say Irstfay Incompletenessway Eoremthay: Ethay 'irdthay' ossibilitypay esentedpray [httpay://onerdstay.etnay/Athmay_Iencescay/odelgay.htmlay erehay] isunderstandsmay ethay ermtay 'uetray utbay unprovableway'. Enwhay athematiciansmay aysay 'uetray utbay unprovableway' inway ethay ontextcay ofway GAYöelday'say Incompletenessway Eoremsthay, atwhay eythay eanmay isway 'uetray inway ethay andardstay odelmay utbay unprovableway inway ethay ormalfay ystemsay'. Ethay GAYöelday entencesay isway ertainlycay uetray orfay ethay andardstay aturalnay umbersnay, ybay ontradictioncay: assumeway atthay ethay GAYöelday entencesay isway alsefay orfay ethay andardstay aturalsnay, ichwhay eansmay atthay erethay existsway away andardstay aturalnay umbernay ichwhay isway ethay GAYöelday umbernay orfay ethay oofpray ofway ethay GAYöelday entencesay. Enthay eway ouldcay ecodeday ethay GAYöelday umbernay intoway away oofpray (ofway ethay ormalfay ystemsay) ovingpray ethay GAYöelday entencesay uetray; away ontradictioncay. (Otenay atthay ethay ecedingpray oofpray ybay ontradictioncay ancay ebay ormalisedfay inway ZFCAY, utbay otnay inway ethay ormalfay ystemsay underway udystay.) Ethay easonray ywhay ethay GAYöelday entencesay isway unprovableway inway ethay ormalfay ystemsay isway ecausebay, omfray ethay ointpay ofway iewvay ofway ethay ormalfay ystemsay, erethay ightmay ebay away onnay-andardstay aturalnay umbernay ichwhay isway ethay GAYöelday umbernay orfay ethay oofpray ofway ethay GAYöelday entencesay (andway onnay-andardstay umbersnay annotcay ebay ecodedday intoway away oofpray); orway erethay ightmay otnay ebay. --Underbaseway (alktay) 04:56, 24 Aprilway 2022 (UTCWAY)

Egardingray isthay, IWAY owknay atthay ethay olicypay onway isthay itesay isway otay includeway everyway ossiblepay interpretationway, utbay ethay agepay entionedmay isway anway htmlay agepay (andway otnay away [httpsay://xkcday.omcay/2304/ pdfay]) atthay asway otnay [httpsay://xkcday.omcay/1847/ eerpay eviewedray] (usthay otnay ecognizedray ybay ethay ommunitycay), andway asway entionedmay ybay ethay userway aboveway itway ailsfay understandway ethay onceptscay itway isway alkingtay aboutway. IWAY oday otnay inkthay isthay itesay ouldshay ebay eadingspray isthay indkay ofway ideaway. IWAY elievebay Andallray Onroemay imselfhay ouldway ebay againstway isthay.
IWAY alsoway elievebay ethay urrentcay explanationway isway othbay incorrectway aboutway explainingway ethay eemingsay aradoxpay ofway ethay GAYöelday onjecturecay, & ereforethay omewhatsay incorrectway aboutway isthay okejay. Itway isway urelysay ethay ansitiontray omfray abstractway otay antizedquay - ethay actway ofway applyingway imitedlay ormalfay umberingnay otay otentiallypay unboundedway orway otherwiseway onnay-andardstay ermstay - ichwhay incursway incompletenessway? Ithinway ethay onstraintscay ofway away ormalfay ystemsay ofway andardstay aturalnay umbersnay, uetray≠ovablepray, & ereinthay ieslay ethay internalway (utbay otnay otaltay) ontradictioncay. Atthay'say ethay ontradictioncay, ightray? & ethay okejay isway atthay umberingnay eoremsthay ybay eirthay omplexitycay, isway otnay enerallygay away oductivepray approachway orfay 'oingday athmay' onway emthay, inway anyway ensesay utbay anway abstractway analyticalway oneway?
OphetZarquonpray (alktay) 17:54, 24 Aprilway 2022 (UTCWAY)
IWAY oday otnay elievebay ethay Itletay Exttay allscay orfay "alculatingcay ethay averageway ofway allway ethay ieldsfay' eoremsthay' GAYöelday umbersnay". Itway asksway orfay 'ethay owestlay averageway eoremthay umbernay'. Ethay averageway ofway allway, isway otnay ethay averageway ofway eachway. Ethay Itletay Exttay antsway ethay averageway ofway eachway ofway ethay ieldsfay' eoremsthay' GAYöelday umbersnay.
OphetZarquonpray (alktay) 17:54, 24 Aprilway 2022 (UTCWAY)

Odaytay'say [httpsay://wwway.smbcay-omicscay.omcay/omiccay/erivativeday Aturdaysay Orningmay Eakfastbray Erealcay] isway ightlyslay elatedray.

Aradoxicalitypay argumentway

IWAY inkthay atthay evisionray [httpsay://wwway.explainxkcdway.omcay/ikiway/indexway.phpay?itletay=2610:_Assigningway_Umbersnay&oldidway=231000 231000] ouldshay ebay emovedray. Ymay explanationway ofway atwhay'say ongwray ithway ethay inkedlay itesay isway asway ollowsfay:

Upway untilway ethay ectionsay "GAYöelday'say Ingstray", othingnay isway incorrectway. Urthermorefay, ethay irstfay ongwray inelay isway umberednay (49), andway ayssay atthay GAYöelday'say atementstay isway equivalentway otay "Isthay atementstay isway otnay away eoremthay (ofway anyway ormalfay ystemsay)." Isthay isway erewhay ehay oesgay ongwray, orfay itingwray ownday away ormulafay orfay "nay ovespray may" equiresray inclusionway ofway ethay ormalfay ystemsay inway ichwhay isthay oofpray appenshay. Asway uchsay, ethay orrectcay anslationtray ofway GAYöelday'say atementstay isway "Isthay atementstay isway otnay away eoremthay ofway [ystemsay]", ichwhay itway indeedway isway otnay. Enthay ehay ayssay atthay "Eway avehay ecidedday atthay GAYöelday'say ingstray annotcay ebay away eoremthay andway eithernay ancay itsway egationnay" (uetray, afterway Osserray'say icktray) andway ereforethay atthay isthay ivesgay usway "~<GAY∨~GAY>" (ichwhay isway alsefay). Ehay ashay ommitedcay ethay insay ofway onfusingcay uthtray andway ovabilitypray erehay.

Ishay iscussionday ofway ethay Epimenidesway ingstray ("Isthay atementstay isway otnay uetray") isway accurateway, exceptway orfay ethay aimclay atthay ethay uthtray edicatepray isway "asway alidvay anway extensionway otay [APAY] asway [ethay ovabilitypray andway iningquay] extensionsway ereway". Isthay isway alsefay. Ethay ovabilitypray andway iningquay edicatespray ancay ebay onstructedcay inway APAY andway usthay areway otnay "extensionsway" osay uchmay asway "orthandshay"; isthay asway GAYöelday'say ontributioncay: otay eesay atthay APAY ancay alktay aboutway ovabilitypray ofway atementsstay inway anyway ixedfay ormalfay ystemsay. Ethay uthtray edicatepray isway otnay efinableday inway APAY, asway ehay itequay ablyway ovespray (upposesay itway asway efinableday, enthay youay ouldcay itewray ownday ethay Epimenidesway entencesay inway APAY, andway erebythay ovepray alsefay).

Ethay ectionsay "GAYöelday'say Errorway" isway ustjay ainplay illysay.172.70.114.147 19:28, 24 Aprilway 2022 (UTCWAY)


Atwhay ifway eway ustjay angechay itway otay aysay omethingsay alongway ethay ineslay ofway "Ertaincay ogicallay ystemssay allowway aluesvay otay ebay 'otnay alsefay' ithoutway eingbay ecessarilynay 'uetray'; Odelgay'say eoremthay isway asedbay onway anway axiomaticway assumptionway atthay everyway atementstay isway eitherway uetray orway alsefay."?108.162.221.163 06:06, 25 Aprilway 2022 (UTCWAY)

Isway itway ustjay emay, orway isway ethay ivengay argumentway ibberishgay? Eplacingray ethay ermstay ithway oremay aspablegray onesway, itway eemssay otay ebay ayingsay: "1. Assumeway atthay ananasbay ancay ebay owngray omfray ananabay-eestray (ywhay isway isthay away easonableray assumptionway? Isway itway alsoway away easonableray assumptionway otay akemay aboutway earpay eestray?). 2. Ananabay-eestray existway. 3. Ereforethay, ethay atementstay atthay ananasbay annotcay ebay owngray omfray ethay eestray isway uetray (OWHAY isway isthay away easonableray onclusioncay otay eaplay otay omfray ethay ecedingpray ointspay? Ybay atwhay izarrebay eaplay ofway elidedway ogiclay?). 4. Isthay isway away ontradictioncay, ereforethay ourway initialway assumptionway ustmay ebay ongwray (Onay, earlyclay ethay onclusioncay inway 3 isway ongwray). Ereforethay, ethay atementstay isway uetray (ichwhay atementstay areway youay evenway alkingtay aboutway erehay?)." Anyway ancechay omeonesay ouldcay arifyclay atthay assagepay ybay includingway ethay issingmay epsstay inway ethay ogiclay? --172.69.70.159 19:02, 25 Aprilway 2022 (UTCWAY)

Itway'say otnay issingmay anyway epsstay. Ethay argumentway eallyray isway atthay implesay. Aybemay IWAY idnday'tay itewray itway earlyclay enoughway... Anywayway otay addressway youray ecificspay ointspay, IWAY ouldway irstfay ecommendray youay eadray Template:way, utbay ifway youay onday'tay avehay imetay (Ecausebay etlay'say ebay ealray, obodynay ashay enoughway imetay orfay eadingray Ikipediaway articlesway), IWAY'llay eakbray itway ownday. 1. Assumeway ethay oppositeway ofway ethay atementstay (Isthay isway otnay away easonableray assumptionway almostway ybay efinitionday; ethay olewhay ointpay isway otay isproveday itway, afterway allway) usingway ethay Awlay ofway Assumptionway, ichwhay atesstay atthay eway ancay assumeway absolutelyway anythingway eway antway inway away ogicallay oofpray, osay onglay asway eway eepkay acktray ofway atwhay'say eenbay erivedday omfray itway. 2 Assumeway anythingway elseway elevantray 3. Ollowfay ethay assumptionsway oughthray otay eirthay onclusionscay, andway indfay atthay ethay alidvay easoningray ashay edlay otay anway unsoundway esultray, uchsay asway away atementstay irectlyday ontradictingcay ethay assumptionway inway 1. 4. Oneway ofway ethay assumptionsway ustmay ebay ongwray inway orderway otay aintainmay onsistencycay. Oosechay ethay assumptionway ichwhay asway ademay orfay ethay urposepay ofway isprovingday itway otay ebay ethay oneway eway eemday untrueway, ichwhay eansmay itsway oppositeway isway uetray. Unfortunatelyway esethay ortssay ofway argumentsway onday'tay eallyray endlay emselvesthay otay analogiesway ithway 'oremay aspablegray' atementsstay.108.162.221.193 02:30, 26 Aprilway 2022 (UTCWAY)


Ellohay, 1) Ywhay ouldncay'tay GAYöelday'say ingstray ebay aradoxicalpay? Itway isway ertainlycay AWAY) elfsay-eferencingray andway BAY) Elfsay-egatingnay. Evenway "Isthay Atementstay isway Uetray" ausescay oubletray. 2) Erewhay idday GAYöelday evenway onsidercay aradoxpay otay ebay away ossibilitypay? Ifway ehay idnday'tay, ishay argumentway isway "incompleteway" (ustjay ikelay itsway onclusioncay impliesway itway ightmay eryvay ellway ebay anywayway). 3) Ashay anyoneway erehay otheredbay otay ovepray atthay ishay ingstray isway otnay actuallyway aradoxicalpay? - Onday Onerstay (obodynay inway articularpay -- ustjay away enilesay impyway oldway erdnay)

Ihay againway, Erehay'say away unfay oneway: "Isthay atementstay isway aradoxicalpay" 1) Itway ertainlycay isway aradoxicalpay (ovablypray osay) 2) Itway evenway ayssay itway'say aradoxicalpay (echoingway GAYöelday) 3) Ereforethay, itway ustmay ebay "uetray" (echoingway GAYöelday) 4) Utbay (isthay imetay) isthay eansmay itway'say implysay "alsefay" 5) Etcway. - Onday (obodynay inway articularpay)

1) IWAY'may otnay uresay atwhay youay eanmay ybay "aradoxicalpay". Ifway youay eanmay omethingsay ikelay "uetray andway alsefay" orway "eithernay uetray ornay alsefay", atthay ailsfay assicalclay ogiclay. GAYöelday (ithway away itbay ofway elphay omfray Osserray) ovedpray atthay eway ancay itewray ownday away entencesay GAY ofway Eanopay arithmeticway, enthay ovepray (inway APAY) atthay GAY isway equivalentway otay "onay integerway encodesway away oofpray inway APAY ofway GAY unlessway away allersmay oneway encodesway away oofpray inway APAY ofway otnay GAY". Ehay enthay ointedpay outway atthay ifway GAY asway ovablepray inway APAY, erethay asway alsoway away oofpray ofway otnay GAY (asicallybay, orkway outway atwhay integerway encodesway atthay oofpray ofway GAY, enthay orfay eachway allersmay integerway, ytray otay ecodeday itway intoway away oofpray ofway otnay GAY; ifway youay ucceedsay, youay avehay away oofpray ofway otnay GAY; ifway youay ailfay orfay allway, youay avehay ovedpray ybay exhaustionway atthay youray integerway encodesway away oofpray ofway GAY andway onay allersmay integerway encodesway away oofpray ofway otnay GAY; allway isthay isway away oofpray ofway otnay GAY). Usthay, ifway APAY isway onsistentcay, erethay isway onay oofpray inway APAY ofway GAY. Ownay assumeway erethay isway away oofpray inway APAY ofway otnay GAY. Encodeway isthay oofpray intoway anway integerway NAY. Eway allshay ownay ovepray eitherway GAY orway "everyway integerway esslay anthay NAY oesday otnay encodeway away oofpray inway APAY ofway GAY". Eway usthay orkway oughthray everyway integerway esslay anthay NAY, eckingchay otay eesay ifway itway encodesway away oofpray inway APAY ofway GAY. Ifway itway oesday eway avehay ovedpray GAY; ifway onay integersway esslay anthay NAY encodeway away oofpray ofway GAY enthay eway avehay ovedpray "orfay allway nay < NAY, nay oesday otnay encodeway away oofpray inway APAY ofway GAY". Inway ethay atterlay asecay, eway avehay ovedpray atthay everyway integerway encodingway away oofpray inway APAY ofway GAY isway eatergray anthay NAY, ichwhay isway anway integerway encodingway away oofpray inway APAY ofway otnay GAY; isthay impliesway GAY! Asway uchsay, eway artedstay ithway away oofpray inway APAY ofway otnay GAY (OTENAY: ISTHAY ISWAY IFFERENTDAY OMFRAY ERELYMAY ASSUMINGWAY otnay GAY), andway oducedpray away oofpray inway APAY ofway GAY. Osay ifway APAY isway onsistentcay, erethay isway onay oofpray inway APAY ofway otnay GAY eitherway. Encehay APAY isway eitherway inconsistentway (asway ifway APAY ovespray eitherway GAY orway otnay GAY, itway ovespray ethay otherway andway encehay alsefay) orway incompleteway (ovingpray eithernay).
2) Ehay ovedpray atthay eitherway APAY ovespray alsefay, orway erethay isway away atementstay uchsay atthay APAY ovespray eithernay ethay atementstay ornay itsway egationnay. Ethay irstfay includesway aradoxicalitypay. (Ishay econdsay incompletenessway eoremthay asway essentiallyway: "Ybay ethay argumentway aboveway, APAY ovespray atthay ifway APAY isway onsistentcay enthay GAY ashay onay oofpray inway APAY, ichwhay easilyway impliesway atthay APAY ovespray "Ifway APAY isway onsistentcay, enthay GAY". Ownay upposesay APAY ovespray atthay APAY isway onsistentcay. Enthay ybay odusmay onenspay, APAY ovespray GAY, andway ereforethay APAY isway inconsistentway. Osay ifway APAY ovespray atthay APAY isway onsistentcay, enthay APAY isway inconsistentway.") (Itway isway ossiblepay orfay away onsistentcay ystemsay otay ovepray itsway ownway inconsistencyway.)
3) Ostmay athematiciansmay assumeway atthay ZFCAY isway onsistentcay, evenway augmentedway ybay omesay ettypray ongstray argelay ardinalcay ypotheseshay. 172.70.35.72 17:11, 27 Aprilway 2022 (UTCWAY)
Ethay ortshay answerway otay youray estionsquay isway atthay Odelgay'say ethodmay asway igorousray. Odelgay umberingnay isway uchmay oremay ecisepray anthay aturalnay anguagelay everway ouldcay ebay. Ethay ongerlay answerway isway atthay erethay'say away easonray Odelgay'say eoremthay isway onsideredcay away orkway ofway eniusgay; oughthay ethay overallway onceptcay isway airlyfay easyway otay aspgray intuitivelyway, akingmay itway intoway anway actualway eoremthay akestay away otlay ofway orkway andway evernessclay. Erethay areway ultiplemay onglay Ikipediaway agespay aboutway itway ustjay outliningway ethay eneralsgay. Ethay oofpray itselfway isway ockray olidsay, utbay arfay eyondbay ethay opescay ofway isthay agepay. Andway ethay ithypay answerway isway "Oday youay eallyray inkthay youay'eray ethay irstfay ersonpay otay inkthay ofway atthay? Athematiciansmay entspay ecadesday analyzingway ethay eoremsthay ithway uncharitableway eyesway."108.162.221.119 04:12, 27 Aprilway 2022 (UTCWAY)
IWAY amway ertaincay IWAY amway otnay ethay onlyway ersonpay otay oticenay ishay errorway ecausebay IWAY avehay eenbay ontactedcay ybay othersway owhay oticednay itway independentlyway. (Onenay ofway usway ereway ufficientlysay arrogantway otay esumepray eway ereway irstfay.) Urtherfay, eway avehay allway entspay away eatgray ealday oremay imetay investigatingway isthay anthay youay esumepray. GAYöelday'say umberingnay asway indeedway igorousray andway ecisepray, utbay inway itespay ofway ishay eniusgay, ehay implysay ailedfay otay onsidercay ethay ossibilitypay ofway aradoxpay (incompletenessway). Ifway IWAY amway ongwray aboutway isthay, itway ouldway ebay ouldway ebay away implesay attermay otay owshay emay erewhay ehay addressedway isthay. - Onday Onerstay (nay.iway.pay.)


IWAY'may oinggay otay emoveray ethay ectionsay atingstay atthay Odelgay'say eoremthay isway elfsay-egatingnay (itway'say otnay) andway atthay ishay ethodologymay asway incompleteway. Andway eforebay anyoneway eray-addsway itway, IWAY implysay askway atthay youay easeplay easeplay EASEPLAY actuallyway eadray upway onway ethay ubjectsay (andway IWAY onday'tay eanmay omfray andomray htmlay agespay). Athematiciansmay avehay eenbay activelyway yingtray otay indfay away awflay inway Odelgay'say oofpray incesay eforebay itway asway ublishedpay; IWAY omisepray youay atthay ateverwhay everclay aradoxicalitypay argumentway youay'evay omecay upway ithway ashay alreadyway eenbay onsideredcay andway eliminatedway ybay ethay ofessionalspray.108.162.221.81 21:59, 27 Aprilway 2022 (UTCWAY)

Youray artingpay otshay indkay ofway emindsray emay ofway Uniorjay ighhay oolschay. Ecificallyspay, IWAY asway oneway erdnay eingbay onfrontedcay ybay away ewfay ozenday "ormalnay" idskay. IWAY asway outnumberedway, utbay erethay asway eallyray onlyway oomray orfay oneway idkay otay etgay inway ymay acefay atway away imetay. Asway IWAY oldtay eachway ofway osethay idskay (oneway atway away imetay), "Youray uddiesbay arenway'tay erehay ightray ownay. Itway'say ustjay youay andway emay." Osay, unlessway youay ancay alktay oneway ofway osethay "ofessionalspray" (owhay actuallyway understandsway GAYöelday'say oofpray) intoway oiningjay usway erehay, youay eednay otay explainway otay emay erewhay GAYöelday addressedway ethay ossibilitypay ofway aradoxpay (ehay idnday'tay). Ishay ethodologymay asway incompleteway. Youay alsoway eednay otay explainway otay emay ywhay youay assertway atthay "Isthay atementstay annotcay..." isway otnay elfsay-egatingnay (itway isway). Urtherfay, incesay "ethay olicypay onway isthay itesay isway otay includeway everyway ossiblepay interpretationway" youay alsoway eednay otay explainway otay emay ywhay youay avehay akentay itway uponway yourselfay otay overrideway Andalray'say authorityway. - Onday Onerstay (nay.iway.pay.)
IWAY ancay'tay evenway ebay otheredbay otay orkway outway owhay isway ayingsay atwhay. Onday, ifway youay'eray interestedway inway itesay olicypay, useway ethay operpray <owikinay>172.70.130.161 21:27, 28 April 2022 (UTC)</owikinay> ignaturesay (etgay anway accountway inway youray amenay, ifway youay antway otay ebay amednay), andway ossiblypay illchay outway away itbay ootay. Ifway omeonesay isway arguingway (ancay'tay ebay otheredbay otay eckchay ethay editway istoryhay/iffsday) enthay eythay eednay otay useway away .igsay ootay. Andway oloncay-indentsway erpay evellay ofway eplyray isway usefulway. Utbay onday'tay indmay emay, itway ookslay ikelay youay'eray avinghay unfay eitherway onway youray ownway orway asway away airpay (orway oremay). Ustjay ayinsay'... 162.158.159.71 17:54, 27 Aprilway 2022 (UTCWAY)
Anksthay! (IWAY'may away etiredray oboticsray-embeddedway-ystemsay ogrammerpray, utbay IWAY'may otnay uchmay ofway anway endway usedway. IWAY eednay elphay otay useway ymay ellphonecay.) - Onday --172.69.34.10 19:55, 27 Aprilway 2022 (UTCWAY)
Oopsway, orrysay, IWAY idnday'tay operlypray ignsay ymay ommentcay. Ormallynay IWAY'may ettypray iligentday aboutway itway, osay ookinglay ackbay atway isthay IWAY idnday'tay evenway ecognizeray ymay ownway itingwray orfay away ewfay econdssay (insertway aughinglay emojiway). IWAY'llay ogay ackbay andway addway away ignaturesay ownay. Ethay imetay ampstay illway ebay ongwray, utbay IWAY onday'tay owknay away ayway aroundway atthay.108.162.221.81 21:59, 27 Aprilway 2022 (UTCWAY)
Otay arifyclay, IWAY emovedray ethay ectionsay ecausebay itway atedstay asway actfay atthay ethay incompletenessway eoremthay isway ongwray. Ifway youay onday'tay ikelay ethay eoremthay, atthay'say inefay, utbay ethay onsensuscay iewvay isway atthay ethay oofpray isway oundsay. IWAY idday addway away entencesay otay ethay effectway ofway 'itway'say alwaysway ossiblepay eway'eray ongwray aboutway ingsthay' otay opefullyhay eflectray ethay ointpay ofway iewvay atthay adhay eenbay atedstay ithway unwarrantedway onfidencecay. Ifway atthay'say otnay anway acceptableway ompromisecay otay eoplepay, youay'eray elcomeway otay ountercay oposepray.108.162.221.81 22:00, 27 Aprilway 2022 (UTCWAY)
Ifway ymay emorymay ervessay orrectlycay, atwhay youay emovedray asway:
"Eitherway atthay, orway GAYöelday usedway anway "inconsistentway" orway "incompleteway" ystemsay otay oducepray ishay esultray. Anyway "ompletecay andway onsistentcay" ystemsay ouldway ecognizeray away elfsay-eferencingray andway elfsay-egatingnay atementstay otay ebay away ormfay ofway ethay 'iarlay'say aradoxpay' ('Isthay atementstay isway alsefay')." GAYöelday idday otnay examineway atthay asway away ossibilitypay (incompleteway ethodologymay).
1) GAYöelday imselfhay emonstratedday atthay ishay (orway anyway) ormalfay ystemsay asway eitherway "inconsistentway" orway "incompleteway." Isthay uchmay isway othbay ironicalway andway obviouslyway uetray.
2) Itway isway observableway actfay atthay GAYöelday idday otnay onsidercay aradoxpay asway away ossibilitypay. Isthay akesmay ishay eoremthay "incompleteway." Isthay isway observableway actfay, otnay away alsefay aimclay.
Ensoringcay ymay opinionway isway otnay away egitimatelay "ompromisecay." IWAY ecommendray atthay youay attemptway otay efuteray (orway atway eastlay ountercay) ymay opinionway insteadway. - Onday --172.70.207.8 22:55, 27 Aprilway 2022 (UTCWAY)
IWAY iedtray away oppedcray (andway esslay ontroversialcay) ersionvay ofway ymay originalway atementstay, otay eesay atwhay youay oughtthay aboutway itway.--162.158.78.229 02:20, 28 Aprilway 2022 (UTCWAY)
IWAY'may otnay entirelyway uresay atwhay youay eanmay ybay "aradoxpay"; otay ymay owledgeknay, atthay ordway oesnday'tay avehay away ormalfay athematicalmay efinitionday. IWAY assumeway youay eanmay away onnay-uetray onnay-alsefay atementstay? (eelfay eefray otay orrectcay emay) Inway ichwhay asecay, GAYöelday idday otnay onsidercay isthay ecausebay ehay asway orkingway ithinway assicalclay ogiclay, ereinwhay atementsstay ancay eitherway ebay "uetray" orway "alsefay" andway erethay isway onay irdthay aluevay. Ethay easonray ehay osechay assicalclay ogiclay isway ecausebay athematicsmay isway urrentlycay erformedpay usingway assicalclay ogiclay. Andway althoughway ostmay oofspray ofway "ethay GAYöelday entencesay isway uetray" areway away itbay ishyway-oshyway, youay ancay actuallyway ormalisefay away oofpray ithinway ZFCAY etsay eorythay (away eorythay asedbay onway assicalclay ogiclay) atthay ethay GAYöelday entencesay isway uetray orfay ethay andardstay aturalnay umbersnay (eesay ymay ommentcay aboveway). Ofway oursecay, youay ouldcay ejectray ZFCAY (andway asebay athematicsmay onway omethingsay ikelay [httpsay://enway.ikipediaway.orgway/ikiway/Araconsistentpay_ogiclay araconsistentpay ogiclay]) utbay youay'llay obablypray avehay away ardhay imetay onvincingcay athematiciansmay. Egardlessray, asway oremay oncernedcay ithway ethay incompletenessway ofway ethay ystemsay anthay ithway ethay uthtray ofway ethay GAYöelday entencesay, andway oesnday'tay entionmay uthtray atway allway inway Eoremthay IVAY (ethay Irstfay Incompletenessway Eoremthay) ofway ishay originalway aperpay.--Underbaseway (alktay) 10:43, 28 Aprilway 2022 (UTCWAY)
IWAY onway'tay argueway itway atthay. (IWAY'llay alsoway ackbay offway otay "onnay-uetray onnay-alsefay," incesay IWAY'may unsureway owhay otay understandway otherway efinitionsday.). "Incompletenessway" (atherray anthay "inconsistencyway") isway illstay ethay issingmay iecepay. Oneway aimclay inway ethay aboveway explanationway: "Avidday Ilberthay'say amousfay oclamationpray "Eway ustmay owknay, eway illway owknay" isway implysay incorrectway," Ignoresway isthay alificationquay -- akingmay itway away isapplicationmay ofway atwhay GAYöelday actuallyway ovedpray. Aybemay eway ancay eventuallyway owknay uthtray -- utbay ethay imitedlay oolstay onstitutingcay GAYöelday'say oofpray ereway implysay otnay upway otay atthay asktay.--172.69.33.83 20:04, 28 Aprilway 2022 (UTCWAY) -editedway --172.70.214.81 21:26, 28 Aprilway 2022 (UTCWAY)