Ýëåêòðîííàÿ áèáëèîòåêà
Ôîðóì - Çäîðîâûé îáðàç æèçíè
 Ñàìîðàçâèòèå, Ïîèñê êíèã Îáñóæäåíèå ïðî÷èòàííûõ êíèã è ñòàòåé,
Êîíñóëüòàöèè ñïåöèàëèñòîâ: Ðýéêè; Êîñìîýíåðãåòèêà; Áèîýíåðãåòèêà; Éîãà; Ïðàêòè÷åñêàÿ Ôèëîñîôèÿ è Ïñèõîëîãèÿ; Çäîðîâîå ïèòàíèå;  ãîñòÿõ ó àñòðîëîãà; Îñîçíàííîå ñóùåñòâîâàíèå; Ôýí-Øóé; Âðåäíûå ïðèâû÷êè Ýçîòåðèêà




Äìèòðèåâñêàÿ Ëèëèÿ - Ðàçðåøèòå ñåáå óñïåõ

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Îò èçäàòåëÿ   Ïðåäëàãàåìàÿ âàøåìó âíèìàíèþ ïðîãðàììà ïî äîñòèæåíèþ óñïåõà - ýòî ñèíòåç âåëè÷àéøèõ îòêðûòèé â îáëàñòè ÷åëîâå÷åñêîãî äóõà. Îáúåäèíèâ êëþ÷åâûå èäåè Í.Õèëëà, Ä.Ìåðôè, Ê.Ñòîóíà, Ë.Õåé, Ð.Ãðèñâîëäà è äðóãèõ ìàñòåðîâ äóõîâíûõ ïðàêòèê ñ ìåòîäèêàìè Õîçå Ñèëüâû, Ê.Íèøè, Áîäåíà è È.Øóëüöà, àâòîð, íàáëþäàÿ çà ðåàëüíûìè èçìåíåíèÿìè ñîáñòâåííîé æèçíè, ìîæåò ñêàçàòü òîëüêî îäíî: ýòà ïðîãðàììà, ðàçðàáîòàííàÿ äëÿ äîñòèæåíèÿ áëàãîñîñòîÿíèÿ è óäà÷è, äåéñòâèòåëüíî ðàáîòàåò.

Ïðàêòè÷åñêîå ðóêîâîäñòâî, ðàññ÷èòàííîå âñåãî íà 20 ìèíóò åæåäíåâíûõ çàíÿòèé, îòêðîåò âàì äâåðè ê èçîáèëèþ, íàó÷èò ïðîãðàììèðîâàòü óäà÷íûé äåíü, ïðàâèëüíî ñòàâèòü öåëè è ðåøàòü ïðîáëåìû, ðàçðóøèò áàðüåð íà ïóòè ê óñïåõó è äàæå ïîìîæåò â ïîèñêå èäåàëüíîãî ïàðòíåðà. Ãëàâíîå, ïðî÷èòàâ êíèãó, íå îòêëàäûâàéòå åå â ñòîðîíó, ïåðåéäèòå îò òåîðèè ê ïðàêòèêå - è âû äîáüåòåñü òåõ öåëåé, êîòîðûå ñåãîäíÿ êàæóòñÿ âàì àáñîëþòíî íåñáûòî÷íûìè.

ÎÒ ÀÂÒÎÐÀ

Òîò, êòî îòêàçûâàåòñÿ îò õîðîøåé èäåè ëèøü ïîòîìó, ÷òî åå àâòîðîì ÿâëÿåòñÿ äðóãîé ÷åëîâåê, îáû÷íî îñòàåòñÿ íè ñ ÷åì. ß èñïîâåäóþ èíîé ïðèíöèï: «Êîïèðóéòå óñïåõ!» È âñå, ÷åãî ÿ äîáèëñÿ è ÷òî ñåé÷àñ èìåþ, áûëî çàèìñòâîâàíî ó äðóãèõ ëþäåé èëè â äðóãîì áèçíåñå.
Äæ. Ìãøáóðí Ñìèò

Åñëè áû îäíàæäû ìíå íà ãëàçà íå ïîïàëàñü ïðèâåäåííàÿ âûøå ôðàçà, âû, óâàæàåìûé ÷èòàòåëü, âîçìîæíî, íèêîãäà íå äåðæàëè áû â ðóêàõ ýòó êíèãó. Èìåííî ïîñëå ïðî÷òåíèÿ ñòðîê Äæ. Ìèëáóðíà Ñìèòà, ÿ ïîíÿëà, ÷òî íå ïðîñòî ìîãó, íå ïðîñòî èìåþ ïðàâî âûðàçèòü èäåè, ïîëó÷åííûå ìíîþ îò äðóãèõ ëþäåé è ðåàëüíî ïðåîáðàçîâàâøèå ìîþ æèçíü, íî è îáÿçàíà ýòî ñäåëàòü. Ïîâåðüòå, ÿ çàïëàòèëà äîñòàòî÷íî âûñîêóþ öåíó çà ïðàâî íàïèñàòü ýòó êíèãó. ß âñå âðåìÿ ó÷èëàñü, äàæå òîãäà, êîãäà æèçíü áóêâàëüíî óñêîëüçàëà èç-ïîä íîã, è ñîáèðàëà èíôîðìàöèþ ïî êðóïèöàì.  ïîèñêàõ çíàíèÿ ïðîáîâàëà âñå, ÷òî ìîãëî ïðèâåñòè ê èñòèíå. Ñîïîñòàâëÿÿ íîâóþ èíôîðìàöèþ ñ ñîáñòâåííûì îïûòîì, ÿ äåëàëà åå ÷àñòüþ ýòîãî îïûòà. È ÿ íå ïîáîþñü ñêàçàòü, õîòÿ ýòî è ïðîçâó÷èò ñîâåðøåííî ôàíòàñòè÷íî, ÷òî â îäèí ïðåêðàñíûé äåíü ïîëíîñòüþ ïåðåâåðíóëà ñâîþ æèçíü. Êîíå÷íî, îñîçíàíèå ýòîãî ïðèøëî çíà÷èòåëüíî ïîçæå. Ïîíàäîáèëîñü âðåìÿ, ÷òîáû íå ïðîñòî çàìåòèòü ïðîèçîøåäøèå ïåðåìåíû, íî è ïîâåðèòü â èõ çàêîíîìåðíîñòü. Âîò îá ýòîì ïðîöåññå äîñòèæåíèÿ áëàãîñîñòîÿíèÿ è óñïåõà, êîòîðûì ñïîñîáåí óïðàâëÿòü ëþáîé ÷åëîâåê, ïîéäåò ðå÷ü â êíèãå.
Ïîèñê, êîòîðûé âûëèëñÿ â îïðåäåëåííóþ ñèñòåìó, — ýòî ïðåæäå âñåãî ñèíòåç âåëè÷àéøèõ, íà ìîé âçãëÿä, îòêðûòèé â îáëàñòè ÷åëîâå÷åñêîãî äóõà, è ÿ íè â êîåé ìåðå íå ïðåòåíäóþ íà ðîëü ïåðâîîòêðûâàòåëÿ â ýòîé îáëàñòè. Ìîÿ çàñëóãà ëèøü â òîì, ÷òî, ñòîÿ íà êðàþ áåçäíû, ÿ íàøëà â ñåáå ìóæåñòâî ïîâåðèòü â ñîáñòâåííûå ñèëû è ðåàëüíî èçìåíèòü ñâîþ æèçíü.  ñâîåé ïðîãðàììå ÿ ïîïûòàëàñü îáúåäèíèòü êëþ÷åâûå èäåè Í. Õèëëà, Ä. Ìåðôè, Ê. Ñòîóíà, Ë. Õåé, Ð. Ãðèñâîëäà è íåêîòîðûõ äðóãèõ, ìåíåå èçâåñòíûõ íàøåìó ÷èòàòåëþ àâòîðîâ ñ ïðàêòè÷åñêèìè ïðèåìàìè Õîçå Ñèëüâû, Ê. Íèøè, Áîäåíà, È. Øóëüöà. È ýòà ïîïûòêà óäàëàñü. Íàáëþäàÿ çà ðåàëüíûìè èçìåíåíèÿìè ñîáñòâåííîé æèçíè, ÿ ìîãó ñêàçàòü òîëüêî îäíî. Ýòà ïðîãðàììà, ðàçðàáîòàííàÿ äëÿ äîñòèæåíèÿ áëàãîñîñòîÿíèÿ, óäà÷è è óñïåõà, äåéñòâèòåëüíî ðàáîòàåò.

×ÒÎ ÂÛ ÍÀÉÄÅÒÅ Â ÊÍÈÃÅ, ÅÑËÈ ÍÀ×ÍÅÒÅ ÅÅ ×ÈÒÀÒÜ
Ëþáàÿ ïðîãðàììà, íàïðàâëåííàÿ íà óëó÷øåíèå ÷åëîâå÷åñêîé æèçíè, òðåáóåò êîìïëåêñíîãî ïîäõîäà, è ïðîãðàììà «Âîñïèòàíèå ñîçíàíèÿ», ïðåäëîæåííàÿ âàøåìó âíèìàíèþ âî âòîðîé ÷àñòè êíèãè, íå èñêëþ÷åíèå. Åñëè âû ÷èòàëè ìîþ êíèãó «Îáìàíûâàÿ âîçðàñò», òî íå ìîãëè íå çàìåòèòü, ÷òî êîìïëåêñíûé ïîäõîä ê çàáîòå î ñåáå è åñòü òîò ñàìûé «Ýëèêñèð ìîëîäîñòè», êîòîðûé ìíîãèå òùåòíî èùóò âñþ æèçíü. Åñëè ðàçðàáîòàííûé ìíîþ êîìïëåêñíûé ïîäõîä ñðàáîòàë â îòíîøåíèè ìîëîäîñòè, êðàñîòû è çäîðîâüÿ, îí ïðîñòî íå ìîã íå ñðàáîòàòü è â òîé îáëàñòè æèçíè, êîòîðàÿ íå ìåíåå âàæíà äëÿ ÷åëîâåêà. Íàñêîëüêî ðåàëüíî äîáèòüñÿ óñïåõà â æèçíè, åñëè ñåãîäíÿ ó âàñ äëÿ ýòîãî íåò (êàê âàì êàæåòñÿ) íè åäèíîé ðåàëüíîé ïðåäïîñûëêè? Âñå êíèãè, êîòîðûå ÿ ïðî÷èòàëà íà èíòåðåñóþùóþ ìåíÿ òåìó, äàâàëè ñêîðåå êîëîññàëüíóþ ïèùó ê ðàçìûøëåíèþ, ÷åì êîíêðåòíûé ïëàí äåéñòâèé. ß íå çíàëà, ÷òî ìíå íóæíî ñäåëàòü çàâòðà èëè ñåãîäíÿ, ÷òîáû õîòü íà ìèã ïðèáëèçèòüñÿ ê òåì çîëîòûì ãîðàì, êîòîðûå ìíå îáåùàþò. Ìíå ãîâîðèëè:
«Ïîñòàâü öåëü», è ÿ ïîíèìàëà, ÷òî ýòî âåðíî, ïîñòàâèòü öåëü íóæíî. Íî êàêóþ? Êàê? À åñëè ó âàñ ñåãîäíÿ îò áåçûñõîäíîñòè íå îñòàëîñü íè ñèë, íè âåðû, òî êàêèå óæ òàì öåëè? À ãäå âçÿòü âåðó? Òåïåðü ïðåäñòàâèì, ÷òî âû ñ÷àñòëèâûé ÷åëîâåê è ó âàñ ýòà öåëü óæå åñòü, íî ïî÷åìó-òî âû íèêàê äî íåå íå äîáåðåòåñü. ×òî âàì ìåøàåò? Ýòè è ìíîãèå äðóãèå âîïðîñû àòàêîâàëè ìåíÿ äî òåõ ïîð, ïîêà íå ëåãëè â îïðåäåëåííóþ ñèñòåìó, êîòîðàÿ íà÷àëà ðàáîòàòü. ß ïîñòàðàëàñü ó÷åñòü âñå ïðîáëåìû, ñ êîòîðûìè ñòîëêíóëàñü, è ðàññêàçàòü îá èõ ðåøåíèè ïðîñòî è äîñòóïíî. Êðîìå òîãî, ýòà ñèñòåìà ïîäòâåðæäàåò óíèâåðñàëüíîñòü Çàêîíà Óñïåõà. Ìíîãèå ëþäè â íàøåé ñòðàíå, ÷èòàÿ êíèãè çàðóáåæíûõ àâòîðîâ, ñ÷èòàþò, ÷òî â Ðîññèè ðåàëèçîâàòü ñâîè æåëàíèÿ íåâîçìîæíî. Âîçìîæíî! Âñå çàâèñèò òîëüêî îò íàñ ñàìèõ, óäèâèòåëüíàÿ ïðåîáðàçóþùàÿ ñèëà ñêðûòà âíóòðè êàæäîãî èç íàñ, è îòíÿòü åå íåâîçìîæíî.

×àñòü I Îñîçíàíèå ñèëû

ÒÎ, ×ÒÎ ËÅÆÈÒ ÇÀ ÍÀÌÈ, È ÒÎ, ×ÒÎ ËÅÆÈÒ ÂÏÅÐÅÄÈ ÍÀÑ, ÍÅÑÐÀÂÍÈÌÎ ÌÅÍÅÅ ÂÀÆÍÎ, ×ÅÌ ÒÎ, ×ÒÎ ËÅÆÈÒ ÂÍÓÒÐÈ ÍÀÑ, ÈÁÎ ×ÅËÎÂÅÊ ßÂËßÅÒÑß ÒÅÌ, Î ×ÅÌ ÎÍ ÖÅËÛÉ ÄÅÍÜ ÄÓÌÀÅÒ.
Ðàëüô Ýìåðñîí

Ñàìîå òðóäíîå íà÷àòü. È íå âàæíî, ê ÷åìó îòíîñÿòñÿ ýòè ñëîâà — ê íàïèñàíèþ êíèãè èëè ê íà÷àëó íîâîãî âèòêà â æèçíè, âàæíî, ÷òî ñåé÷àñ ÿ ñäåëàëà ïåðâûé øàã, íàïèñàâ ïåðâûå ñòðî÷êè, à âû, ïðî÷èòàâ êíèãó, ñäåëàåòå ïåðâûé øàã ê áëàãîïîëó÷èþ. Åñëè ÿ ïðåðâó ñâîå ïîâåñòâîâàíèå, âû íå óçíàåòå, î ÷åì ÿ ñîáèðàëàñü ðàññêàçàòü, íî åñëè âû ÷åëîâåê èùóùèé, âû ðàíî èëè ïîçäíî ïîëó÷èòå îòâåòû íà ñâîè âîïðîñû èç äðóãèõ èñòî÷íèêîâ. Íó à åñëè îñòàíîâèòåñü âû íà ïóòè îò òåîðèè ê ïðàêòèêå? Âàì âñå ðàâíî ïðèäåòñÿ ïèñàòü ñöåíàðèé ñîáñòâåííîé æèçíè. Òîëüêî â ñëó÷àå îñòàíîâêè îí ìàëî ÷åì áóäåò îòëè÷àòüñÿ îò âàøåé íàñòîÿùåé æèçíè.  âàøèõ ðóêàõ ñåãîäíÿ âçÿòü íà âîîðóæåíèå ïðèåìû, îïèñàííûå â êíèãå è ïîçâîëÿþùèå âûñòðîèòü ñþæåòíóþ ëèíèþ ñâîåé ñóäüáû òàê, ÷òîáû äîñòèæåíèå ñ÷àñòüÿ áûëî îáóñëîâëåíî ëîãèêîé åå ðàçâèòèÿ.
Âàøà ñóäüáà — ýòî âàø îáðàç ìûñëåé è ìèð âàøèõ ôàíòàçèé. Ñîöèàëüíûé ñòàòóñ ÷åëîâåêà, åãî îêðóæåíèå è ôèíàíñîâîå ïîëîæåíèå — òî÷íîå îòðàæåíèå åãî ìûøëåíèÿ. Êàêèì âàì áûòü — áåäíûì èëè áîãàòûì, ñ÷àñòëèâûì èëè íåñ÷àñòíûì, óäà÷ëèâûì èëè íåò, — ðåøàåòå òîëüêî âû ñàìè. Íåîãðàíè÷åííàÿ ñèëà, ñèëà äóõà ïîçâîëèò âàì ïîëó÷èòü îò æèçíè âñå, ÷åãî âû õîòèòå. Íàó÷èòüñÿ èñïîëüçîâàòü ýòó ñèëó ìîæåò êàæäûé. Äëÿ ýòîãî ñóùåñòâóþò ïðîñòûå è ñîâåðøåííî êîíêðåòíûå ïðèåìû âîçäåéñòâèÿ íà ñâîå ïîäñîçíàíèå. Èñïîëüçóéòå èõ â ïîâñåäíåâíîé æèçíè, è âû ïîëó÷èòå âñå, î ÷åì ìå÷òàëè, è äàæå áîëåå òîãî. Ñèëà, ñîêðûòàÿ â âàøåì ïîäñîçíàíèè, óíèêàëüíà. Êîãäà âû íàó÷èòåñü îáùàòüñÿ ñ ñîáñòâåííûì ïîäñîçíàíèåì, åãî ìóäðîñòü âûâåäåò âàñ íà íóæíûé ïóòü. Âàñ ïîñåòÿò èäåè, ðåàëèçàöèÿ êîòîðûõ ïîçâîëèò âàì ñîâåðøèòü ïåðåâîðîò èëè, åñëè õîòèòå, êà÷åñòâåííûé ñêà÷îê â âàøåé æèçíè è âûéòè íà äîðîãó áëàãîïîëó÷èÿ è óñïåõà. Äëÿ ýòîãî î÷åíü âàæíî íå ïðîñòî çíàòü î ñóùåñòâîâàíèè âíóòðåííåé ñèëû, à îñîçíàòü åå. Åñëè âû äåéñòâèòåëüíî õîòèòå ñòàòü áîãàòûì, ñ÷àñòëèâûì è ïðåóñïåâàþùèì ÷åëîâåêîì, íà÷íèòå ðàáîòàòü íàä ñîáîé, ÷òîáû áëàãîñîñòîÿíèå ñòàëî âàøèì åñòåñòâåííûì âíóòðåííèì ñîñòîÿíèåì. Èìåííî ïîäîáíîãî ðîäà ðàáîòå íàä ñîáîé è ïîñâÿùåíà ïðàêòè÷åñêàÿ ÷àñòü äàííîé êíèãè.  îñíîâó òðåíèíãà ïîëîæåí ïðîñòîé íà ïåðâûé âçãëÿä äåâèç:
«Èçìåíèòå îáðàç ñâîèõ ìûñëåé, è âû èçìåíèòå ñâîþ ñóäüáó». Èçìåíåíèå ñîçíàíèÿ—äîñòàòî÷íî äëèòåëüíûé ïðîöåññ, êîòîðûé ïîòðåáóåò îò âàñ êîëîññàëüíîé âåðû, òåðïåíèÿ è íàñòîé÷èâîñòè, ïðåæäå ÷åì ïðîÿâÿòñÿ êîíêðåòíûå ïîëîæèòåëüíûå ðåçóëüòàòû. Íî ýòî, ïîæàëóé, åäèíñòâåííûé âåðíûé ïóòü ê óñïåõó, èçâåñòíûé ñåãîäíÿ ëþäÿì.
Âåñü îêðóæàþùèé íàñ ìèð ïîä÷èíÿåòñÿ îïðåäåëåííûì çàêîíàì ìèðîçäàíèÿ, è ìû, íåîòúåìëåìàÿ ÷àñòü ýòîãî ìèðà, íå ìîæåì áûòü èñêëþ÷åíèåì. Ðàáîòàÿ íàä ïðîãðàììîé, âû îñîçíàåòå ýòè çàêîíû, ïîéìåòå, ÷òî âàøå ïîäñîçíàíèå âñåãäà ïîääåðæèâàåò ñâÿçü ñ áåñêîíå÷íûì èñòî÷íèêîì æèçíè è íåîáúÿòíîé ìóäðîñòè. Ñ÷àñòëèâ, êòî äîâåðÿåò ñâîåìó ïîäñîçíàíèþ, åãî áîæåñòâåííîé ïðèðîäå, èáî ïîñëåäîâàâøèå åìó íàïîëíÿò æèçíü ïîêîåì, ðàäîñòüþ è áëàãîïîëó÷èåì. Ïîäñîçíàíèå çàáîòèòñÿ î íàñ 24 ÷àñà â ñóòêè, è â íàøåé âëàñòè çàêàçûâàòü áàë. Êàê òîëüêî âû ïîäàåòå èäåþ ïîäñîçíàíèþ, îíî íà÷èíàåò ðàáîòàòü íà âàñ. È îíî íå áóäåò ðàçëè÷àòü, íàñêîëüêî õîðîøà èëè ïëîõà âàøà èäåÿ, åãî çàäà÷à — ðåàëèçàöèÿ. Çäåñü èìååò ñìûñë çàìåòèòü, ÷òî ïîäñîçíàíèå íå ïðîâîäèò ðàçëè÷èé, íå ðàçìûøëÿåò è íå äóìàåò íè î êàêèõ êîíêðåòíûõ âåùàõ, ýòî ñôåðà äåÿòåëüíîñòè ñîçíàòåëüíîãî ðàçóìà. Ïîäñîçíàíèå è ñîçíàíèå — äâå ñôåðû äåÿòåëüíîñòè â ïðåäåëàõ îäíîãî ðàçóìà. Êàê òîëüêî âàø ðàçóì ïðèíèìàåò êàêóþ-ëèáî èäåþ, ïîäñîçíàíèå íà÷èíàåò ñâîþ ðàáîòó. Øóòêè ñ ïîäñîçíàíèåì íå óìåñòíû. Âñåãäà ïîìíèòå, ÷òî ïîäñîçíàíèå âçðàùèâàåò ëþáîå, ïîñàæåííîå âàìè, ñåìÿ.
Ýôôåêòèâíîñòü ðàáîòû ïîäñîçíàíèÿ âî ìíîãî ðàç ïîâûøàåòñÿ çà ñ÷åò âíóøåíèÿ èëè ñàìîâíóøåíèÿ. Èìåííî ýòîò ñïîñîá çàëîæåí â ëþáóþ èç ïðîãðàìì, íàïðàâëåííûõ íà ïðîöâåòàíèå è óñïåõ. Ìû âñå çíà÷èòåëüíî ïîñòðàäàëè îò íåðàçóìíîãî âíóøåíèÿ ñ ñàìîãî äåòñòâà. Ôðàçû: «Òû íè íà ÷òî íå ñïîñîáåí», «Áîãàòñòâî—óäåë èçáðàííûõ», «Íå æäè îò æèçíè ìíîãîãî» è ïðî÷èå, ïðîèçíåñåííûå ñíà÷àëà ðîäèòåëÿìè, ïîòîì äðóçüÿìè è êîëëåãàìè ïî ðàáîòå, ñäåëàëè ñâîå äåëî. Ê ñ÷àñòüþ, â âàøåé âëàñòè ïðîòèâîñòîÿòü ðàçðóøèòåëüíûì èäåÿì. È âûáîð âñåãäà áûë çà âàìè. Âîçìîæíî, âû ïðîñòî íå çàäóìûâàëèñü îá ýòîì.
Âñå ðàçî÷àðîâàíèÿ è íåïðèÿòíîñòè â æèçíè ïðîèñõîäÿò îò íåðåàëèçîâàííûõ æåëàíèé. Ñ ïîìîùüþ ïðåäëîæåííîé ïðîãðàììû âû ïîñååòå ñåìåíà óñïåõà â ñâîåì ñîçíàíèè, à ïîäñîçíàíèå ïîçàáîòèòñÿ îá èõ ðîñòå. Âû íàó÷èòåñü îòñëåæèâàòü ñâîè ìûñëè è ïîéìåòå, ÷òî, ïîâòîðÿÿ âñå âðåìÿ: «ß íå ìîãó ïîçâîëèòü ñåáå êóïèòü òàêóþ äîðîãóþ âåùü»,—âû åå äåéñòâèòåëüíî íå ïîëó÷èòå, òàê êàê îá ýòîì îáÿçàòåëüíî ïîçàáîòèòñÿ ñèëà âàøåãî ïîäñîçíàíèÿ. Çàáóäüòå ñëîâî «íå ìîãó», çàìåíèòå åãî íà «ÿ ìîãó» è, êàêèì áû óäèâèòåëüíûì íå áûëî âàøå æåëàíèå, äîâåðüòå ðåøåíèå ïðîáëåìû ïîäñîçíàíèþ, ïóñòü îíî ïîçàáîòèòñÿ î ïîëîæèòåëüíîì ðåçóëüòàòå. Âû ìîæåòå íà÷àòü ïðÿìî ñåãîäíÿ, óÿñíèâ, ÷òî ëó÷øåå âðåìÿ ðàáîòû ñ ïîäñîçíàíèåì — ÷àñ, êîãäà âû çàñûïàåòå è ïðîáóæäàåòåñü.  äðåìîòíîì ñîñòîÿíèè ìûñëèòåëüíàÿ äåÿòåëüíîñòü ñâåäåíà ê ìèíèìóìó, ñîçíàíèå óõîäèò íà âòîðîé ïëàí, à âîò äëÿ ïîäñîçíàíèÿ êàê ðàç íàñòóïàåò ïåðèîä àêòèâíîñòè. Ïîìíèòå îá ýòîì áëàãîäàòíîì âðåìåíè, âðåìåíè ðåøåíèÿ ëþáûõ æèçíåííûå ïðîáëåì, òàê êàê ïîäñîçíàíèå çíàåò îòâåòû íà âñå âàøè âîïðîñû. Îòáðîñèâ âñå ñîìíåíèÿ, íåïîêîëåáèìî âåðÿ, ÷òî îòâåò ñóùåñòâóåò óæå ñåé÷àñ, à íå â áóäóùåì, ïðîêðó÷èâàéòå êàæäûé âå÷åð è óòðî ëþáóþ ñâîþ ïðîáëåìó. Íàïðèìåð, èìåÿ äåíåæíûå çàòðóäíåíèÿ, âû ìîæåòå îáðàòèòüñÿ ê ñâîåìó ïîäñîçíàíèþ ñëåäóþùèì îáðàçîì: «Ìíå íåîáõîäèìî ïîëó÷èòü îïðåäåëåííóþ ñóììó äåíåã äëÿ ðåøåíèÿ îïðåäåëåííîé ïðîáëåìû (íàçîâèòå æåëàåìóþ ñóììó è ñóùåñòâóþùóþ ïðîáëåìó). Çíàÿ î òâîåé ãëóáî÷àéøåé ìóäðîñòè, î òîì, ÷òî òåáå âåäîìû îòâåòû íà âñå ìîè âîïðîñû, ÿ äîâåðÿþ òåáå, ìîå ïîäñîçíàíèå, ðåøåíèå ìîåé íàñóùíîé ïðîáëåìû, ÿ âåðþ, ÷òî îíà ðàçðåøèòñÿ â áëèæàéøåå âðåìÿ, è áåñêîíå÷íî áëàãîäàðåí çà ýòî». Îòâåò íå âñåãäà ïðèõîäèò ñðàçó, íî îí îáÿçàòåëüíî ïðèäåò â âèäå íåïðåîäîëèìîãî ïðåä÷óâñòâèÿ, îùóùåíèÿ è äàæå ÷åòêîãî îñîçíàíèÿ òîãî, ÷òî âû çíàåòå, êàê ïîñòóïèòü â äàííîì êîíêðåòíîì ñëó÷àå. Ñëåäóéòå âàøåé èíòóèöèè. Âñåãäà çàñûïàéòå ñ âåðîé â çàâòðàøíèé äåíü, âåðüòå, ÷òî âû ðîæäåíû äëÿ óñïåõà, è â êîíöå êîíöîâ âàì óäàñòñÿ âíåäðèòü ýòó èäåþ â ñâîå ïîäñîçíàíèå.
Ìíå î÷åíü íðàâèòñÿ óñòàíîâêà Äæîçåôà Ìåðôè, ïîâòîðÿéòå åå ïåðåä ñíîì è ñðàçó ïî ïðîáóæäåíèè, îíà ïîìîæåò âàì ïðåîäîëåòü òðóäíîñòè è îñóùåñòâèòü íàìåðåíèÿ. «Íåîáúÿòíûé ðàçóì, âäîõíîâèâøèé ìåíÿ, âåäóùèé è íàïðàâëÿþùèé ìåíÿ, îòêðûâàåò ìíå áåçóêîðèçíåííûé ïëàí äëÿ îñóùåñòâëåíèÿ ìîèõ æåëàíèé. ß ïîëíîñòüþ îñîçíàþ ãëóáîêóþ ìóäðîñòü îòâåòà ìîåãî ïîäñîçíàíèÿ, è òî, ÷òî ÿ ÷óâñòâóþ è ïðîøó â ñâîèõ ìûñëÿõ, ïîëó÷àåò ñâîå îôîðìëåíèå â ìàòåðèàëüíîì ìèðå. ß ñïîêîåí, óðàâíîâåøåí è ïîëíîñòüþ âëàäåþ ñîáîé».
Íà÷èíàÿ ñâîé ïóòü, âû ìíîãîå åùå íå ñìîæåòå ñåáå ïîçâîëèòü, ýòî áóäåò âàøà ðåàëüíîñòü. Íî âû íè â êîåì ñëó÷àå íå äîëæíû äîïóñòèòü ìûñëü «íå ìîãó». Ãîâîðèòå ñåáå: «ß ïîëó÷àþ ýòî», «ß äîñòîèí (äîñòîéíà) ýòîãî», «ß ïðèíèìàþ ýòî», «ß áëàãîäàðþ çà ýòî». Ïðîéäåò âðåìÿ, è âû óâèäèòå, êàê ðàñøèðÿþòñÿ âàøè âîçìîæíîñòè, êàê íà÷èíàåò âîïëîùàòüñÿ â æèçíü òî, ÷òî ñåãîäíÿ âû ïîëó÷èëè íà ìûñëåííîì óðîâíå. «ß ìîãó ñäåëàòü âñå ÷òî óãîäíî ñèëîé ñâîåãî ïîäñîçíàíèÿ». Çàïîìíèòå ýòó ôðàçó. Ïîâåðüòå â äîáðóþ ñóäüáó è áîæåñòâåííîå ðóêîâîäñòâî. Ñëåäèòå çà êàæäûì ñâîèì ñëîâîì è çà êàæäîé ìûñëüþ. Êðîìå âàøèõ îòðèöàòåëüíûõ ìûñëåé, íåò íèêàêèõ ïðåïÿòñòâèé íà ïóòè ê ñ÷àñòüþ. Òîëüêî âû â îòâåòå çà ïîñëåäñòâèÿ âàøèõ ìûñëåé. Êàæäûé âàø ñîçíàòåëüíûé ïîñòóïîê — ýòî ðåàëèçàöèÿ âàøåãî æåëàíèÿ, âàøåé ìûñëè. Ñëîâà æå — ñèìâîëû. Îíè èíñòðóìåíòû ìûñëè. Ñëîâî ìîæåò îçíà÷àòü íå òîëüêî ïîíÿòèå èëè îùóùåíèå, íî è öåëûé êîìïëåêñ èäåé. «Ìîãó» — ñîçäàåò ñòèìóë, «íå ìîãó» — ðàçðóøàåò ëþáîå äîáðîå íà÷èíàíèå. Áóäüòå îñòîðîæíû â âûáîðå ñëîâ. Æèâèòå ëåãêî! Ñîâåðøåííî íåïðàâèëüíî, ÷òî ðàçáîãàòåòü ìîæíî ëèøü â ïîòå ëèöà. Ñòàðàéòåñü äåëàòü òî, ÷òî äîñòàâëÿåò âàì ðàäîñòü. Èìåííî â ýòîì òðóäå íàèáîëåå ïîëíî ðàñêðîþòñÿ âàøè ñïîñîáíîñòè è ïðèâåäóò ê óñïåõó. Èäòè ñâîèì ïóòåì âîâñå íå óäåë èçáðàííûõ, à ïðàâî êàæäîãî. È óñòàíîâêà «íå ñòîèò ìíîãîãî îæèäàòü îò æèçíè» â êîðíå íåâåðíà. Ïðîñòî íà êàêîì-òî âðåìåííîì îòðåçêå âû óòðàòèëè ñïîñîáíîñòü ñâîáîäíî ñëåäîâàòü çà ñâîåé ìå÷òîé. Ïîâåðüòå â ñåáÿ. Âû ñïîñîáíû æèòü îæèäàíèåì ëó÷øåãî, âåðîé â èñïîëíåíèå æåëàíèé. Âû äîëæíû ëèøü ÷åòêî îñîçíàâàòü, ÷òî âû äîñòîéíû ñ÷àñòüÿ. Åñëè âû íå ñ÷èòàåòå ñåáÿ äîñòîéíûì è ñïîñîáíûì ïîëó÷èòü âñå, ÷òî âàì íóæíî, òî êòî ïîâåðèò âàì? Ñìåÿñü íàä ñâîåé ìå÷òîé, âû äåìîíñòðèðóåòå íåäîâåðèå ê æèçíè, è åå ìîãó÷èé ïîòîê îñòàâëÿåò âàñ â ñòîðîíå. Åñëè âû íå äîïóñêàåòå â ñâîå ñîçíàíèå, ÷òî áîãàòñòâî áåçãðàíè÷íî, áóäüòå óâåðåíû — îíî óïàäåò íå â âàøè ðóêè.
Ïðåæäå ÷åì âàøè ìå÷òû ñòàíóò òàêîé æå ðåàëüíîñòüþ, êàê äåíü è íî÷ü, çèìà è ëåòî, æàðà è õîëîä è ìíîãîå äðóãîå, ÷òî íå ïîäâåðãàåòñÿ ñîìíåíèþ, âàì íóæíî ïîðàáîòàòü íàä ñâîèì ñîçíàíèåì. Íóæíî óáåäèòü ïîäñîçíàíèå, ÷òî âû çàñëóæèâàåòå áîëüøèõ ñóìì äåíåã, ÷òî áëàãîñîñòîÿíèå — ýòî âàøå åñòåñòâåííîå ñîñòîÿíèå. Èäåÿ èçîáèëèÿ äîëæíà ñòàòü äëÿ âàñ êëþ÷åâîé. Ñóùåñòâóþò äâà ìàãè÷åñêèõ ñëîâà: «áîãàòñòâî» è «óñïåõ». Ïðîèçíåñèòå èõ. ×óâñòâóåòå? Âíóòðè âàñ íå âîçíèêàåò äàæå íàìåêà íà êîíôëèêò. È ýòî ïîòîìó, ÷òî ÷åëîâåê íå ñîçäàí äëÿ íóæäû è áåäíîñòè. ×àùå âñåãî ïñèõîëîãèÿ áåäíÿêà áûâàåò íàâÿçàíà ÷åëîâåêó ñ äåòñòâà. Åå âîçìîæíî èçìåíèòü. Êàæäûé äåíü íå ìåíåå 3 ðàç â äåíü â òå÷åíèå 5—10 ìèíóò ïîâòîðÿéòå ýòè äâà ñëîâà: «áîãàòñòâî», «óñïåõ», è âû ïîëó÷èòå íåîáõîäèìûé òîë÷îê íà ïóòü, êîòîðûé ïðèâåäåò âàñ ê ðåàëüíîìó óñïåõó.
Ïðè ðàáîòå íàä ñâîèì ñîçíàíèåì îùóùåíèå áîãàòñòâà áóäåò òåì ñèëüíåå, ÷åì ãëóáæå áóäåò ñòàíîâèòüñÿ èäåÿ áëàãîñîñòîÿíèÿ. Íó à åñëè íè÷åãî íå ïðîèçîéäåò? Ïðè÷èíà áóäåò òîëüêî îäíà: âû íå ïðèíÿëè âñåì ñåðäöåì èäåþ, ÷òî ðîæäåíû äëÿ áîãàòñòâà è áëàãîïîëó÷èÿ, à îáìàíóòü ïîäñîçíàíèå ïóñòûìè ñëîâàìè íåëüçÿ. Âåðà èãðàåò êîëîññàëüíóþ ðîëü â æèçíè è â ðàáîòå íàä ñîáîé. Ïåðåéäÿ îò òåîðèè ê ïðàêòèêå, åæåäíåâíî ðàáîòàÿ íàä ñâîèì ñîçíàíèåì, ïîâòîðÿÿ ôîðìóëû óñïåõà è áëàãîñîñòîÿíèÿ, ãäå êëþ÷åâîé ÿâëÿåòñÿ óñòàíîâêà: «Ìîå ôèíàíñîâîå ñîñòîÿíèå óëó÷øàåòñÿ êàæäûé äåíü», íå ëîìàéòå ñåáå ãîëîâó íàä òåì, êàê ýòî ïðîèçîéäåò. Äîâåðÿéòå ñâîåé æèçíè. Ñî âðåìåíåì, îãëÿíóâøèñü íàçàä, âû óâèäèòå ðåçóëüòàòû, êîòîðûå, âîçìîæíî, ñðàçó íå îñîçíàëè, òàê êàê ðîñòêè âàøåé ðàáîòû òîëüêî íàáèðàëè ñèëó è åùå íå áûëè õîðîøî âèäíû. Íå áîéòåñü áóäóùåãî, äîâåðÿéòå åìó è ðàäóéòåñü òîìó, ÷òî êàæäûé íîâûé äåíü óâåëè÷èâàåò âàøå áëàãîñîñòîÿíèå è âàøó çíà÷èìîñòü äëÿ ìèðà. Ðàáîòàÿ íàä ïðåäëîæåííûì âî II ÷àñòè òðåíèíãîì, ÷óâñòâóéòå, îñîçíàâàéòå è æèâèòå. Íå çàäàâàéòå ñåáå ëèøíèé âîïðîñ: «À ïî÷åìó äî ñèõ ïîð íè÷åãî íåò?» Óæå åñòü. Íóæíî âðåìÿ. Òîëüêî â ïîëíîì ïîêîå, äîâåðèè è âåðå â ñåáÿ âû ïîçâîëèòå áëàãîòâîðíî ðàáîòàòü âàøåìó ïîäñîçíàíèþ. Äóøåâíûé ïîêîé — êëþ÷ ê óñïåõó. Äîâåðÿéòå ñåáå, ðèñóéòå ñ ïîìîùüþ âîîáðàæåíèÿ ñ÷àñòëèâóþ æèçíü, ýòî óñêîðèò ïðîöåññ. Ëþáàÿ íåãàòèâíàÿ ìûñëü («ó ìåíÿ íè÷åãî íå ïîëó÷àåòñÿ», «ìíå íå÷åì îïëàòèòü ñ÷åòà» è äðóãèå ìûñëè ïîäîáíîãî ðîäà) íåéòðàëèçóåò âàøè ïîçèòèâíûå óòâåðæäåíèÿ. Ïðåäñòàâüòå ñåáå: ñåãîäíÿ âû ïîñàäèëè ñåìåíà, à çàâòðà âûêîïàëè, êàêèõ æå âñõîäîâ ìîæíî îæèäàòü? Êàê òîëüêî ïî÷óâñòâîâàëè íåãàòèâíóþ ìûñëü â ñâîåì ñîçíàíèè, çàìåíèòå åå óñòàíîâêîé Ä. Ìåðôè: «áîãàòñòâî», «óñïåõ» èëè «Ìîå áëàãîñîñòîÿíèå ïîñòîÿííî óâåëè÷èâàåòñÿ» — è áîëåå íè î ÷åì íå âîëíóéòåñü. Ðåøåíèå ïðîáëåìû ïðèäåò ñàìî. ×àñòî ÷åëîâåê äàæå ïîíÿòèÿ íå èìååò, îòêóäà åìó âçÿòü äåíüãè. Íî ó ïîäñîçíàíèÿ íåò íåäîñòàòêà â èäåÿõ. Êàê òîëüêî âû èçìåíèòå ñâîå ìûøëåíèå, ýòè èäåè íà÷íóò âëèâàòüñÿ â âàøó æèçíü, ïðèíîñÿ «áîãàòñòâî» è «óñïåõ», êîòîðûå âû ñíà÷àëà ïðîñòî âçðàùèâàëè ñ ëþáîâüþ, è ïîääåðæêîé âàì áûëà òîëüêî ñëåïàÿ âåðà, ñèëîé êîòîðîé âû è ïîáåäèëè.
Åñëè âàøå ñîçíàíèå ôîðìèðîâàëîñü â íèùåòå è âñþ æèçíü âàñ ïðåñëåäîâàëè íåóäà÷è, âàì îñîáåííî ñëîæíî ïîâåðèòü â òî, ÷òî ëþáîé ÷åëîâåê, èçìåíèâ ñâîå ñîçíàíèå, ñïîñîáåí äîñòè÷ü áëàãîñîñòîÿíèÿ. Ïîýòîìó ðàçâèâàéòå â ñåáå ñïîñîáíîñòü ìûñëèòü ïîçèòèâíî, ïîêà íîâûå ìûñëè, íîâûå ïðèâû÷êè, íîâûå äåéñòâèÿ íå ñòàíóò âàøåé âòîðîé íàòóðîé. Âû äîëæíû ÷åòêî îñîçíàâàòü, ÷òî, ïðåæäå ÷åì âàì ïîçâîëÿò äîáèòüñÿ äåéñòâèòåëüíîãî óñïåõà, âàñ íåîäíîêðàòíî ïðîâåðÿò íà ïðî÷íîñòü, òî åñòü íà íàñòîé÷èâîñòü. È åñëè âû âûäåðæèòå, òî ïîáåäèòå. Ýòî òðóäíî òîëüêî âíà÷àëå, çàòåì, êîãäà åæåäíåâíàÿ ðàáîòà íàä ñîáîé è ïîñòàâëåííûìè öåëÿìè ñòàíåò âàøåé ïðèâû÷êîé, âû èñïûòàåòå ðàäîñòü îò âîëíóþùåãî ÷óâñòâà êîíòðîëÿ íàä ñîáñòâåííîé æèçíüþ è áëàãîäàðíîñòü çà ïðåäîñòàâëåííóþ âîçìîæíîñòü æèòü, à íå òàùèòüñÿ ïî æèçíè.
Îäíàêî âû îøèáàåòåñü, åñëè äóìàåòå, ÷òî äëÿ äîñòèæåíèÿ öåëè äîñòàòî÷íî âäîõíîâåííûõ ìå÷òàíèé, ÷òî æèçíü ñàìà î âàñ ïîçàáîòèòñÿ è äàñò âàì âñå, ÷òî âû ïîæåëàåòå, áåç êàêèõ-ëèáî óñèëèé ñ âàøåé ñòîðîíû. Äà, âñå íà÷èíàåòñÿ ñ ìå÷òû, äà, æèçíü èçìåíèòñÿ ñðàçó, êàê òîëüêî âû èçìåíèòå ñîçíàíèå, âåäü, ìåíÿÿ ñîçíàíèå, âû ìåíÿåòå ñâîþ äåéñòâèòåëüíîñòü. Íî áåç ÿñíîãî ïëàíà äåéñòâèé íà áàçå çäðàâûõ ðàññóæäåíèé, áåç óâåðåííîñòè â òîì, ÷òî âû ñïîñîáíû íàïðàâèòü ñîáûòèÿ ñâîåé æèçíè â íóæíîå ðóñëî, âû íå ñìîæåòå îñóùåñòâèòü âñå ñâîè ìå÷òû. Åñòü è åùå îäíà îøèáêà — îòíîøåíèå ê âîçðàñòó. Ìíîãèå, ññûëàÿñü íà âîçðàñò, îòêàçûâàþòñÿ ÷òî-ëèáî èçìåíèòü â ñâîåé æèçíè, ñ÷èòàÿ, ÷òî óæå ïîçäíî. À òåïåðü ïðåäñòàâüòå ñåáÿ ÷åðåç äåñÿòü ëåò òàêèì, êàêîé âû åñòü ñåãîäíÿ, ñî âñåìè âàøèìè ïðîáëåìàìè, íåóäîâëåòâîðåííîñòüþ, ñòðàõàìè, — è òàêèì, êàêèì âû ñìîæåòå ñòàòü, åñëè òåïåðü íàéäåòå â ñåáå ìóæåñòâî ïðèñòóïèòü ê ðåàëèçàöèè öåëè, êîòîðàÿ ïðèâåäåò âàñ ê âàøåé ìå÷òå. Ýòè äåñÿòü ëåò âñå ðàâíî ïðîéäóò. Íåóæåëè âû íå âîñïîëüçóåòåñü âîçìîæíîñòüþ âñå èçìåíèòü? ß çíàþ æåíùèíó, êîòîðàÿ â ñîðîê ëåò áðîñèëà ñâîþ ñòàáèëüíóþ, ðàçìåðåííóþ, íî íå óäîâëåòâîðÿþùóþ åå æèçíü è ðåøèëà ðåàëèçîâàòü äàâíþþ ìå÷òó. Îíà ïîñòóïèëà â ìåäèöèíñêèé èíñòèòóò, óñïåøíî åãî çàêîí÷èëà è ñåãîäíÿ ñ÷àñòëèâà, ïîòîìó ÷òî íàøëà ñïîñîá ñàìîâûðàæåíèÿ â ýòîé æèçíè è ñïîñîá ðåàëüíî íåñòè äîáðî è ïîìîùü îêðóæàþùèì ëþäÿì. Äëÿ íåå ýòî áûëî î÷åíü âàæíî. À åñëè áû äåñÿòü ëåò íàçàä îíà íå ñäåëàëà ýòîò øàã?
Ãîäû ïðîøëè áû, òàê íè÷åãî íå èçìåíèâ â åå æèçíè, îñòàâëÿÿ â äóøå ïóñòîòó è ãîðå÷ü íåóäîâëåòâîðåííîñòè.
Íî âåäü è â øåñòüäåñÿò ëåò íå ïîçäíî íà÷àòü ñâîé ïóòü. Åñëè öåëü æåëàííà, åñëè îíà äåéñòâèòåëüíî âàøà, âû äîëæíû íàõîäèòü ÷óâñòâî ðàäîñòè â ïðîöåññå åå äîñòèæåíèÿ. È äàæå åñëè Áîã ðàñïîðÿäèòñÿ òàê, ÷òî âû íå óñïååòå ïîäíÿòüñÿ íà âåðøèíó, âñå-òàêè ýòè ãîäû áóäóò ãîðàçäî áîëåå îñìûñëåííû è íàñûùåííû, ÷åì æàëêîå ïðîçÿáàíèå çà çàïåðòûìè âîðîòàìè â æèçíü, íà êîòîðûå âû ñàìè ïîâåñèëè íàäïèñü «Âõîä âîñïðåùåí. Âàì óæå ïîçäíî». Ñìåíèòå íàäïèñü, è âîðîòà ðàñïàõíóòñÿ. ß íå çíàþ, ñêîëüêî âàì ëåò, íî âíóøèòå ñåáå ìûñëü, ÷òî èìåííî òåïåðü æèçíü òîëüêî íà÷èíàåòñÿ. Âñå âðåìÿ îñîçíàâàéòå ìîãó÷óþ ñèëó, ñîêðûòóþ â âàñ, ñèëó âàøåãî ïîäñîçíàíèÿ è åãî ñïîñîáíîñòü ðåàëèçîâàòü ëþáóþ âàøó ìå÷òó è ïîìî÷ü âàì.
 âàøåé æèçíè îãðîìíîå êîëè÷åñòâî âîçìîæíîñòåé äëÿ âñåãî, è äëÿ çàðàáàòûâàíèÿ äåíåã â ÷àñòíîñòè. Íå îãðàíè÷èâàéòå èõ â ñâîåì ñîçíàíèè, äîâåðÿéòå æèçíè, íå óñòàâàÿ ïîâòîðÿòü: «ß â ïîòîêå æèçíè. ß äîâåðÿþ æèçíè. È ÿ áëàãîäàðþ çà ýòî».  ýòîì ìèðå âñåãî äîñòàòî÷íî äëÿ âñåõ, à íå äëÿ èçáðàííûõ. Ýòî íå âàì íå äàþò, ýòî âû ñàìè íå áåðåòå.
Ë. Õåé ñïðàøèâàåò: «×òî ó âàñ â ðóêàõ, êîãäà âû ìûñëåííî ïðèáëèæàåòåñü ê îêåàíó — èñòî÷íèêó èçîáèëèÿ? Êðóæêà, êóâøèí èëè, ìîæåò áûòü, âåäðî?» — è äîêàçûâàåò, ÷òî ëþáàÿ èç ýòèõ åìêîñòåé — ýòî ïîêàçàòåëü âàøèõ îãðàíè÷åíèé, ïðåäëàãàÿ ïðîëîæèòü ïðÿìîé ïóòü îò ñîçíàíèÿ ê èçîáèëèþ. Ïðåäñòàâüòå ñåáå òðóáîïðîâîä, êîòîðûé íàïðÿìóþ ñîåäèíÿåò âàñ ñ
èñòî÷íèêîì âñåõ áëàã, è åñëè âàì íðàâèòñÿ ñðàâíèâàòü ýòîò èñòî÷íèê èçîáèëèÿ ñ îêåàíîì, ïðîëîæèòå âàø òðóáîïðîâîä ïðÿìî â íåèññÿêàåìûå ãëóáèíû. Îäíî èç ïðåêðàñíûõ óïðàæíåíèé Ë. Õåé ÿ õî÷ó ïðèâåñòè ïðÿìî çäåñü, ÷òîáû îíî âîøëî â âàøó æèçíü óæå ñåãîäíÿ ñî ñëîâàìè «áîãàòñòâî», «óñïåõ».
Óòðîì ðàñïàõíèòå îáúÿòüÿ, ïîäíèìèòå ðóêè ëàäîíÿìè ââåðõ è ñêàæèòå âñëóõ èëè ìûñëåííî, íî ýìîöèîíàëüíî: «ß îòêðûò(à) äëÿ âñåõ áëàã Âñåëåííîé è ÿ ïðèíèìàþ èõ».
È â çàêëþ÷åíèå ýòîé ãëàâû õî÷åòñÿ äîáàâèòü åùå íåñêîëüêî ñëîâ.
Çà÷àñòóþ, ðàáîòàÿ íàä ñâîèì ñîçíàíèåì, èçìåíÿÿ åãî ñ ïîìîùüþ ïîçèòèâíûõ óñòàíîâîê, ëþäè íå çàäóìûâàþòñÿ î òîì, ÷òî ýòà ðàáîòà íå ìîæåò áûòü íàïðàâëåíà òîëüêî íà ñåáÿ. Âû äîëæíû èçìåíèòü ñâîå îòíîøåíèå è íàñòðîé êî âñåì ëþäÿì. Íóæíî áûòü îñîáåííî îñòîðîæíûì â ñâîèõ ìûñëÿõ î äðóãèõ ëþäÿõ. Äóìàÿ î äðóãîì ÷åëîâåêå íåãàòèâíî, âû ïðîãðàììèðóåòå îòðèöàòåëüíîå ñîáûòèå ñîáñòâåííîé æèçíè. Ëþáàÿ ìûñëü ïî îòíîøåíèþ ê äðóãîìó ÷åëîâåêó âåðíåòñÿ ê âàì â òîé æå ìåðå. Äóìàÿ õîðîøî î äðóãèõ, âû ôàêòè÷åñêè äóìàåòå î ñåáå è íåñåòå áëàãî ñåáå.
Íå òîëüêî «îòíåñèòåñü ê ÷åëîâåêó òàê, êàê æåëàåòå, ÷òîáû îí ê âàì îòíåññÿ», íî è «äóìàéòå î ÷åëîâåêå òàê, êàê æåëàåòå, ÷òîáû îí äóìàë î âàñ». Ýòî äîëæíî ñòàòü îñíîâîé âàøåãî îòíîøåíèÿ ê äðóãèì ëþäÿì. Êðîìå òîãî, íèêîãäà íèêîãî íå îñóæäàéòå, íå ïîðèöàéòå è íå çàâèäóéòå ÷óæîìó áîãàòñòâó, èáî ýòè íåãàòèâíûå ýìîöèè íå ïîçâîëÿò áîãàòñòâó ïðèáëèçèòüñÿ ê âàì. Íå çàâèäóéòå, à ïîðàäóéòåñü áëàãîñîñòîÿíèþ äðóãîãî ÷åëîâåêà è ïîæåëàéòå åìó åùå áîëüøåãî ïðîöâåòàíèÿ. Òîëüêî â ýòîì ñëó÷àå áîãàòñòâî îáåðíåòñÿ ê âàì ëèöîì è âû ïðèâëå÷åòå ê ñåáå óäà÷ó. Ïðèçíàâàéòå êàæäîãî ÷åëîâåêà ðÿäîì ñ ñîáîé äîñòîéíûì óâàæåíèÿ. Êàæäûé ÷åëîâåê óíèêàëåí, èùèòå â íåì ëó÷øåå è ïîâåðüòå â íåãî. «Âåðü ëþäÿì, è îíè òåáÿ íå îáìàíóò, îòíåñèñü ê íèì õîðîøî, è îíè áóäóò õîðîøèìè, äàæå åñëè èõ õîðîøåå îòíîøåíèå ê òåáå ñòàíåò äëÿ íèõ ëèøü èñêëþ÷åíèåì èç ïðàâèë».
Ìûñëåííî ïîñûëàéòå ïîæåëàíèå ñ÷àñòüÿ, ëþáâè, áëàãîñîñòîÿíèÿ è óñïåõà êàæäîìó, êîãî âñòðåòèòå â æèçíè. Ñëåäîâàíèå ýòîìó çîëîòîìó ïðàâèëó èçìåíèò âàøó æèçíü â ëó÷øóþ ñòîðîíó.



ÈÑÊÓÑÑÒÂÎ ÑÒÀÂÈÒÜ ÖÅËÈ

Ãëàâíûé ïðèíöèï óñïåõà — çíàòü, ÷åãî òû äåéñòâèòåëüíî õî÷åøü... ß ýòîãî õî÷ó. Çíà÷èò, ýòî áóäåò.
Ã. Ôîðä

×èòàÿ êíèãè î òîì, êàê äîáèòüñÿ óñïåõà è áëàãîñîñòîÿíèÿ, ÿ íå ìîãëà íå çàìåòèòü, ÷òî ëþáîé óâàæàþùèé ñåáÿ àâòîð îáÿçàòåëüíî çàòðàãèâàåò âîïðîñ ïîñòàíîâêè öåëè â æèçíè. Íî íàñêîëüêî âàæíî ïðàâèëüíî ñôîðìóëèðîâàòü öåëü, ê êîòîðîé ñòðåìèøüñÿ, à òåì áîëåå ïðàâèëüíî åå çàïèñàòü, ÿ ïîíÿëà ïîçäíåå, ðåàëèçóÿ ñâîþ ïðîãðàììó íà ïðàêòèêå.
Âñå íà÷àëîñü ñ òîãî, ÷òî, ÷èòàÿ îäíó èç êíèã, ãäå ïðåäëàãàëîñü ïðÿìî íà ñòðàíèöå â îòâåäåííîì äëÿ ýòîãî ìåñòå íàïèñàòü, êàêîé öåëè âû õîòèòå äîñòè÷ü â áëèæàéøåå âðåìÿ, ÿ íàïèñàëà: «Õî÷ó, ÷òîáû ìíå ïðåäëîæèëè èíòåðåñíóþ ðàáîòó». Áûëî óæå 23 ÷àñà. ×åðåç ïÿòü ìèíóò ðàçäàëñÿ òåëåôîííûé çâîíîê, è ìíå ïðåäëîæèëè ïðèéòè íà ñëåäóþùèé äåíü íà ñîáåñåäîâàíèå ïî ïîâîäó ðàáîòû, êîòîðàÿ ìåíÿ î÷åíü çàèíòåðåñîâàëà. Êîíå÷íî, ýòî áûëî ñîâïàäåíèå. Åñëè áû ÿ ïåðåä ïðî÷òåíèåì êíèãè íå äàëà îáúÿâëåíèå î ïîèñêå ðàáîòû, ìíå áû íå ïîçâîíèëè íè â êàêîå âðåìÿ. Ñîâïàäåíèå — äà! Íî ðàáîòàÿ íàä ñîáîé, íàä âûïîëíåíèåì ïîñòàâëåííûõ ïåðåä ñîáîé çàäà÷, ÿ ïðèó÷èëà ñåáÿ ïðèñëóøèâàòüñÿ è ïðèñìàòðèâàòüñÿ ê òåì çíàêàì, êîòîðûå ïîäàåò íàì æèçíü, ïîòîìó ÷òî ñêàçàòü íàïðÿìóþ ó íåå ïðîñòî íåò âîçìîæíîñòè. ß çàïèñàëà öåëü, è îíà ìàòåðèàëèçîâàëàñü. Ýòî áûë ïåðâûé çíàê. ß ñôîðìóëèðîâàëà öåëü íåïðàâèëüíî è ïîëó÷èëà ñîîòâåòñòâóþùèé ðåçóëüòàò. ß íàïèñàëà, ÷òî õî÷ó, ÷òîáû ìíå ïðåäëîæèëè (à íå ïðåäîñòàâèëè) ðàáîòó. Íà ðàáîòó ÿ íå óñòðîèëàñü. Íî åñëè ïîïûòàòüñÿ íàéòè â íåãàòèâíîì ïðîÿâëåíèè æèçíè ïîëîæèòåëüíûé àñïåêò, îí îáÿçàòåëüíî îòûùåòñÿ. Îá ýòîì ìû ïîäðîáíî ïîãîâîðèì â ãëàâå 3 «Áëàãîñëîâè íåóäà÷ó». ß îöåíèëà ñâîþ íåóäà÷ó êàê åùå îäèí âàæíûé äëÿ ñåáÿ æèçíåííûé îïûò, âìåñòî òîãî ÷òîáû îòáðîñèòü â ñòîðîíó êíèãó è ñêàçàòü ñåáå, ÷òî âñå, íàïèñàííîå â íåé, ÷óøü.
 êîíå÷íîì èòîãå, ïðîäîëæàÿ äâèãàòüñÿ âïåðåä, ÿ íå ïðîñòî íàøëà ðàáîòó — ÿ íàøëà ñâîå ìåñòî â æèçíè è âîçìîæíîñòü ñàìîâûðàæåíèÿ. Ñåãîäíÿ ÿ áëàãîäàðþ âñå ñâîè íåóäà÷è, êîòîðûå ïîçâîëèëè ìíå âûðàñòè, à íå îñòàòüñÿ äàëåêî ïîçàäè, òîï÷àñü íà îäíîì ìåñòå. Êðîìå òîãî, âñåãäà ñòîèò ïîìíèòü, ÷òî âû ñàìè ãîðàçäî âàæíåå ëþáîé ïîñòàâëåííîé âàìè öåëè. Íà ïóòè äàæå ñàìûõ óäà÷ëèâûõ ëþäåé îáÿçàòåëüíî áûëè òðóäíîñòè, è íå ñî âñåìè îíè ñïðàâèëèñü òàê, êàê ïðåäïîëàãàëè. Îíè ïðîñòî íàøëè â ñåáå ìóæåñòâî èäòè äàëüøå. Ýòè ëþäè óìåëè ðàñïîçíàâàòü ñëó÷àé, êîòîðûé èíîãäà ñêðûâàåòñÿ ïîä ìàñêîé íåóäà÷è. È íàâåðíîå, îíè ñ äåòñòâà õîðîøî çàïîìíèëè ïîñëîâèöó: «Íåò õóäà áåç äîáðà». Íå îòêàçûâàéòåñü îò íàìå÷åííîé öåëè ïðè ïåðâîé æå íåóäà÷å. Ïîëîñà íåóäà÷ — ýòî íîðìàëüíî íà ïóòè ê öåëè, è íóæíî áûòü áëàãîäàðíûì íåóäà÷àì çà òî, ÷òî îíè óêàçûâàþò íà âàøè íåäîñòàòêè êàê âíóòðåííåãî, òàê è âíåøíåãî ïîðÿäêà, íà íåäîñòàòî÷íî ãëóáîêî ðàçðàáîòàííûé ïëàí, òî åñòü êîððåêòèðóþò âàø ïóòü. Ïðîäîëæàéòå ïîèñê è ðàáîòó, êàê âíóòðåííþþ, òàê è âíåøíþþ. Åñëè âû îñòàíîâèëèñü íà ïîëïóòè, ýòî ãîâîðèò òîëüêî î âàøåé ëåíè, à ïîáåäèòåëè íå ìîãóò ïîçâîëèòü ñåáå ðîñêîøü èìåòü ïîäîáíûé íåäîñòàòîê.
Ïî÷åìó ÿ íà÷àëà ñ îïèñàíèÿ íåóäà÷è, à íå ñ ðàçãîâîðà î ãðîìêèõ ïîáåäàõ?
Ïîòîìó ÷òî áûëî áû íàèâíî ïîëàãàòü, ÷òî, êàê òîëüêî âû çàïèøåòå ñâîè öåëè, âñå â âàøåé æèçíè èçìåíèòñÿ êàê ïî âîëøåáñòâó. Èçìåíèòñÿ — äà! Íî íå ïî âîëøåáñòâó, à â ðåçóëüòàòå îïðåäåëåííîé ðàáîòû, êîòîðàÿ ìîæåò áûòü âûðàæåíà â ñëåäóþùåé ôîðìóëå:
ÆÅËÀÍÈÅ (ÒÎ ÅÑÒÜ ÖÅËÜ) ÏËÞÑ ÏËÀÍÈÐÎÂÀÍÈÅ ÍÀÌÅ×ÅÍÍÎÉ ÖÅËÈ ÏËÞÑ ÍÀÑÒÎÉ×ÈÂÀß ÐÅÀËÈÇÀÖÈß ÏËÀÍÀ ÐÀÂÍÎ ÄÎÑÒÈÆÅÍÈÅ ÆÅËÀÅÌÎÃÎ.
Öåëü. Êîíå÷íî, êàæäûé çíàåò, ÷òî ýòî òàêîå. Íî ïîðîé åæåäíåâíàÿ ðóòèíà òàê çàñàñûâàåò â áîëîòî ïîâñåäíåâíîñòè, ÷òî íà÷èíàåò êàçàòüñÿ: à íåò íèêàêèõ öåëåé! È âîò ýòî óæå íåâåðíî. Õîòèòå óçíàòü âàøè öåëè? Âîçüìèòå áóìàãó è ðó÷êó è ïåðå÷èñëèòå ïðèÿòíûå ñîáûòèÿ, êîòîðûå âû îæèäàåòå, ïóñòü äàæå íà óðîâíå ìå÷òû, çàâòðà, ïîñëåçàâòðà, ÷åðåç ãîä. Âû âåäü ìå÷òàåòå î ÷åì-òî? Òîãäà ïèøèòå. Çàïèñûâàÿ, âû óæå îáíàðóæèòå (äàæå åñëè ïåðâîíà÷àëüíî ýòîãî íå çàìåòèëè), ÷òî íå ïðîñòî ìå÷òàåòå, à ïëàíèðóåòå îïðåäåëåííûå ñîáûòèÿ. À åñëè çàïèñàííîé íà áóìàãå ìå÷òå ïðèäàòü êîíêðåòíîñòü, ñðîêè è ïëàí âûïîëíåíèÿ, à òàêæå ñîáñòâåííóþ óâåðåííîñòü â ðåàëüíîñòè äîñòèæèìîãî, ýòî óæå öåëü. È åñëè íà ïóòè åå äîñòèæåíèÿ âû íå îñòàíîâèòåñü, îíà ñòàíåò ìàòåðèàëüíîé. Êðîìå òîãî, öåëü — ýòî ñâîåãî ðîäà æåëàíèå, à æåëàíèå — ýòî ñâîåãî ðîäà ìîëèòâà. Æåëàíèå æèçíåííûõ áëàã èñõîäèò èç âàøèõ ãëóáî÷àéøèõ ïîòðåáíîñòåé, à ýòî çíà÷èò, ÷òî ìîëèòâà âàøà ïîäëèííàÿ, è çíà÷èò, áóäåò óñëûøàíà. Ïðîñòî íóæíî íå äàòü åé îñòàòüñÿ íà óðîâíå ìå÷òû, à íàó÷èòüñÿ ðàáîòàòü íàä íåé. Íà ñàìîì äåëå ïîñòàíîâêà öåëåé íå òàêîå óæ ïðîñòîå äåëî. Íî, ðåàëüíî íàó÷èâøèñü ýòîìó, âû ïîëó÷èòå îãðîìíûå ïðåèìóùåñòâà. Âî-ïåðâûõ, êîãäà âû ÿñíî âèäèòå ñâîþ öåëü, ïîäñîçíàíèå òóò æå íà÷èíàåò ïîìîãàòü âàì â åå äîñòèæåíèè. Ó âàñ íà÷íåò âûðàáàòûâàòüñÿ ñêëîííîñòü ê âûáîðó ïðàâèëüíîãî ïóòè. Âû íà÷íåòå äåéñòâîâàòü. À åñëè öåëü æåëàííà, òî è ðàáîòà íàä íåé ñòàíåò ïðàçäíèêîì. À ðàäîñòü òðóäà — ýòî áåñöåííûé äàð. Çíàÿ, ÷åãî âû õîòèòå, ìíîãîêðàòíî âûðàñòåò âåðîÿòíîñòü óâèäåòü è ïðåäñòàâèâøóþñÿ âîçìîæíîñòü. È íå ñòîèò ïóãàòüñÿ îøèáîê, êîòîðûå è ñóùåñòâóþò âñåãî ëèøü äëÿ òîãî, ÷òîáû ó âàñ áûëà âîçìîæíîñòü îòêîððåêòèðîâàòü ñîáñòâåííóþ ïðîãðàììó óñïåõà. Ëó÷øå íå çàáûâàéòå, ÷òîáû íàó÷èòüñÿ äîñòèãàòü ïîñòàâëåííûõ ïåðåä ñîáîé öåëåé, íóæíà, ïðåæäå âñåãî, ïðàêòèêà, äåíü çà äíåì è ãîä çà ãîäîì. «Óñïåõ òðåáóåò íåïðåðûâíîé ïðàêòèêè, èíà÷å îí âçìàõíåò êðûëüÿìè è ñêðîåòñÿ èç âèäó».
Î÷åíü ÷àñòî èäåè, êîòîðûå ïðèõîäÿò â ãîëîâó, êàæóòñÿ íåâåðîÿòíûìè è òðåáóþò îïðåäåëåííîé õðàáðîñòè, ÷òîáû ïðèñòóïèòü ê èõ ðåàëèçàöèè. Íî çà÷àñòóþ èìåííî ýòè èäåè ïðèâîäÿò ê ôåíîìåíàëüíîìó óñïåõó. Âñå, ÷òî âû çàäóìàåòå, — äîñòèæèìî, äàæå åñëè ýòî íåâåðîÿòíî. Âíóòðåííÿÿ ñèëà, êîòîðàÿ äàëà âàì âàøå æåëàíèå - öåëü, çíàåò è òî, êàê âîïëîòèòü åãî â ðåàëüíîñòü. Äîâåðüòåñü åé.
ÎÏÐÅÄÅËÅÍÈÅ ÖÅËÈ
Ïðåæäå âñåãî ïåðå÷èñëèòå íà áóìàãå âñå, ÷òî âû õîòèòå îò æèçíè âî âñåõ åå ñôåðàõ. Ïðè ýòîì íå äóìàéòå íè î êàêèõ ñäåðæèâàþùèõ ôàêòîðàõ, íàïðèìåð î âàøåì ìàòåðèàëüíîì ñîñòîÿíèè íà ñåãîäíÿøíèé äåíü è âàøåì âîçðàñòå. Çàäà÷à ýòîãî ñïèñêà—âàøè íàñòîÿùèå æåëàíèÿ. Íå çàáóäüòå î òîì, êåì âû õîòèòå áûòü, âñïîìíèòå ñâîþ äåòñêóþ ìå÷òó, åñëè ñåãîäíÿ âû óæå íè÷åãî íå õîòèòå. ×òî âû ñîáèðàåòåñü ïîëó÷èòü íà ìàòåðèàëüíîì, à ÷òî íà äóõîâíîì óðîâíå?
Ñïèñîê ìîæåò ñîäåðæàòü áîëåå ñòà ïóíêòîâ. Âîò ïðèìåðíûå äåñÿòü ïóíêòîâ æåëàíèé, êîòîðûå áûâàþò ôàêòè÷åñêè ó êàæäîãî ÷åëîâåêà:
1. Óëó÷øèòü ñâîå ìàòåðèàëüíîå ïîëîæåíèå, èëè ñòàòü ôèíàíñîâî íåçàâèñèìûì.
2. Óëó÷øèòü ñâîè æèëèùíûå óñëîâèÿ.
3. Óëó÷øèòü çäîðîâüå. Áðîñèòü êóðèòü. Çàíÿòüñÿ çàðÿäêîé.
4. Ïîõóäåòü.
5. Âñòðåòèòü ëþáèìîãî (ëþáèìóþ).
6. Íàïèñàòü êíèãó, êàðòèíó, ìóçûêàëüíîå ïðîèçâåäåíèå, òî åñòü íàéòè âîçìîæíîñòü òâîð÷åñêîãî ñàìîâûðàæåíèÿ.
7. Ïîìåíÿòü ðàáîòó íà áîëåå èíòåðåñíóþ è âûñîêîîïëà÷èâàåìóþ.
8. Ñäåëàòü õîðîøèé ðåìîíò â êâàðòèðå.
9. Îáúåõàòü íà ñâîåé ìàøèíå âñþ Åâðîïó. (Êðóãîñâåòíîå ïóòåøåñòâèå åùå ëó÷øå.)
10. Ïîâûñèòü óðîâåíü ñâîåãî îáðàçîâàíèÿ. Íàïðèìåð, âûó÷èòü èíîñòðàííûé ÿçûê.
Ñïèñîê î÷åíü ïðèìåðíûé, êàê âû ïîíèìàåòå. Íî ìíå êàæåòñÿ, ÷òî õîòÿ áû îäèí èç ïóíêòîâ âàì îáÿçàòåëüíî ïîäîéäåò. Ñ íåãî è íà÷íèòå ïèñàòü î âñåõ ñâîèõ æåëàíèÿõ. Íà ýòîì ýòàïå çàïèñè ñàìîå âàæíîå — ïîëó÷èòü èäåþ äëÿ ïîñòàíîâêè öåëè. Åñëè æåëàíèå, êîòîðîå âû ðåøèòå ïðåâðàòèòü â öåëü, òùåòíî, à íàäåæäà íåîáîñíîâàííà, òî îíî îòñååòñÿ ñàìî ñîáîé â äàëüíåéøåì, òàê êàê íå ñìîæåò ñòàòü êîíêðåòíûì. Âåðíî âûáðàííàÿ öåëü íà÷èíàåò ñáûâàòüñÿ êàê áû ñàìà ñîáîé, ïóòü äîñòèæåíèÿ âûñòðàèâàåòñÿ áåç îãðîìíûõ óñèëèé è ïîòåðü ñ âàøåé ñòîðîíû. Ãëàâíîå — íå îñòàíàâëèâàéòå ñåáÿ ñàìè ñòðàõîì ïîòåðïåòü íåóäà÷ó.
Åñëè çàäà÷à êàæåòñÿ òðóäíîâûïîëíèìîé, ñïðîñèòå ñåáÿ, âûïîëíÿë ëè åå êòî-òî äî âàñ. Äà? Çíà÷èò, âû òîæå ìîæåòå ñ íåé ñïðàâèòüñÿ. Êîíå÷íî, óñïåõ âî ìíîãîì çàâèñèò îò òîãî, íàñêîëüêî öåëü ñîîòíîñèòñÿ ñ âàøèìè âîçìîæíîñòÿìè. Íî åñëè ýòèõ âîçìîæíîñòåé íåò ñåãîäíÿ, ýòî íå çíà÷èò, ÷òî èõ íå áóäåò ÷åðåç ãîä, ÷åðåç äåñÿòü ëåò è äàëåå. Ñëåäîâàòåëüíî, âàæíî íàó÷èòüñÿ ðàçëè÷àòü öåëè:
•
|ð◊∫| ⟩ð ⌋∑ ∫ ∑⟩| ⌊ | ™ ∑⌈™ ∑⟩| ⌊ | ∑™∑⌊
• ⟩ð∑™ ∑⟩ð ⌋∑ ∫ ∑⟩| ⌊ | ∑™∑⌊ ™ © ™◊
• ™ ⌊© ⟩ð ⌋∑ ∫© ™◊ ™◊⌊∑∑
⊇ð◊∫| ⟩ð ◊ ∑⌊ ∑∫⟨⌋∫ ∑⟩® ◊ ⌈⟩™ ⌊© ⟩ð ⌈◊ ∑∫ð◊⟨ ∫◊∫ ◊ ∑∑⊆◊|ð ∑ð|ð◊∫| ⟩ð ◊ ∑⌊ —| | ∫ ⟨ ® ™ |∫ ⟨ð — ∑⟩⌋©ð◊∑∫ |◊| ⌈ð ⌊ ®| ⟩∫◊®⌊∑ ⌈®◊ ™ ⌊© ⟩ð ⌈ ∑⌊ —⟩∫◊∫ ◊ ⟩ ® ∑ ◊® ⟩ ⌋ ∑ð∑ ™∑⟩ ∫ ⌊∑∫ ∑∫ ◊⟩ ∑∫ ®⟨◊ |∑ |ð∑™∑⌊∑ ⟩ ™∑ ∑©⊆ ™ð ©◊ |ð◊∫| ⟩ð ◊ ∑⌊ —| ⌊ ∫ ™ | ⌊ ∫∑⌊ ∑ ⟨ð◊ ®◊ ∑ ∫ ⟨⌋⟩ ∑ ∫ ð◊⟨ ∫ ◊ ◊ ∫ ⌊ ∫ ◊∫∑ð ◊⌊ ∑| ⌊ ∑ ∑—®∑™∑∫|◊|ð◊ |∫ ⌈⟩◊ ⌈™ ⌊© ⟩ð ⌈ ∑⌊ ⟩ ⟩ ∑∫ ®⟨◊ |∑ℜ◊ ◊ ◊™◊ ◊—⟩∫◊® ∫ |ð◊® ⌊ ⌋∑ ∑⌊ ∫ ∑ ◊ ∫ ∫ ∫ ™ ◊|ð◊∫| ⟩ð ◊ ™ ◊⟩ð∑™ ∑⟩ð ◊ ™ ◊™ ⌊© ⟩ð ◊ ∑⌊ ∪ ∑∫⟨⌋∫ © ⟩ ⟨∑ |ð◊∫| ⟩ð ⌋ ℘ð◊ ™ ◊ ◊™◊ ◊®◊ ∑⌈ |◊ ∑∫⟩ ∑®⌋| ⌊ ⌈™ ∫∑ | ð| |◊®⌋ ∑ð◊ ⟨ ∑∫∑∑∑ ◊ ∑⟩| ⌊ | ®∑ ∑®⊇|ð ∑ð ®⌋ ∫ ∫∑ ∑∫ ⟩ ⟨⟩∫®∑ ∑™∑⌊ ◊⟩∑© ™ ®⌊ ∑∫∑⟩ ⟨∑ ð◊⟨ ∫ ⌋ ⊇◊ ◊⌊ ⟩ ⟨⌋ ∑ ∑⌊ ◊⟩|⌊ ◊ ⌊⌊ ⊆ ∫ ∑∫◊|∩™∑⟩ ®◊ |ð∑™∑⌊ ∫ ⟩ð | ⊆∑⟩∫ð∑ ∫∑⟩ | ⌊ ∫ ®⟩∑⟩ð◊ ™◊∑⌉∑™◊ð ℜð ™⌊ ®⌋ ∫|ð ∑∫∑⟩® ∑™∑⌊ ∑ð∑ ∑™∑⌊ ∑ð∑ ∫ð | ∫ ⌊∑∫ ∫ ®| ⌊ ∑ð∑◊⌊ ∑⟩⌊ ⟩∑© ™ ®⌋®⌋⟨∑ð∑∫∑®∑ð ⌋⌈| ∫
ℵ|◊| ◊∫ ◊⟩| ⌊ | ®∑ð ®⌋⟨ð◊ ?∠∑ ® ∫ ®◊ |ð∑ ™∑®⟩∑© ◊ ∫∑™∑⌈⟩∫® ®◊∫ ·∫ ⟨⌋ ◊∫ ™∑⌈⟩∫® ∫∑⌊ ⌊ ®⌋⟨ð◊ ⌋⌈| ∫ |ð ®∑™∑∫| ◊ ∑ ∑ ⌈ ∑⌊ ◊⟨⌊ ™◊⌈∫∑® ◊∫∑⌊ ◊ ◊⌊∑⌈ ∑ ∑ ® ⊕⟩⌊ |ð ⟩ ™ ⌉∑∑®◊⟩ ∑ ⟩∫ð◊ ®◊∑∫ ð∑ ◊∫ ◊™◊ ⌋ ⟩| ⟩ ⟨ ⊆∑|⌋∫◊⌈∫∑⟩ |ð ⟨ ∫ ⟩∫∑ © ⌊ ® ⌈ℜ◊ ⟩ ⌊ ∫ ⌊ | ∫ ©™◊ ∑ ∫⟩ ⌋⟩⌊| ©™◊ ∑⌊ | ⟩∫◊®⌊∑ ◊|ð◊® ⌊ | |ð∑∫ | ™™◊∑∫⟩ ◊⟨⌊ ™∑ ◊| ∫ ∑∑™ ⟩∫ ∑ —| ðð∑|∫ ð ®|∑
⊗◊®◊⌈∫∑|ð∑ ™∑®⟩∑© ◊ ⟩ ◊| ⟩⌋®◊∫ ∑⌊
∩ℵ∉∪∇⇐√⊕⊄∪
⊇ð◊∫| ∑⟩ ™∑ð ◊ ∑ ∑⌊
⊗◊∫◊| ⟩∫◊ ®| ∑⌊
⊗◊∫◊ ◊®∑ð ∑ ◊ ∑ ∑ ⌈ ∑⌊
∉ ⌊ ◊∑ ⌋∑® ⟩∫
·∑ ®⌋ð◊⟩| ⌊◊©◊∑∫∑⟩∑© ™ ™⌊ ™ ⟩∫ ∑ ∑⌊
∉⌊◊ ð◊⟨ ∫| ™ ⟩∫ ∑ ∑⌊
·∫ ⟩∫ ∫ ◊| ∫ | ∑⌊
∇| ⟩ ⟨ð∑ ∑ ⟩ ⌉∑⟩∫® ⌉ |ð ⟨⌊∑
⊇ ∑ ⌋⌈ð∑ ⌊ ∫◊∫∩◊| ⟩⌋®◊⌈∫∑|ð◊∫| ⌈◊ ◊⌊ | ∫ ™ ⟩∫ ∑ ∑⌊ | ⟩⌊∑∫ © |◊| ∑⌊ ∑™ ⟩∫ © ∫◊⊕⟩⌊ ∑⌊ ∑™ ⟩∫ © ∫◊⟩ ð ⌊ ð ⌈∫∑|ð∑™| ⌊◊©◊∑ ⟨|
®∑|∑ð ™◊®◊⌈∫∑| ™ð ⟨ ð◊ ⟨∑ð∑ |◊ ™⌋⌈| |∫|ð∑™⌊◊©◊∑ ⌈⟩ ∑ ⌋
⊇ð◊∫| ∑⟩ ™∑ð ◊ ∑ ∑⌊
∪ ∑ ◊| ⟩◊® ∑⌊ ®⌋⟩™∑⌊◊∑∫∑⟩◊ ⌋⌈®∑ð ⌋⌈ ◊©|∑∑™ ⟩∫ ∑ ℜ ⟩∫ ™ ⟩∫ ∑⌊ | ⟩⌊∑∑∑ ⌊ ∑ ◊⟨ ◊©∑ ®∑⌊ ∫⟩ ®™∑⟩ ∫| ð◊ ⊇ð ∑∫ © ⟩ ∫ © ∑ ∫◊®⟩∑®◊ ™∑⌈⟩∫® ◊ ∫®⌋⟩∫ð◊ ®◊∫ ⟩ ® ◊|ð◊®⌊∑ ℜ⌋®™ð © ◊ ∑∫∑| ⌊ ◊∫ ®⟩∑ ∑ ⟨ ™ ∑™⌊ ð∑◊⌊ ◊ ⟩® ∑© ∑⌊◊ ⟩ ®∑ð ∑ ∑ ™◊ ⌋ ™⌊ ®◊⟩⟩| ⟩ ⟨ ℜ ∫ ®◊ ⟨∑ ⟩⌊ ® ∑ ∑ | ™™∑ð | |◊ ∑∫|ð◊|∫ ∑⟩|◊ ð◊⟨ ∫◊ ◊™⟩ ⟨ ⌈ ⌊ ∑ ◊ ® ΙΙ ◊⟩∫ | ©
√∑⌊ ™ ⌊ ◊⟨⌋∫ |ð∑ ™∑®⟩∑© | |ð∑∫ ⌈ |ð◊® ⌊ ⟩ ð ⌊ ð ®◊ ⌈⊕⟩⌊ ®⌋ ◊| ∑∫∑↔∏ ⌊ ∫ ⟩® ∑ ◊∫∑ð ◊⌊ ∑| ⌊ ∑ ∑≈∫ ∫ ⟨ ™∑∫⟩| ð∑∑®◊ ∑ ∑⌊◊ ∑√∑⌊ ⟩∫◊ ∑∫||ð ∑ð ◊⌈∫ | ⌊ ∫ ð |⌊◊ ®◊∑ ð◊⟨ ∫ ⊆◊⌈∫ ð◊⟨ ∫ ∫ ∑ ∑| |ð∑∫ ⊇◊| ð◊⟨ ∫ ?∇| ⌊ | ®⌋ ∫ ∫∑| ⌊ ◊∫ ◊ ∑∑?
∉ð∑ ™∑ ∑ ◊ ◊∫ ™∑⌈⟩∫® ®◊∫ | ™ ◊⌈∫∑™∑⌈⟩∫® ∫∑⌊ ⌊ ∫ ∫ ∫ ®◊ ® ∫ ⟨⌋ ⌊ ∫ ⟩® ∑ ◊∫∑ð ◊⌊ ∑| ⌊ ∑ ∑®⌋® ®⟩∑ ∑ ∫ ∫∑ð◊⟨ ∫◊∫ ◊ ∫∑⌊ ⟨⌋ ™◊ ®⌋⌈∫ ◊ ⌊ ∑ ∫ ⟩ √∑⌊ |◊ ™ © ⟩® ℘⌊◊® ∑— ◊ ∫ ⟩ ∫ ®⌋ð◊ ◊∫
·∫ ⟨⌋ ∑| ™®∑ð©◊∫ ⟩∑⟨ ð ⟩| ⟩ ∫ ⟩ ®| ⟩∫◊®⌊∑ ⌈ ∑⌊ ∑⟩∫ ∫ð◊⟩⟩|◊ ⌋®◊∫ ∑⌈|ð∑ ™∑®ð∑ ∑ ⌊ ™ ®ð∑◊| | ∫ ð⌋ ®⌋ ∑ ®∑ð∑ ⌋∈|ð ∑ ∑® ⟨⌉∑ ∑ ®◊ ◊|∑ð® ∫◊|∑ð◊⟨ ∫⌋ ◊™⟩ ⟨ ⌈⊕⟩⌊ ∑∫® ⟩∫ |ð ∫ ⟩∑⟨ ⌊ ™ | ∫ ® ⌋⟩⌊ ⌉ |∫ ⟩∫◊ ⌊ ∑|◊| ∑∫ ®ð∑ | ⟨⌋∫ ™ ∠∑ ∑ ™∑∫ ⟨⌊ ◊⌈ ð ™⟩∫®∑ |◊
⊗◊∫◊| ⟩∫◊ ®| ∑⌊ ∑∫⟨⌋∫ ⌊ ⟨ ⌈ ⌊ ∑⟩∫◊® ∫ ⟩⌊ ∫ © ™ ®| ∫ ð⌋⌈ ∑⌊ ⟨⌋⌊◊ ◊| ⟩◊ ◊ ∫ ⟨ ⌊ ∑∫®◊⟩
⊗◊∫◊ ◊®∑ð ∑ ◊ ∑ ∑ ⌈ ∑⌊ ∩™∑⟩ ®◊ ∑∫ ð | ∫ ®ð∑ ◊ ∫ ⟩ ◊™◊®◊∫ ð∑◊⌊ ⌋∑⟩ð | ⊕⟩⌊ ®◊ ◊ ∑⌊ —⟩® ⟨ ™ ®⌊◊™∑∫ ⟩∫ð◊ ⌋ ⌋| | ∫ ð⌋⌈ ∑® ®⌋ ∫ ◊ ™ ∑⟩ ∑⌊ ◊®∫ ◊∫ ∑⟩| ⟩∫◊ ® ∫⟩ ™ ⌊© ⟩ð ⌈⊆ ∫ ⟨⌋®⌋ ∫ ⌋|®◊ ◊ ◊∫ ∑© ∫ ∫ ∑⟩∫ ◊⌈∫ | ™ ™ ⌉ ∑| ð⟩⌋ ⌊ ∫∑⌊ ∫ ∑ ∑⌊ ⌊ ⟨ |ð◊∫| ⟩ð ◊ ⌊ ⟨ ⟩ð∑™ ∑⟩ð ◊ —® ◊® ⟩ ⟩∫ ∫∫ © | ©™◊®⌋ð∑ ∫∑|ð ⟩∫ | ∫ |∑∑ð∑◊⌊ ◊ ∇ð | |◊ ◊ ⌋⌈®◊ | ® ⌊ ∫|ð ∑∫ © ⌊ ∑⟩| ∑ ∫ð ð ®◊∫ ⟩ ◊®⌋| ⌊ ∑ ⌈ð◊⟨ ∫∑⊆ ∑⟩⌊ ®⌋ |◊ ◊⌊ ⟩ð |||ð ∑ð
Ι ◊ ∫ ∑ ◊ ∫ ∫ ®◊ ◊ ∑⌊ ⟨ ™∑∫ð∑◊⌊ ®◊ ◊™∑ ®™∑ ⊇ ⌊∑⟨◊ ®|ð∑™∑⌊◊ ∑⟩ ◊◊⟨⟩ ⌊ ∫ ™ | ⟩∫ ⌋⊕⟩⌊ ∑®⌋ ®⟩∫® ∑∫∑ ∫ | ◊ ∑ ∑ ⟩ð | | ⌊| ∫ ∑|ð ⌊ ® ◊|ð◊®⌊∑ ◊ ∫| ™| ðð∑|∫ ð ⌈∫∑⟩ð |®⌋| ⌊ ∑ | ⟩∫◊®⌊∑ ⌈ ∑⌊ ∑ ◊™ ∫|◊ ⌋®◊∫ ⟩ ∫⟩◊ ⌈ ∑⌊ © ∑ ∑⟩∫ ∑⌊ ⟩ð | ™ ⟩∫ ∑ | ∫ ð ⌈ |∑ð∑ ⟩ ⌊◊∫ð ™⌋| |◊ ◊| ∑ ∑| ⌊◊ ∫ ∑© ∫ ®◊|∑∑ð∑◊⌊ ◊ ∫◊||◊| ◊⟩∑© ™ ⌈™∑ ∑ ⟨ ⌊ ∑® ⌊ ∫™ð © ∑® |ð ⟩⌋⊆ ∑⟩ ∑®◊ ⟩ ∫ | ⟩∫∑ ∑ |ð∑™∑⌊∑ © ®ð∑ ∑ ∫◊ ∑⌊ ⟩∫◊ ∑∫™⌊ ∑ ®◊ ∑∑™ð © ∫ ©™◊ ∑∫ ⌊ | ⟩ð |⟩∫◊ ∑∫ð∑◊⌊ ⌋ | ∫ | ð ∫|
∉ ⌊ ◊∑ ⌋∑® ⟩∫ ∈| ∫∑®⟩∑ ð ∑∑ ∫ ®⌋| ⌊ ∫∑®ð∑ ⌊ ∫◊∫∑®⌋| ⌊ ∑ ∑⌊ ⇑∫ ®◊ ⊆∑|ð ⟩∫ ◊| ⟩⌋®◊⌈∫∑◊|ð∑™⟩∫◊®⌊ ⌈∫∑|◊| ®∑∑| ∑ ⌋⌈| ⌊ ∫∑⌊ ⌋⌈ð∑ ⌊ ∫◊∫∇ ⟨⟩∫®∑ ⟩ ∫ © ◊ ◊∑∫⟩ |ð ©ð◊ ð ®◊ ∑ ∑⌊ | ∫ ð | ⌈™∑∫ð∑
ΙΙ ◊⟩∫ | ©
·∑ ®⌋ð◊⟩| ⌊◊©◊∑∫∑⟩∑© ™ ™⌊ ™ ⟩∫ ∑ ∑⌊ ·∑∫| ◊ ∑ ®⌋ð◊⟩| ⌊◊©◊∑∫∑ ◊⟩∑© ™ ⌈™∑ ∑⌉∑ð◊ ⟨ð◊∫ ∫∑® ◊ ∑ ◊⟩ð | ⟩| ⌊ ∑ ◊ ∑ ∑ ⌈ ∑⌊ ∑∫⟨⌋∫ ⟩⌊ | ◊⌊◊® ∫ð∑⟨ ∑∫⟩ ◊ ∑∫ ∫ ∑⌉∑ ™ ∑⌊ |ð∑ ™∑ ∑ |ð ⟩∫ | ∫ |ð∑◊⌊ ◊ ∑⌊◊ © ®◊| ∑ ∫ ∫| |∫| ∑∫⟩ ™◊∫ |⌊◊ ð◊⟨ ∫⌋| ™ ⟩∫ ∑ ∑⌊
∉⌊◊ ð◊⟨ ∫| ™ ⟩∫ ∑ ∑⌊ ∑∫⟨⌋∫ |◊ ™⌋⌈ð◊ ⟩ ®∑ð ∑ ⌋ ℵ® ∫| ©™◊∑© ® ®⟩∑ ∑⟨ ™∑∫ ∫ ⟨⌋®◊∑∫ ◊|∑ð® ◊ ◊⌊ ∫◊|∑| ©™◊ © ∑ ∑⌊ |◊ ∫⟩ ∑™ ⟩∫ ⌋ | |◊®⌋ ∑ð∑◊⌊ ∑∫∑® ∫ ⌊ | | ⌊ ∑™ ®∑ð ∑⟩® ∑ | ™⟩ ◊ ∪ ∑ ∑ ®⌋| ð ◊∑∫∑ð◊ ð◊⟨ ∫◊∫ |⌊◊ ™ ⟩∫ ∑ ∑⌊ ∫ ∑⟩∫ ®◊ | ∫
⊇◊ ™⌋⌈ð◊ |ð∑ ™∑ ∑ ⟩ ∫ ⟨ð◊⌉◊⌈∫∑⟩ |⟩® ∑ | ™⟩ ◊ ⟩|ð ⟩ ⟨ ⌈| ®™ ⟩∫ ∑ ∑⌊ ◊ ® ∫∑∑∑∇|◊ ∫∑ ∫ ®⌋ ◊∑∫∑ ∫ ®◊ ∑| ™⟩ ◊ ∑⟩| ⟩ ⟨ ◊⌈∫ ⟩| ⟩ ⟨∑∑™ ⟩∫ ∑ ∪®⌋⟨∑⟩| ∑ ⟨⌊◊© ™◊ð ⌋ ◊| ⌉ ∉ ®∫ ð ∫∑®◊ |ð ⟩ ⟨ ∫ð ⟩ð◊ ∑|◊||ð ⟩ ∑∫∑⟩ ∑®⌋ ™ ð◊⟩⟩⌊◊⟨⌊∑ © | ⌊ ⟩ © ⟩ ⟩∫ ∠◊⟨ ∫◊⌈∫∑∫◊|⟩ ∑⌊ ∫ð ®∑ ∑ð | |◊® ™ |ð∑|ð◊⟩ ⌋⌈™∑ ∑| ®⟩∫® ∑∫∑ ∫ | |ð∑∫ ⟩™∑⌊◊∫
∇∑⌈ ◊⟩ ® ⌊◊∫∑∫ð◊™ ⟩ ⟩® |∑ð®⌋ ◊| ⟩◊ ⌋ ∑⌊ ⊆◊∫ ∫ ∑ ∫ ® ⟨⌉∑ ∑ ◊⌊◊|◊| © ∑ ð∑ ◊∫ ®⟩∑ ⟨⌋⌊ ð∑ ∑ ⌋∉⌊◊ ® ∫®∑ ™∑| ∫ ™ ◊| ® | ∫ ® ⌋∑ ∫®∑ð ™∑ ®∑ð∑ ⟩∫ ®⟩∑⟨∑∠◊⟨ ∫◊⟩ ∑⌊ ∫ð ð◊ ◊®™∑
⊇◊|ð◊⟨ ∫◊∫ ⟩ ∑⌊ ®⌋|ð ∫∑∫∑® ΙΙ ◊⟩∫ | © ℵ ™∑⟩ ®⌋ ∑∫∑ ⟨ð◊∫ ∫ ® ◊ ∑ ◊∫ ∫ ∑∫| ⌈|⌊◊ ™∑⌈⟩∫® ⌈®⌋ð ⟩ ®⌋®◊∑∫⟩ ™◊⌊∑| ∑⟩ð◊ ⊇ ∑ ∫◊|⟨⌋®◊∑∫ ∑® ®⟩∑ ⟩⌊ ◊ ⊕⟩⌊ ||ð ∑ð ®⌋ ∫ ∫∑| ⌊ ∫ ® ™ ∫∑⌊ ⟩| ∑|ð◊®◊®◊ |⌊◊ ⟨ ™∑∫®|⌊ ◊∫ | ⟩| ð ∑⌈◊®∫ | ⌊⌋ |ð ∑⟩ ®∑ð ∑ | |ð∑∫ ⌋∑™∑⌈⟩∫®
·∫ ⟩∫ ∫ ◊| ∫ | ∑⌊ ◊|ð ⌉∑© ® ð |◊| ∑⟩ ⌉∑⟩∫® ∫|ð∑| ∫⟩∫® ∩™∑⟩ ∫ ∑ ∑ ∑∫⟨⌋∫ ∑™ ⌈ ð ⌊ ð ®| ⊆ ◊⟩∫ ∫ ∫⟩ ∫⟩∫® ∑ ∑ ⟨ ™ ⌈⟩ ⌋™∑ ∑© ∑ ®∑ð∑ ⟩∫ ®⟩∑⟨∑⌊∑ |ð ∑∑
∇| ⟩ ⟨ð∑ ∑ ⟩ ⌉∑⟩∫® ⌉ |ð ⟨⌊∑ ⌊
|ð∑ ™ ⌊∑ |ð∑| ∫⟩∫® ⌈⊕⟩⌊ |ð∑| ∫⟩∫® ® ∫ð∑ ∑© ◊ð◊|∫∑ð◊ ∑ ®∑ð∑ ⟩∫ ⟩∫ð◊ ⌊∑ — ™∑⟩ ® ∑ð∑ ∑ ∑∫ ⌊ | ®| ∫ ® ⌋ ◊⟩∫ð ∫ð∑ ©◊↔ℜ ⟩| ∫◊ ∑⟩ ◊ ≈⊕⟩⌊ |ð∑| ∫⟩∫® ∑ ◊|⌊ ◊∑∫⟩ ® ∫⟩ ∫⟩∫® |◊| ⌈⌊ ⟨ ⟩ ⌋™∑ ∑©⟩∫◊® ∫∑∑⌉∑ ™ | |ð∑∫ ∑⌊ ∫| ™◊ ® ∫ ⊕⟩⌊ ® ⟨⌉∑ ∑ ◊∑∫∑ ∫ ™∑⌊◊∫ ∫ |◊| ®⟩⌊ ◊∑⟩®⌋ð◊⟨ ∫| ⌈|⌊◊ ◊ ∑⟩ ∫∑|ð ⟨⌊∑ ⟩® ∑ | ™⟩ ◊ |◊ ™⌋⌈®∑ ∑ð |◊ ™ ∑ ∫ð ð∑ ∫⇑∫ ∫◊| ∑®∑ð |◊| ∫ ∫ ®⌋ ∫◊∑∫∑ ∫ | ©
⊇ ∑ ⌋⌈ð∑ ⌊ ∫◊∫⇑∫ ⌈⌊ ⟨ ⌋⌈| |∫⇓ | ©™◊ ∑ ◊⟨⌋®◊ |◊ ◊∫ ∫ ∑⌊ ®⌋| ⌊ ∑ ◊ ®|◊| ⌈⟩ð |⇑∫ |⟩∫◊∫ | ©⌊ ∑ ◊ ∫ ⟩ |ð∑™∑⌊ ∫ |ð◊® ⌊ ⌋∑⟩ð | | ∫ ∫ ®⟩ | ⌈ð◊ ∫ ∫⟩∫◊®◊⌊◊ ∫ ⟨⌋⌊ ⟩ ® ⌋ ∑™ ⟩∫◊∫| |ð ð◊⟨ ∫∑⟩ ∑⌊ ⊗ ⟩∫ © ∫◊ ∑⌊ ⟨∑⟩| ∑ ® ™ ∑®⌊ ∑∫ ◊| ⟩∫◊®| ®⌋| ⌊ ∑ ∑ ®⌋ ◊™◊ ⊇ð ∑∫ © | ⟩∫∑ ∑ © ™◊| ©™◊®⌋|ð ⌊ ⟩∫◊∑∫∑⟩® ∫∑∫ð◊™ ® ™ ∫∑|◊| ⟩|∑ ®™ ⟨ ⌊ ⟩ ®⌋| ◊⟩∫ ⌉∑ ⟨ ™∑∫∑© ð™ ∫ ⟩ ⟩ ⟨ ⌈⇑∫ ⌊ ⌈⟩| ⟩ ⟨ ⟨ð∑⟩∫ ®∑ð∑ ⟩∫ ®⟩∑⟨∑ | ®∑ð ∫ ®⟩∑⟨ ⟩® ⟩ ⌊⌋ ⟩® ∑| ™⟩ ◊ ∑
⊕⟩⌊ ∑⌊ ∑ð∑◊⌊ ®◊ ◊ ◊| ∫∑| ∑ ∈⟩ ® ◊ ⟨|◊ ◊|⌊ ◊∑∫⟩ ®∫ ∫ ∑⌊ ⌊ ⟨ |ð∑ ™∑®ð∑ ∑ ◊ ∫ ©™◊®◊ ⟩∫ ∫®∑ð ∫ ⟩ | ∑⌈| ™ ∑∑⌊ ⟨ ∑™ ⟩∫◊∫ ◊®◊ ®⌋ ◊⟨⌋®◊∑∫∑ ∑⌈ð◊⟨ ∫◊ ◊™™ð © ®∑⌉◊ ◊ ◊⟨⌋∫ ∑⌊ ð∑◊⌊ ®◊∫ ∑®

⊗⊕∇⇓®⇐∇∈ℜ⊕®∈ℜ⊇∈®∈∠⇔⊕∉∈⊂∈℘©®∠⊕ℵ⊄∪∩∈ℜℵ®⇐√⊕⊄⇐
↔∠∑ ⌊∑|⟩ ∑⌊ ∑⟩∫ ⟩ ® ◊ ð ◊ ∑ ⌈ ∑ð© |◊ ™ © ◊⟩∅ ∫ ⌊ | ™⌊ ∫ © |ð◊⟩ ◊ ⟩ ⌊ ◊|∫ ®⟩ ⟩∫ð∑ ∫⟩ || ⟩∫ ™ ⟩∫ ©◊∑ ⌈ | ©™◊ ∑™ ⟩∫ ⌈ ∑⌊ ℜ⟩ ®⟩∑∑∑ ⌊ ∑ ®⟩ ∑∑| ⌊ ∫ ð◊™∑⌊◊∑∫⟩ ð∑ ⌊∑|⟩ ∑⌊ ™∑⌊◊∑∫⟩ ∫ ⌊ | ⌊ ™ ⟩∫ð∑ ⌉ ⟩ |∫ ⌈ ⌊ ™ð © ⌈| ⟩∫◊®⌊∑ ⌈ ⟩∑⟨∑® ∑⌊ ≈—| ⟩◊⌊®∑⌊ | ⌈ð ⟩⟩| ⌈ ∑ ⌋⌈∪∉∉◊®⌊ ®
∉ ⟩∫◊ð◊⌈∫∑⟩ |ð∑™∑⌊ ∫ ⟩® ⟩◊ ⌋∑⌊ ⟨ ⌋∑ ◊ ∫ ◊ ◊⌈∫∑ð◊⟨ ∫◊∫ ∑ ® ∫ ⌈ ⟨⌊◊⟩∫ ⊕⟩⌊ ∑⌊ ®∑|⌊ ⟨ ∫⟩® ð◊⟨ ∫ — ⟩|∑ ∑ ©◊ð◊ ∫ ð ®◊
⊂ © ∑ ∑ ◊ ∫®|◊| ⌈⟩ ∑ð∑™∑ ∫∑⌊ ⟩∫ | ⌊ ∫⟩ ⌊ ∑ð◊⟩|ð⌋∫ ⟩ ∫ ⟨⌋®⟩∑® ◊ ◊⌊ ⟩⌊ ∫ ™ ⟩∫ ∑ ⟩|∑ ◊∩™∑⟩ ∫ ⌊ | ™ | ∫ ∉ ®∫ ð ⌈∫∑|∑ð∑™⟩ ⟩ð◊ | |ð ⟨ ™∑ ⟩⌊∑™ ⌉ ∑⟩⌊ ®◊↔ℑ∑⟩| ∑ ⌋⌈ð◊ ∑© | ™⟩ ◊ ð◊⟩|ð⌋®◊∑∫ ∑ ⟩∫ ∑ ∑⟩∫ ® ≈∉ |ð ∑⟩∫® |ð∑™∑⌊∑ © ®ð∑ ∑ ®⌋ ⟨ ◊∫∑⌊ | ⌊ ∫∑ ∫®∑∫ℜ⌋|ð ⟩∫ | ®⟩∫® ∑∫∑ ∫ ®◊ ∑ ∑ ⟨ ™ ℜ⌋⟨ð◊® ◊ ∫ ∑⟩∫◊ ∫∑|ð ∑⟩⟩ ◊⌊
∉ |ð ⟨ ⌈∫∑ ∑⟩® ™ ∫ ®⟩∑|⟩ ⟨⟩∫®∑ ⟩|∑ ·∫ ⟨⌋®⌋ ™∑⌊◊⌊ ® ⟩ ®∑™ ⌊ ◊⟨⌋∫ ∑⌊ ⟩⌊ ∑ ⌊ ™ ⊇◊| ®⌋⟩ | |◊ð ∫ ® ∫ ∑ ∫ ⟩| ⟩ ⟨ |ð ®∑⟩∫ ®◊⟩| ⟩|∑ ⊕⟩⌊ ®⌋ ◊ | ∑∫∑⟩ ∫ ⌊ | ◊⟩ ⟨⟩∫®∑ ⟨⌊◊© | ⌊ ®®◊ ∑⌈ © ∫| ® ∫ ⟩ ∑©◊∫ ® ⌋∑|ð ∑⟩⟩⌋ ◊ ∫® |◊∫ |ð∑| ∫⟩∫® |ð∑◊⌊ ◊ ∑⌊◊∑ © ∑ ™◊ ⌋∑|ð ⟨⌊∑ ⌋⟩ ™ ð ® ∑ ∈⟩ ⟨∑ ∫ |◊⟩◊∑∫⟩ ™ ⌊© ⟩ð ⌋ |⌊◊ ® ◊| ∫ ð⌋∑ð◊⟨ ∫◊ ∫|ð◊∫| ⟩ð ⌋∑ ∑⌊ ⊆ ∑⟩⌊ ®◊ | ∑ ⌋∑ ∑⌊ ◊|ð◊®⌊∑ ⌋ ◊∫ ∫ ⟨⌋ ∑|ð ⟩∫ ⟩™∑⌊◊∫ ⟩ ◊⟩∫⌊ ®⌋ ⟩∑⟨ | ® ∑⟩∫ |ð∑™∑⌊∑ ⌋⌈®|⌊◊™®ð◊ ® ∫ ∑ ∑⌊ ®∑ ∑⟩∫®◊ |◊ ◊∫ | ⟩ ⌊ | ⌉ ™◊ ⌉ ⟩ ◊ ∫ ⟩ ⟨⌊◊© ∫® ð ∫∑⌊ ⟩∫ | ◊⟨ ∫ ∫ ⟩ ⟨ | ⌊ © | ®∑ð ∫∑®◊ ∑⌊ ◊ ∫⟩⟨⌋®◊∫ ⟩ © ð◊ ™ ⟨⌋⟩∫ð∑∑◊ ™∑⌈™ ⟩∫ ∑ ∑⌊ | ⟩∫◊ ®| ®⌋ |◊ ∑∫⟩ ⟩∫ ⌊ | ∫ ®⌋⟨ ™∑∫∑™ ◊∫ ∫ ⌊ | ⟨ ™ ↔∏®◊∫ ⌊ ⟨⌋ ◊®⟩∑®ð∑ ∑ ≈
∪⌉ ∫∑ ∑⟩∫ ⌋∑| ∫ ™ ⟩∫ ∑ ∑⌊∑⌈⊇ ∑ |ð∑ ⟩|∑∫ ⟨ ◊ ⌋ | ∫∑ ⌊ ™∑⌈© ∫ ®⌋ | ⌈∫ ◊ ∫ ∑ ◊⌊ ⊆ ∫ ⌊ ™ ®⟩∑©™◊ ⌊ ∑ ◊|◊ ◊ ⌋ ⌊ ⟨ ™ ∫ ◊|◊ ◊ ⌋ℜ ™ ® ∑ ⟩∫ ð ®⌋|ð ⟩∫ ∑ ◊∑∫∑ ◊⟩∫ ⌉ |ð ⟨⌊∑
∈⟩ ◊®◊ ⟩® ® ∫ð∑ ⟩ ⌊ | ⌉ ⟩® ∑© | ™⟩ ◊ ®⌋| ⌊ ∫∑ ®∑ð∑ ⟩∫ ® ⟩| ⌊ ∑ ⌊ ⟨⌋ ⟩® ∑⌊◊ ⌈ℜ⟩∑©™◊| ∫∑∫ ∑© ®⌋ ⌉∑∫∑ ⌉∑∫®◊⟩ℜ⌋ ⌉∑∫∑ð◊⟨ ∫ ◊|∫ ∫ ð∑ ®⌋ ◊⌈ ™◊∑∫⟩ ∑ ®®◊ ◊ ⟩| ⟩ ⟨ ⟩∫ ℜ⌋ ∫ ∫∑|ð ™◊∫ ◊|∫ ∫ ∑∫| | ∫ ∑ ∫ ®∑⌉
℘⌊◊® ∑|ð◊® ⌊ ™ ⟩∫ ∑ ∑⌊◊∑ © —⟩ ð ð ®◊∫ ∑⌊ ◊ ◊∫ ™∑⌈⟩∫® ®◊∫ ∉ð ∫ ™∑⌊◊∫ ⟨ ⌊ ∑◊ ∑⟩∫ ⌊ | ⟩| ⌊ | ®⌋ ◊|⌊◊ ð ®◊⌊ ⊕⟩⌊ ®⌋ ∑ ◊ ∑∫∑™∑⌈⟩∫® ®◊∫ ∑⟩™∑⌊◊∑∫∑|∑ð®⌋⌈ ◊© |◊| ∑©⌊ ⟨ | ⌋⟩⌊∑ ⌋∑ð◊⟩⟩ ™∑ ð◊ ⌋ ⌊∑ ◊∫∑ ®◊ ® ⟩∫∑⌈| ⌊ ⌋®◊ ∑|ð ∑⟩ ∫ℑ ™ ∫∑∫∑ð|∑⌊ ®⌋ ◊⟨⌊ ™◊∫∑⌊ ⌋⊗∑⌈⟩∫® ⌈∫∑ ◊⟩∑| ™ ∑®⌋| ⟩|◊ ∑⌊ ® ™◊
ℑ⌋⌊ ⟨⌋ ◊ ∑ ◊∫∑⌊ ⟩|⌊◊ ð ®◊∫ |ð ©ð◊ ™ ⟩∫ ∑ ∑⌊ ∫ℵ™ ⇓⊆ ∫ ∑®⟩∑©™◊® ∫◊||◊| ∑ ™ ◊ ◊⌊ | ◊ ∑ ™∑⌈⟩∫® © ∫® | ∫ ∑ ™◊ ⌋∑® |ð ⟩⌋| ∫ ð⌋∑| ∫ð∑⟨ ∫ ◊⌈∫ ð∑ ∑ ∑ ∑⟩| ⌊ | ®⟩∫ ð ∑ ∫®⌋⟨ð◊ © | ð⟩◊ℜ◊ ∫ ⟨⌋|ð ∫ ®⌋ ◊⌊ | ™◊ ™∑∫∑ ∫ ©™◊® ®ð◊⌉◊ ⟩ ◊®⌋⟨ð◊ ™ ð © ®⌋ ◊© ◊ ◊© ∫ ∑⟩∫ ð∑ ◊ ⟨⌊ ◊⌈ ∑ |ð ∑ ∫ ⌋∑ ∑⌊ ® ⌈™∑∫∑ ◊®∑ð | ⟩∫◊®⌊∑ ⌈|∑ð∑™⟩ ⟨ ⌈ ◊™◊
√∑⌊ ∫∑⟩ ®⌋⟩ | ∉ð ⟩ ∫∑⟨ ⌊ ∑ ∑ ® ◊⟩⌊ ®◊∑∫∑ ◊⟩∑© ™ ⌈™∑ | ⟩| ⌊ | ∑⌊ ®∑|⟩|⌊ ∑ | ™ ◊∫ ⟩ ∑ ◊∫ ∫ ð ®∑ | ∫ ð⌋⌈⟩◊ ⟩∑⟨∑|ð∑™| ®⌊ ∑∫
⊕⟩⌊ ⟩∑© ™ ®⌋®⌋ ™∑ ⌋™∑⌊◊∫ ∫ ∫ ®◊ ∑ ð◊® ∫⟩ ◊ ∫∑⟩ ð◊⟩⟩ ◊∫ð ®◊∫ ⟩| ∑ ∫∑ð∑⟩ ð◊⟨ ∫ |◊| ◊©®∫ ◊|ð◊®⌊∑ | ∫ ð ∑®⌋ ⟨ð◊⌊ ∫ ⌊ | ∫ ©™◊ ∫◊ð◊⟨ ∫◊ ™ ®⌊∑∫® ð ∫®◊⟩∉ð∑™| ⌊ ®⌋ð∑ ⌊ ∑ ∫ ⟩® |ð ∑⟩⟩ ®⌋⟨ ð◊∑∫∑∫ | ∫ ð◊ ⟨⌊ |◊®◊ | ™ ⟩| ⟩ ⟨ ◊ ◊∫∑ð ◊⌊ ⟨∑⟩|∑ ∫ ⊗⌊ ∫ © ®◊ ⟩| ð∑∑®⟩∑© |ð ™∑∫⟩ ∫ ⟩ ◊™⌊ ⟨ ∑ ⌋™∑ © ⊇∫ ∑ ∫ ⟨⌋ ∫ ⟩ ®◊ ◊ð◊⟨ ∫◊| ∫ ð◊ ⟩∫◊® ∫®◊ ™⌊ ∫ © ⟨ ∑ ®ð∑ © ∫⌋®◊ ®⟩∑ ∫ | | ⟩∫◊®⌊∑ ⌈ ∑⌊ ®⌋®⌋™∑ð ∫∑∫◊||◊|⟨ ™∑∫∑ ◊∫ ∫ ®◊⟩ ™∑∫®|∑ð∑™
∇∫◊® ®⌋∑ ∑⌊ ™◊⌈∫∑| ™⟩ ◊ ®ð∑ | ⟩|◊| ∫ | |◊® |ð ©®◊⟩®ð ™∑⟨⌋ ∑© ∑|ð ⟩ ™ ∫ ◊|∑ð®⌋⌈® ©⌊ ™ ®⟩∫® ⌈∫∑ ⟩|∑ ™ ⟩∫ © ∫ © ⟩∑⌈ ◊⟩
⊆∑ ®∑ð∑ ⟩∫ — ⟩ ® ◊ |ð ◊ ∑ ™◊ ℜ⌋™ ⌊ ⌋ ∑∫| ⟩ ◊®◊∫ ∫ ∑⟩⌊ | ™⟩ ◊ ∑|ð ◊∑∫ ™∑ |ð ∑ ∑®◊ — ð ⌊ |⌊ ∫ ∫ ∑|ð ⟩∫ |◊∑∫|∑∑ð∑◊⌊ ◊ ℜ◊ ∑ ∑ ⟨ ™ ⟨∑™ ∫ | ™⟩ ◊ ∑|ð ∫ ®◊ ™∑ ⌊ |ð ⟩ ⟨ ∉ ™⟩ ◊ ∑ |ð ⟩ ∫ ⟩®∑ð ⌈® ™∑ ®ð∑◊⌊ ⟩∫ ∑∑ ⟩ ⌉∑⟩∫®⌊∑ ∩◊⟩∫◊® ∫ | ™⟩ ◊ ∑ð◊⟨ ∫◊∫ ◊®◊⟩ ∑⌊ ∪™∑ ⌊ ∑⌊ ⌊ |ð ⟩ ⟨◊™ ⌊ ⌋⟨⌋∫ ®⟩∑©™◊ ∑∫| ⟩ ð ⌊ ð ®◊ ⌋ℜ⌋™ ⌊ ⌋ ⟩ ⟩ ◊®◊∫ ∫ ð∑ ∑ ∑|ð ⟨⌊∑ ⌋ ∑⟩ ⌉∑⟩∫® ∑∫®◊ ∑| ™⟩ ◊ ∑ ∑ ◊∑∫ ∫®∑∫ | ∫ | | ∫ ð ™∫ ℜ∑ð ∫∑® ∫ ⟨∑ © ® ð ®∑ð ∫∑®| ⌊ ∫∑⌊ ⌋⌈ð∑ ⌊ ∫◊∫ ®⌋| ⌊ ∫∑∑©

ℑ⊄ℵ℘∈∇⊄∈ℜ∪

©⟩|∑ ∑ð ∑∫⟩ ∑⟩∫ ⌊ | ∫∑ | ⌊ ∑ ∑ | ∫ ð © ∑⌊ ®∑|™ ⟩∫ ©® ⟩| ⌊ | ∫∑ |ð∑©ð◊™◊ | ∫ ð⌋∑ |ð∑ ™ ⌊∑⌊ ◊| ∫ | ⟩|∑
®ℜ◊ ©∫

⇑∫◊©⌊◊®◊—|ð ∑|ð ™ ⌊ ∑ ∑ð◊ © ® ð◊ ⟨ ⟩| ⟩⟩∫®∑⟩∫◊® ∫ ∑⌊ ∫◊||◊| ◊| ∫ ™ ⟩∫ ∑ ®⌋⟩| ð∑∑®⟩∑© ⟩∫ ⌊| ∑∫∑⟩ ⟩∫ð ™ ⟩∫ ð◊ ⌊ © ◊ð◊|∫∑ð◊
⊆∑⟩∫ ∫™ ◊∫ ∫ |⟩®∑∫⌊ ⌈ ⟨⌊◊© ð ™ ⌈ ∑⌊ | ®∑™∑∫©⌊◊™|◊ ⌊∑©|◊ ™ ð ©◊∅ ®◊ ◊ ∑®∑ð ∫ ⟨⌊∑© ∫⟩ ®|ð ∑⟩⟩∑ð◊⟨ ∫⌋ ◊™|ð∑™⌊ ∑ ⌈® ΙΙ ◊⟩∫ |ð ©ð◊ ⌈ ∑⟨⌋ ∫∑⌊ ⟩ ∫ ⟨⌋®◊⟩ ∑⟩⟨ ⌊ ⟩∫ ⌊| ∫ð ™ ⟩∫ ™◊ ∑ ⟩|⌋∫◊ | ∫ ð⌋∑ ◊ ∫® |◊∫ | |ð ∑⟩∫® |ð∑™∑⌊∑ © ®ð∑ ∑ ð◊⟨ ∫⌋ ◊™⟩ ⟨ ⌈© ∑ | ð ⌈⟩|⌊◊™⌋®◊⌊ ⟩ ®|∑ ◊∫⌊∑ ∑ ∫ ∑|∫ ⟩|⌋∫⌋®◊∑∫ ∑ ◊|ð ⟩∫ ∇◊ ◊ ⟨ ⌊ ◊ ⟨|◊—® ⟩|ð ◊∫ ∫ ∫ð ™ ⟩∫ |◊|™ ð ⌋∑ ◊| ⌊ |◊|| ® ™ ∫|◊ ◊∫ ⟩ ∫™◊⌊ ∑⌈ ⟩ ⌊ ⌈ ð◊⟨ ∫⌋ ◊™⟩ ⟨ ⌈ ⌊ ⟩® ∑⌈ ∑⌊ ⊆◊|ð ∫ ®ð◊™ ⌈∫∑⟩ |ð ⟨⌊∑ ◊ ®⟩∫◊ ⌉ ◊®◊ ∑ | ∫ ⟨ —⟩∫ |∑ ⌊∑⟩∫ ⌋®∑™ ⌉∑⌈| ⟩|∑ ⊕⟩⌊ ®⟩® ∑⌈ ®⌋| ©™◊ ⟨ ™ ™ ⟩∫ ©◊⌊ |ð∑™∑⌊∑ ⌈| ⟨∑™⌋|ð ⟩ ® ∑⌈ð◊™ ⟩∫ ™ ®⌊∑∫® ð∑ ∑∫ ∑|ð∑ ∑ ®⟩| ∫∑ ∫ ∑⌈ ◊ ◊⟩∫ |ð∑™ ∑⟩∫® ®◊⌊ ∑ð∑ ∑ ∑ |ð∑™∑⌊∑ ⌈|ð ⟨⌊∑ ⌋∉ ∫∑®⟩∑ ∫ ™∑⌊◊∑∫⟩ ®⟩∑|⌊ ∑ ∉ ∫ ⟩∫◊⌊| ®◊ ⟩ ⟩|ð ⟨⌊∑ ⌈ ⌉ ∫∑ ◊⌊ ∑ ® ∑⌈® ⟩∫ ™ ⟩∫ ∑ ⟩|∑ ◊⟩| ⌉ | ™⟩ ◊ ⊇◊ ™⌋⌈®∑ ∑ð |◊ ™ ∑ ∫ð © ® ð ∫∑⟩® ∑ | ™⟩ ◊ ®◊ ∫ð ™ ⟩∫ ™ ∫∑ ∫®∑∫ℜ ™ ∑ ∫®⌋| ⌈ ∑∫∑ ⌊ | ®⟩∫® ∑∫∑®|◊| ◊|ð◊®⌊∑ ™® ©◊∫ ⟩ ℘⌊◊® ∑ ◊⟩∑| ™ ∑⟩ ∑®◊⌈∫∑⟩ ®| ⟨∑™∑∉ ⟩∫ |◊ ∫◊| ⟨ð◊ ∫ ∑⟩∫ |⌋∫◊ ⟩ ∫⌋⟩|◊∫ | ⌊ ∫∑⌊ ⌋⌈◊⟩|∑|∫®|ð∑™⌊ ∑ ⌈ |ð ⟨⌊∑ ∑®⌋ ◊ ∑∫ ∫∑|◊|↔ ∑©◊∫ ®≈ ⟨ ð◊ ®◊∑∫⟩ ™⌊ ®◊⟩⟨ ⌊ ® ⟩∫ ↔⊆∑⟩ ⌉∑⟩∫® ∑∫∫◊| ⌈∫ð ™ ⟩∫ | ∫ ð◊ ∑|ð ∑⟩⌊◊⟨⌋ ∑ ∫ ®| ™◊ð |≈∪⟩◊ ∑ ∫∑ð∑⟩ ∑ ∫ ⟩∫◊⌊| ®◊ ⟩ ◊| ∫ ⟩|ð∑| ∫⟩∫® ®⌋ ∑|ð ⟩∫ ™ ⟩∫ © ∑∫∑ ∑⌊ ®⌋| ⌊ ∫∑ ◊ ∫∑⌊ ⟨ ⌊ ∑ ◊™ ◊ © ®◊ |∑ð® ◊ ◊⌊ ℑ ™™ ⟩∫⌋⟩|ð◊ ®◊ ∫↔·∫ ∑⟩∫ ™◊ ◊◊ ∫ ∑®∑ ∑ ∑?≈⊇∫ ◊∑∫ ∫ |ð ∑⟩∑∫ ◊ ð∑ ∑ ∑|ð ⟨⌊∑ ⌋?
⊗◊ ∑ ∑ ™◊ ◊ ◊⟩∫ ∫|ð⌋®◊∑∫™®∑ð ™⌊ ®⌋ ® ⟩∫∑⌈⊆◊ ∫∑⟩ |ð∑®ð◊⌉◊∫ ∑ ™◊ ®|⌊◊ ™∑⌈⟩∫® ⌈⊆ |∫ ∑ ◊⟩∫ð◊ ®◊ ∫ ⟨ | |ð ⟩∫ ∫ ®◊ |ð ™® ∑ ®®∑ð ∑⟩⌊ ®⌋ ∫⟩∫ | ∫∑®◊⟩⟨∑ ◊⌊ ⟩∫ ®⌋ð ∫® · ∫◊ ⟨ ©ð◊ ®⌋™◊ ⌉ ⟩ ⌊ ™∑⌈ ∑ ◊⟩∫ ◊ ∑∫ ∫ ∫ ∑ ⟩|⌋∫◊ ⟩∫ð◊™◊ ◊⟩∫ ⟩∫◊ ® ⌊ ⟩ ∫ ⌈⟩ ⌊ ⌈| ∫ ð◊ | ⌊ ⟩∫ ∑ ⌊◊ ⟨ð◊ ◊⟩∫◊®⌊ ⌊◊™® ©◊∫ ⟩ ®|∑ð∑™
ℜð∑ ∑ |ð ⟨⌊∑ ⌋ ⟨ð∑∫◊∑ ⟩ ⌊ ™ð ⟩∫ ∫ ⟩◊ | ⟩∑⟨∑⟨∑⟩ ∑ ∫◊||◊|⟩| ⟩ ⟨⟩∫® ∑∫ð ⟩∫ ⌊ ⟩∫ ⊆∑ ™◊ ◊∫ ⌊ | ®™ ®⌊ ∑∫⌊ ™∑ð◊◊ ∑®◊⌊ ∫∑© ⟩ ©ℜ⟩∑ ◊® ⟩ ∫⌊ ∫∫ © |◊| ∑⌊ ®∑| ∫ ∑⟩∑∫⟩ || ð◊ ∑ ⟩™∑⌊◊∑∫∑© |ð∑©ð◊™ ⌈ ⌊ ⟩⌊∑™ ⌉ ◊© | ⟩|∑
⊆∑ ™◊ ◊—⟨⌊◊© ⟩⌊ ®∑ ∑ ⟨ ◊⟩∫ ∑| ⟩|◊∑∫ ◊⟩∫ ™◊©™∑ ◊⟩ ™∑∫⟨∑™◊◊ ∑ð◊™ ⟩∫ ⊆∑◊ ©∑⌊⌊ ð◊ ∫∑⌊ ⟩∫ ∫®⟩ | ⌈ð◊ ◊ ∑ ™◊ ∑⌈ |◊ ⌋®◊ ◊ ™ð © ®∑ð ™ ð © ?
∪∑⟩⌊ ∑ ™◊ ⟨ |®◊⌊ |ð∑⟩⌊∑™ ∫®◊⟩ ◊⌈∫ ®⟩∑⟨∑ ∑⟩∫® ◊ ® |∑ð∑⟩ ∫ð∑∫ ®⟩∑⟩® ∑ ⌋∑|ð |⌋ | ◊ ◊∫ ⟩ ◊ ◊⌊◊ ∑® ð◊ ◊ ∫ ℜ ∫ ⟩∫ ∑®∑⌊ ∑⟩ ⌊ ⌋ ™ ⌊ ™∑⌈⊇ ©™◊ð ◊∫⟩ |⌊◊ ⌋ ∑ ⟩∫◊®⌊ ⌈∫∑| |⌋∫| ◊⌈∫ ⟩® ⌈| ∫ ⊗ ⟨◊® ∫∑| ∑⟩ ⌉∑⟩∫® ⌉∑ ® ð∑ ∫ ∫ ⟩® ∑ ®⌋|∑ð∑ ◊© ∑∫∑| ð © ⟩|∑ ◊⇑∫ ∫ ∫ ∑∫ ∑⌊ | ∫ |◊| ◊ð∑ ∑® ®ð∑ ®⟩|⌊∑⟩|◊®™ ®∑ ◊| ⟩⌋®◊⌈∫∑⌊ ⟨ ⟩◊ ∑®∑ð ∫ ⌋⟩⌊ — ™∑ ⊂ ∑∫⟨⌋∫ ∑ ◊| ® ⌊ ∫®◊ ◊ ∫ ⟩® ® ∫ ⌈ ∈ ⟨ | ⌊◊©◊∫ ∫ ⌊ ∑ ∑⟩∫◊ ∑™◊® ◊ ∫⌋ℜ ∫ ð∑™⌊ |◊ ™ © ∑⟩∫ ∑⟩∫ ®◊ ⟩™∑⌊◊∫ |ð◊® ⌊ ⌋⌈®⌋⟨ ð∈ ∑ ◊⟩∫ ⟩ ®∑ð ∑ ©∑ ◊⌊ ◊ ™∑ | ∫ ð◊ ∑∫⟩™∑⌊◊∫ ®◊⟩ ⟨ ©◊∫⌋ ⟩ ◊⟩∫⌊ ®⌋ |ð ™ ∫ ∑ ∫ ©™◊| ©™◊®⌋®⟩∫ð∑ ◊∑∫∑⌊ |⌊ ∑ ™◊ ⊗◊®◊⌈∫∑ ◊ ⟩ ⟨⌊◊© ™◊ð ∫ ∑∑® ™∑∫ ® ∑⌈⟩ |◊⟨⌊◊© ⟩⌊ ®⌊ ∫ ∑∑ ®∑ð ∫ ® ⟩|∑

ℑ⊄ℵ℘∈⊗ℵ∠⊆∈∇®⇐ℜ∈∩ℜ∠ℵ∧ℵ⊕®ℑ⊄ℵ℘∈∉∈⊄©·∪⊕

ℑ⌊◊© ™◊ð ⟩∫ ∑⟩∫ ⟩◊ ð◊⌈
©ℑ⌊∑⌈|

⊂◊© ⟨⌊◊© ™◊ð ⟩∫ —∫◊| ⟨⌋⌊ ⟨⌋ ◊ ®◊∫ ∫ ∫ð◊ ™∑⌊∪ ∑⟩⌊ ◊⌈ ⊂⌋ ∫ ⟨⌊◊© ™◊ð | ©™◊|ð ⟩ ™ ∫ ∫ ∫ ◊ ◊ ® ©⌊ ™⟩∫ ⌉∑∑ ◊⟨⌋®◊∑ ⟨⌊◊© ™◊ð ⟩∫ | ©™◊ð◊⟩∫∑ð ⌋∑ |ð | ∫⌋∑ ∑ ™◊ ◊ ∑ ∫ |ð ∫ ∑ð∑™ ∑ ⟩|⌋∫◊ ∑ ℵ|∫ ◊⟩ ∑∫⟩ ®∑ð∑ ⟩∫ ⟩|◊ ◊∫ ∫ ⟨⌊◊© ™◊ð ⟩∫ — ∫ ⟨ð◊ ◊ ∑⌈ ∑∑⟩∫ ⌊ ?∪∑⌉∑ ∑ ∑⌊ ™∑⌈ ◊ ∫ ®∑⌊ ◊⌈ ∑⌈ð ⌊ ⟨⌊◊© ™◊ð ⟩∫ ® ◊ ∑⌈ ⊆◊ ∫∑⟩ ⟨⌊◊© ™◊ð ⟩∫ ⟩|∑ ⟨⌊◊© | ⌊ ∑⟩∫◊ ∫ ð ⌈®◊ ∑⌈ ⊆◊ ∫∑⟩ ⟩|⌋∫⌋®◊∫ ⟨⌊◊© ™◊ð ⟩∫ ∑∫ ⌊ | ◊∫ ð◊™ ⟩∫ ∫ ∑⟩∑∫ ◊ |◊ ™⌋⌈ ®⌋⌈™∑ ⟨ ™ ∫∑⟨⌊◊© ™◊ð ⌋ |∫∑ ⟩ ⟨⌋∫ ⟨⟩∫ ∫∑⌊ ⟩∫®◊ | ∫ ð⌋∑®⌋™ ⌊ ⌋|ð∑ ™ ⌊∑∫ ℜ ⟩|ð ◊⌈∫∑∫ð ™ ⟩∫ |◊|⟨∑⟩ ∑ ⌋⌈ ð | ®⌋◊®∫ ◊∫ ∑⟩| |ð∑®ð◊∫ ∫∑ ∫ð ◊∫∑⌊ ⌋⌈ |⌋∫®| ⌊ ∫∑⌊ ⌋⌈ℜ⌋⟨ ð◊ ⟨⌊◊© ™◊ð ⟩∫ ®|◊ ∑⟩∫®∑⟩∫ ⌊ ®⌋ ⟨ð∑ ∑ ⌋ ◊ ⟩|∑ ⟩ ◊⟩∫ ∑ ™ ð ® ∑∈⟩∫◊∑∫⟩ ⟩™∑⌊◊∫ ⟨⌊◊© ™◊ð ⟩∫ ©⌊◊® ⌋ |ð◊® ⌊ ®◊ ∑⌈
⊇◊ ™⌋⌈®∑ ∑ð ◊| ⟩⌋®◊⌈∫∑ ∑ ∑ ∑∑⟨⌊◊© ™◊ð⟩∫®∑ ⌋ | ⟩⌊◊ ⌈∉ ® ™ |⟨⌊◊© ™◊ð ⟩∫ ® ®⟩∑ ∑™ ⌊ ⟨⌋∫ ∫ ∫ ð ™◊® ®⌋ ™ ⌉∑∑™◊ ∫∑|⟩∫| ⟩⌊◊ ⌈ ∑∫| ®∫ ð ∫ ⟩ ™ ®™∑ ℜ∑™ |◊ ™⌋⌈™∑ ®⌋ ∑∫∑⌊∑©| | ⟨⌊◊© ™◊ð ∫ ◊|ð⌋ ◊™© ⌊ ® ⌈∑™ ™ð ∑⌈ ™ ð ®⌋ ™∑∫∑⌈ ◊∫ ∫ ∑∫∑® ™∑∫ ⟩ ∑∑ ∑⟨ ⟩⌊⌋ ◊∫ ð ™ ™ ◊ | ⟩ ™ ® ©| |ð∑⟩⌊∑ℜ ™∑∫ ⟩⌊⌋ ◊∫ ™⌋ ◊∫ ™ ∫ ®⟩∫® ®◊∫ ⌊ ⟨ ∫ —|ð ⟩∫⌋∑|ð ®⌋ ⌋∑®∑⌉ ◊⟩∫ ⌊ | |ð ®⌋ ⌋∑ ∫ ⌋| ð ⌈ ∑ ◊ ∑ ◊∑ ℵ| ∫ ™◊ ∑ ∑ ◊∑ ◊⟩| ⌊ | ⌋⟩ ◊⟩∫⌊ ®⌋
⊇◊|∫ ⌊ | ®⌋⟩™∑⌊◊∑∫∑|ð ®⌋ | ⌈ ◊ ∑ ◊∫ ®⟩∑ ð ∑∑® ∑ ⟩∫◊ ⟨⌊◊© ™◊ð ∫ ◊ ∫ ®◊ ◊ ∑ ◊®◊∑ |ð∑ ⟨ð◊ ∫⟩ ∉ |ð ⟨ ⌈∫∑ ∑ ◊⌊ ®◊∫ ⟩ ◊ ∫⟩ ∫⟩∫® ∑ ◊ ⌋| ©™◊®⌋ | ∑∫∑ ◊ ⟩∫◊ ®|∑◊®⟩| ∫∑ ∫ ®◊⟩ ™ ð ®⌋∑ © | |ð ⟨ ⌈∫∑ ∑⟩ ◊⌊∑∫ ∫ ∫ ◊|⌊◊∫ ∫ | ⟩ ∑∫◊ ◊| ⟨⌊◊© ™◊ð ∫∑ ◊∫ ∫ ®◊⟩∑⟩∫ ® ⟩∫ |⌊◊∫ ∫ ® ⌊ | ⟩ ⟩ð∑™ ∫ ®◊ ⟩ ◊ ⟨ ⌊ ®⌋® ∑⟩∑∫∑∑© ®⟩®
ℜ⌋ð◊ ◊ ⟨⌊◊© ™◊ð ⟩∫ ®⌋ ◊ ∑∫∑ ⌊ ◊∫ | ⌊ ∫∑⌊ ∑ð© | ∫ ð◊ ⟩⌊ ® ◊© ∫|ð ®⌊∑|◊∑∫® ◊ ∫ ⌊ | ð ∑⟩ ⟨⌋∫ ◊ ∑ ◊∫∑⌊ ⌋ ⌊ ™∑⌈⇑∫◊ ∑ð© ⟨⌊◊© ™◊ð ⟩∫ ⟨⌊◊™◊∑∫⟩ ⌊ ⌈|ð∑®ð◊⌉◊∫ |ð ⟨⌊∑ ⌋®ð∑ ∑ ◊| ∫∑ð ®|ð ⟨ð∑∫∑ ℑ⌊◊© ™◊ð ⟩∫ — ⌊ ∫®◊ ⌊ ∫®◊ ⟨ ⌊ ⟨⌊◊© | ⌊ ∑∑⟩ ⌊◊®∑⌊ |◊◊⌉∑™ð ⟩∫ ⟨∑ ©ð◊ ◊ℜ∫∑ ∑ ∑™ ⟨⌊◊© ™◊ð ∫∑⟩∑⟨ |ð ◊ ⌉ | ⟩∫ ⊂ ð ◊∑∫ ∫ ®⌋⟩ ◊⟩∫⌊ ®⌋ | ®∑ð ∫∑ ∫ |ð ⟩∫ | ⌊ ∫ ® ð ⟨⌊◊© ™◊ð ⟩∫ ®⌋⟨∑⟩| ∑ © ⟩™∑⌊◊∑∫∑™⌊ ⟩® ∑⌈ ® ∑⌊ ℑ⌊◊© ™◊ð ∫∑ ∑ð◊⟩⟩ ™◊ ™ ⟩∫ ⌈ ⌊ ∫ ®◊ ∑⌈⟨⌊◊© ™◊ð ⟩∫ ℑ⌊◊© ™◊ð ∫∑⟩® ∑|ð ⌊ ∑ ®⌋⟩∫◊ ∑∫∑⟩ ◊⟩∫⌊ ®∑∑® ◊⟩∫ ⌉∑ ∫◊||◊|®◊ ◊⟨⌊◊© ™◊ð ⟩∫ ⟩ ∑⌊ ∫ ◊⌊∑ ∫™ ∑® ⌋∑ð◊ ⌋∈⟨ð∑∫◊ ⟨∑ ⟩⌊ ® ⟨⌊◊© ™◊ð ⟩∫ ®⌋⟩∫◊ ∑∫∑ ⟩ ⌋⟩⌊ ∫ ®⌋⟩∫◊ ∑∫∑⟨ ⌊∑∑|ð ◊∫∑⌊ ⌋ | ⌊ ∫∑⟨⌊◊© ⟩⌊ ®∑ ∑⟩®⌋ ∑
⊇◊ ™⌋⌈™∑ | |ð ⟨ ™∑ |∑ð∑™⟩ ∑ ◊⟨⌋®◊⌈∫∑⟩|◊ ◊∫ ↔ℑ⌊◊© ™◊ð ∫∑⟨ ◊ ∑⟨⌊◊© | ⌊ ∑ ◊ ∑⟨⌊◊© ⟩ ⟩∫ ∑ ◊ ™ ð ® ∑ ∑ ⟨⌊ | ◊⟩◊ ⌋⌈ ™∑⟩ ⌋⌈™∑ ® ∑⌈ ≈

⊕∅⊕⊗⊆⊕ℜ⊆∈⊕∉⊄ℵ⊆∪∠∈ℜℵ⊆∪⊕ℜ∠⊕⊂⊕⊆∪
⊆∑ ∫|⌊◊™⌋®◊⌈ ◊ ◊®∫ð◊∫ ∫ ⟩™∑⌊◊∫ ⟩∑© ™
⊄ ⟨ ∫∑⌊ ∫ ∫ ®ð∑ ◊ ® ⟩∫ ∑ ∫ ⟨⌋| ®∑ ∑ ◊⌊ ®◊∫ ⟩ ◊∑© ∫⟩ ∫⟩∫® ∑∈⟨⌋ ◊ ∫© ® ð|◊↔ ∑∫®ð∑ ∑ ≈ ◊ ⌊ |⌋®◊∑∫|∑ð∑™ ™®∑ð | ⟩|∑ ↔⊆∑ ∫|⌊◊™⌋®◊⌈ ◊ ◊®∫ð◊∫ ∫ ⟩™∑⌊◊∫ ⟩∑© ™ ≈∇ ⌋⟩⌊ ∫ ⌈| © ® ð| ∫ð ™ |∑ð∑ ∑ ∫ ⊕ ∑™ ∑® ∑⟩ ð∑® ®◊ ∑®⟨∑©∑⟩ ®ð∑ ∑ ∑ ∫ð∑⟨ ∑∫| ⟨∑™⌋ℜ ∫∫ ⌊ | ∑⌈?⊕⟩⌊ ®⌋ ™ ⌊∑∑∫∑ ∑™⌊ ∫∑⌊ ⟩∫ |ð ◊ ð∑ ∑ ∑ ◊ ∑∫∑™∑⌈⟩∫® ®◊∫ ®ð∑ ⟩∫◊ ∑∫®◊ |◊ð∫ ∑ð ⟨ ™∑∫⟨⌊◊© |ð ∫⟩∫® ®◊∫ ®◊ — ◊⌊∑ ®◊ ®◊ ð◊ ⌋ ∫ ∑ ™◊ | ∫∑ð ⟩|ð◊®⌊ ∫ ®◊ ⟨| |ð∑®ð◊⌉◊∫ ®◊ ™∑⌈⟩∫® ®⟨⌊◊© | ⌊ ∑ |ð ®∑∫◊ ∑
↔ℜð∑ — ∫ ≈∈ ∑ ⟨ð◊∫ ∑© ∑⌊ ® ⟩| ⌊ ∫ ∠◊⟩∫ð◊ ®◊ ™ð◊© ∑ ⌋∑⟩∑| ™⌋®⌋| |ð ⟩∫ ð◊⟩∫ð◊ ®◊∑∫∑⟩® ℜ ∫ ®ð∑ | ™| ∫ð ⌊ ⟩| ⌊ ®◊∫ ∑© ∑|∫ ® — ◊™◊ ◊®| ⌊ ∑ð∑◊⌊ ◊ ∫ ◊ ∫ ⟩ ℑ∑ð | ™| ∫ð ⌊ ®ð∑ ®⌋ ®⌊◊™∑®◊∑∫∑⟩ ⟨⟩∫®∑ ⌈ ℜ⌋®™ð © ◊ ◊∑∫∑| ◊∫ ∫ ®◊⟩™ ⟩∫◊∫ ®ð∑ ∑ ™⌊ ®◊ ™∑⌊∪™⌊ ∫ © ® ®⟩∑ ∑ ®|◊™◊∫ ®|ð◊⌈ ⟩∫ |ð∑®ð◊⌉◊ ⟩ ®⟩®∑ð ð©◊ ®◊ © ∑⌊ ®∑|◊| ∫ ð⌋⌈ ◊⟨ ∑ ð◊ ◊⌊ ⌋ ð◊⟩ ™ ®◊ ∑ |◊ ™ ⌈ ∫⌋⟩® ∑⌈ ∇ ∫◊∫ ∫⌋ ∑ ∫ ∑⟩⌊ ®⌋| |ð ⟨ ∑∫∑| ™⟩ ∫◊∫ ∑ ∫⌋◊ ◊⟩⌋ð◊⟩∫ð◊ ∑ ⌋∑®| ⟩∫ ®⌋⟨ ™∑∫∑ ∑|ð ∫ ™ ®⌊∑ ⌋
ℜ ⟩ ®∑| ∫ð ⌊ ◊™®ð∑ ∑ ∑ ⌊∑ ∫∑ ∑™ ∑® ∑∑© |⌊◊ ð ®◊ ∑∇| ⌉ ⌊∑ ∑ ∫◊ð © |⌊◊ ð ®◊ ®⌋ ∑∫∑|∑ð∑ ∑⟩∫ ⟨ ™ ⌉∑∑® ◊⟩∫ ⌉∑∑ ð∑◊⌊ ◊|ð◊® ∫ ∑© ® ∑®◊ ð ⟩⌊ ⊆◊⟩◊ ™∑⌊∑⟩ ⟩∫◊®⌊∑ ∑ |⌊◊ ® ◊ ◊ ∫⟩ ®⟩∑ ∫| ™◊®| ®∑ ∑ð ™ ∫ © ©™∑|ð ®∑⟩∫ ⟩⌊∑™ ⌉ ⌈ ∫| ⟩| ™◊⌊∑∑⊆ ∑|∫ ® |⌊◊ ð ®◊ ∫ ⟩ ∈™ ð◊ ® ∑|⌊◊ ð ®◊ ∑ ∫ ∑| ∑∫ ™ ⌊ |∑ð∑⌈∫ ®⟩ ⟩∫∑ ®∫◊| ∑|ð ®⌋ | |◊|∑ ∑™ ∑® ◊ ⟩∫|◊ ⟨ ®∈ ™ ⌊ ⟩∫◊∫ ®◊ ∑⌈ ◊⟩ ⌉ ⌈| ∫ð∑⟨ ⟩∫ ∇∫◊® ™ ⌊© ⟩ð ⌋∑⟩ð∑™ ∑⟩ð ⌋∑ |ð◊∫| ⟩ð ⌋∑ ∑⌊ ∑ ◊⟨⌋®◊⌈∫∑ ∑ ∑™ ∑® |⌊◊ ð ®◊ ℜ⟩∑© ∫ ∫ð | ∫ð◊ ∑ ⌋ ◊|⌊◊ ð ®◊ ∑ ◊⟩∫ |◊ ⌉∑© ™ ®| ⌊ ∑™ ⟩∫◊∫ ∫ ⟨⌋ ®∑ð∑ |ð◊®⌊ ∫ ⟩ ⟨⟩∫®∑ ⌈
⊇◊| |ð ð◊⟨ ∫∑⟩ ∑⌊ |⌊◊ ™ ⌊ ∑ ⟨⌋∫ ⟩ ⟩∫◊®⌊∑ | ⟩ ∑ ◊ ∑ ⟩∫ ⇑∫ ⟩™∑⌊◊∑∫∑© ⟨ ⌊∑∑| |ð∑∫ ⌋ ð ⌋ ↔| ⟩∫ © ∑ ∫◊ ≈|ð∑®ð◊∫ ∫®ð∑◊⌊ ∑™∑⌈⟩∫® ∑∩◊| ⟩◊ ⌋⌈|⌊◊ ⌊∑© ∑| ™™◊∑∫⟩ | ðð∑|∫ ð ®|∑| ® ⌊ ∑∫|ð ⟩⌊∑™ ∫ ◊|ð ⟨⌊∑ ◊ | ∫ ð⌋∑® |◊ ∫|ð ∑© ð∑◊⌊ ◊ ◊ ◊ ∫™◊∑∫® ⟩∫ | ⟩∫ ⟩ ®∑ð ∑ ⟩∫® ®◊∫ ⟩ ⟨⟩∫®∑ ∑|⌊◊ ð ®◊ ∑
∉⌊◊ ⌊ ∑⟩ ⟩∫◊®⌊ ∫ ®∑ ∑ð ◊ ◊⟩⌊∑™ ⌉∑∑ ∫ð ∑© | ™| ðð∑|∫ ð ®◊∫ ◊⟩®∑ © ⌊ ® ®∑ ⟨ ⌊∑∑ ∫ ◊ ⟨⌊◊© ™◊ð ð◊⟨ ∫∑| ™⟩ ◊ ®◊⟩ © ∫® | ∫ ®⌋∑ ™∑ ∉ð ⟩∫ |◊ ||⌊◊ ð ®◊ ⟩ ⟩∫◊® ∫∑⟩| ⟩ |™∑⌊| ∫ ð⌋∑®◊ ∑ ⟨ ™ ⟩™∑⌊◊∫ ®∫∑ ∑ ∑™ ∉ ∫∑ ∫ ∑ ∑™ ∑® ∑|⌊◊ ð ®◊ ∑™ ⌊ ð◊⟨ ∫◊∫ ◊®◊ |ð◊∫| ⟩ð ⌋∑⟩ð∑™ ∑⟩ð ⌋∑ ™ ⌊© ⟩ð ⌋∑ ∑⌊ ∠◊ ™∑⌊ ∫∑| ⌊ ∑ ⌋⌈⟩| ⟩ | ◊©ð ||⌋ ⟩ ™ ◊ ⟩∫ |◊ ™ © |⌊◊ ð ∑ © ™∑⌈⟩∫® ⊆◊|ð ∫ ®|◊ ™ © ™∑⌊◊ |∑ð® ⌈©ð ||⌋| ⟩∫◊® ∫∑ ð ®∫ ð ⌈©ð ||⌋— ð ∫ð∑∫ ∑⌈—⊗∑⌊◊ |∑ð® ⌈©ð ||⌋™⌊ ®◊⟩⟩∑© ™ ◊ ⟨ ⌊∑∑®◊ ⌋ ∑ ∑ ⟨ ™ ™∑⌊ ∫ ⟩ ® ∑® ◊ ∑⊇ð ∑∫ © ® ∫ð |◊ ™ ⌈©ð ||⌋ ⟨ ◊ ∫∑™∑⌊◊ ®| ð ™|∑ ◊ ⟩∫ | ◊⌊ ◊® ∫ ⊆◊|ð ∑ð◊®◊∩◊®© ∫◊|™◊⌊∑∑∪ ∑ ®⌋ |ð∑™∑⌊ ∑∫∑ ∑ ⟩∫ |◊ ™ © ™∑⌊◊ ∫ ∫ ®◊ ⟩ ⟨∑ ®◊ ⟩∑© ™ ◊®∫ð◊ ∑∫|∑ð∑⌈∫ |∑ð® ⌈©ð ||⌋®∫ð∑∫ ⊆◊|ð ∑ð®⌋ ◊∑∫∑ ⟩∫ð◊ ⌋⌈ ⌋|⊆◊⟩∑© ™ ⌈™∑ ∑ ∑™ ∑® ◊ ð◊⟨ ∫◊ ◊™ ⌋| ⟩∫◊ ® ∫⟩ ™⌊ ®◊⟩™∑⌊ |∑ð® ⌈©ð ||⌋⊆ |ð ∑ ∫ © ®⌋© ∫ ® ∫∑© ™ ® ⌈⟨ ©◊⌊∫∑ð⟩| ⌈ ∫ ∑∫⟩® ∑© |ð∑™|ð ∫ ∫ ∑⟩ ∑ ∫ ⟩ ∫⟩ |™∑⌊◊ |∑ð® ⌈©ð ||⌋⊇◊| ∑ ∫ ™® ™∑⌊◊◊|◊| ∑—⟨⟩| ⌊ | ®ð∑ ∑ ™∑⌊ ∫ |◊ ™ —ð∑ ◊∫ ®◊ ∉ð ð ∫∑∫⌋ ◊|◊ ™⌋⌈™∑ ⟨∑ ⟩⌊ ® © ∫ ∑ ∫ ⟩ ™∑⌊◊ ∫ð∑∫ ∑⌈©ð ||⌋| ∫ ð⌋∑ ◊ ∑ ∑∑ ◊ ⌋ ®⌋| ⌊ ∑ ∑| ∫ ð⌋ ®⌋ ∑∫∑⟨∑ ⌉∑ð⟨◊™⌊ ⟩∑⟨ |∑ð∑ ∑⟩∫ ◊™ð © ∑™ ® ™ |ð∑|ð◊⟩ ⌋⌈ ∑ ∫⟩∫◊ ∫ ◊⟩ ⌉ ⌈| ∫ð∑⟨ ⟩∫ |∑ð∑⌈™ ∫®|∑ð® ©ð || ⊆◊|ð ∑ð© ∫ ® ∫ ∑∫ ◊ ⌋|® ⟩| ∫⌋®◊ ™∑∫∑⌈®⌋ ∫ ∑⟩⌊ ⟨ ð| |®◊ð∫ ð⌋|∫ð∑∫ ∑⌈©ð ||∑⊆ ∑⟩⌊ ®⌋⟨ ™∑∫∑ ™ ®™∑ ∫|⌊◊™⌋®◊∫ ∫ ⟨ ð| ∫ ∑ð∑ ∑⟩ ◊∫ ⟩∫◊ ∑∫™∑⌊ |∑ð® ⌈©ð ||⌋
∇ ⟩∫◊®⌊ ð◊⟩| ⟩◊ ∑ ◊|◊ ™⌋⌈™∑ ∫⌋®◊⌈∫∑®ð∑ | ∫ ð ∑®⌋∫ð◊∫ ∫∑ ◊∑ ∑™ ∑® ⌋∑| ®∫ ð ⌉ ∑⟩ ™∑⌈⟩∫® ™∑®◊ ∑ ⌋®◊ ∑ ⌋∫ ∑| ⟩ ™⌋ ⟨ ð| ⇑∫ ™∑⌈⟩∫® | ∫ ð⌋∑| ð ⌈⟩ ®∑ð ◊ ∫⟩ ◊®∫ ◊∫ ∑⟩| ®ð∑ ⌊ ∫◊∫∑ © ∫| ⌊ ⟩∫ ◊®⌊◊™∑∫ ®◊ ∑⌈ ® ®⟩∑ ∑ ⟩∫◊® ∫ ®ð∑ ∑ ™⌊ ∫ © ∫ ®◊ ™∑⌈⟩∫® ∫∑⌊ ®◊ ⟩∑© ™ ℵ ∑ ™◊ ⌋∑| ∑ ?ℜ⌋∫⌉◊∫∑⌊ ⟩|⌊◊ ð ®◊⌊ ™∑ ◊ ◊ ⌊ ®⟩∫ð∑ ® ®ð∑ ®⌋ ⌊ ™ ◊ |ð ∑ ◊ ⌉◊ ◊ ◊ ⟨⌊ ⌊◊®◊⟩⟩© ⌊ ®⌋™ ©©ð ®◊ ∑© ™ð © © ∑ ⟩∫◊∑∫⟩ |◊|®∑ð ∫ ⟩ ™ ⌈|∑ð∑ ™∑∫ ⟩ ® |∑ð∑ ∑⟩∫ ®⟩∫ð∑ ◊| ∫ ð ®⌋⟨∑ ◊™∑ | ™◊⌊ ℜ⟩∑® ∑⟩∫∑— ∑ ⟨ ™ ⌋∑∑ ∑™ ∑® ⌋∑™∑⌊◊|⌊ ⟩| ∑ |ð ⟩⌋— ∑∫® ®⟩∑⌊ ∫ ®◊⟩ ◊™∑ ™⌋ ◊⌈∫ ∑⟩| ⌊ | ∫™⌊ ◊ ∫ ⌈| ◊⟩∫ ⌉∑ ®◊ ⌋ ™∑⌊ ⊆∑| ™™◊®◊⌈∫∑⟩ ð ∫ ∑∪|ð∑ ™∑®⟩∑© ◊⌈™ ∫∑®ð∑ ™⌊ ⟩ ⟩∫◊®⌊∑ ∑ ∑™ ∑® ⌋ |⌊◊ ®
∠◊ ® ∑™∑⌊ ◊|ð ∑ð®⟩ ⟨⟨ ∫ ◊ ◊⌊ ð ⌈∫∑®◊ ð◊⟨ ∫ ®∫∑ ∑ ∑ ∑™∑⌊ ∇ ⟩∫◊® ∫∑|ð∑™®◊ð ∫∑⌊ ⌋⌈|⌊◊ ◊®⟩ ⟩⌊∑™ ⌉ ∑™∑⌊ ∑ ◊⟨⌋®◊ ®◊ ∑⌊ ∑ ∑™ ∑® | ðð∑|∫ ð ⌈∫∑∑© ™ | ⌊ ⌊ ∑ ℜ∫∑ ∑ ∑™ | ©™◊® |◊ ∫| ∑ ∑|ð∑™® ™∑ ⌋∑ ⟨⟩∫ ∫∑⌊ ⟩∫®◊® ⟩ ∫∑| |ð◊®| ®⟩® ⌈|⌊◊ |ð ™ ⌊ ◊⌈∫∑™∑⌈⟩∫® ®◊∫
∈⟨ð◊∫ ∫∑® ◊ ∑®|◊| ∑®ð∑ ™ ®⌋ ◊ ⟨ ⌊∑∑◊|∫ ® ⌋ ®⌋™∑⌊ ∫∑∑© ™⌊ ⟩◊ ⌋ ®◊ ⌋ ™∑⌊ℜ ∑∑∫⟩ ⌋⟩⌊|∑ð∑⟩ ∫ð∑∫ ð∑ ™ ⊕⟩⌊ ®⌋ |◊| ∑ ∑∫∑ ◊⌈∫ ®ð∑ ™⌊ |◊| © ∫ ™∑⌊◊ð∑ ∫∑ ∫ |ð ⟨⌊∑ ◊⟩ ∑∫ð◊ ∑© ∫ð◊∉ |ð ⟨ ⌈∫∑®⟩∫◊®◊∫ ® ∫ð◊⇑∫ ⟨ ⌊ ⌈| ™® ©™⌊ ∫∑ |∫ |ð ◊™⌊∑ ∫|∫◊| ◊ ⌋®◊∑ ⌋ ↔⟩ ®◊ ≈— ∫∑ ™ ð ∑| ⟨∑™◊∉ |ð ⟨ ⌈∫∑⟨⌋∫ © ⟨| ⊇⟩∫◊∫ ∑ ◊⌉∑®⌋⟨ ™∑∫∑ ∑ ∫ ð∑ ™ ∫∑ ∑ ∑® ⟩∫∑⌈®⌋⟨ ™∑∫∑ ⟩∫◊®⌊ ∫ ®◊ |ð ®⌋ |◊ | ∫ ð⌋∑| ð ⌈⟨∑ð ∫⟨ð◊ ™⌋|ð◊®⌊∑ ®⟩® ∑|| ∑ð | | ™ ∫ ◊⟩⟩∑⟨∑ℜ|ð ∑ ®⌋ ∑∫∑ ◊⟩∫◊® ∫ |ð ®⌋ | | ⟩⌊ ∫ ⟩∑⟨∑|◊ ™⌋⌈™∑ ®⌋™∑⌊ ™ ∫ ∑®ð∑ ™⌊ ®⌋| ⌊ ∑ |ð∑™∑⌊∑ © ™∑⌈⟩∫®
·∫ ⟨⌋ ⟩® ⟨ ™ ∫ ⟩ ™⌊ ð∑ ∑ ®◊ ⌋ ⟩®◊ ∑⌈∫ | ð∑ |ð ⟨⌊∑ ∫|◊ ∫∑⟩ ∫|ð ⟩ ∫ð◊∫∑⌊∑|∑ð∑™◊ ⌊ ∫ ⟨⌋∫ð◊∫ ∫∑ ◊ ∫ ∑ ∑®ð∑ ∑ ⊕⟩⌊ ∑ ∑∫∑ ∫|◊ ◊∫ ⟩ ∫∫∑⌊∑® ð◊⟩ ®⟩∑ ⟩ |ð◊∫ ∫∑®ð∑ |ð ⟩ ∫ð◊|∑ð∑™◊ ™ ð◊ © ◊⊕⟩⌊ ®⌋® ◊∫∑⌊ ®⟩⌊ ◊∑∫∑⟩ ®©⌊ ™ ∫∑⟩ ®∫ ∫ ®◊ ∑ ∑™ ∑® ®∑⌉◊ ∫⟩ |ð◊ ® ◊ ◊ ⟩ð∑|⌊◊ ⌋ ® ⟩∫∑⌈ | ◊ ⌊ ◊ ®⌋| ⌈ ∑∫∑ ∫| ™◊⟨∑ð∑∫⟩ ∑©◊∫ ®®®◊ ∑⌈ ∈∫|◊ ∫∫∑⌊∑® ™∑ ◊®ð∑ ⟩® ∑ |ð∑™⌊ ∑ ⌈®| ©∑|ð ©ð◊ ⌋— ™ ⟩⌊ ® ⌈|ð ð◊⟨ ∫∑ ◊™® ⟩| ∫◊ ∑ ⟩ ◊ ®◊||◊|∑⟩⌊ ⟩ ∫ð◊®⌋ ◊| ⌊ ∫∑⟩® ∑⟩ ◊ ∑| ⌊ ∫∑⌊ ⌋ ∫®∑ð ™∑ ∫ |◊↔ℜ ∑⌈ ®⟩∑|ð∑|ð◊⟩ ⟨ ™∑∫∑⌉∑⌊ ∑≈— ◊ ∑ ◊ ∑ ◊∫∑⌊ ∑∫∑⌊∑® ™∑ ∑ ⟨ ◊∫∑⌊ ⟩®∑™∑∫ ◊ ∑∫®⟩∑®◊ ⟩ ⌊ ® ∑ ⟩|◊ ◊∫ ⟨ ⌊ ®◊ð ⌈|ð∑⟩⟩∑ ◊| ∫ ð © ∑∫ð◊∫ ∫ ⌈ ™∑ ∑© ®ð∑ ∑ © ™ð © ®∑⌉◊ | ∫ ð⌋∑ ∑ ◊| ⌊ ∫®◊ ⟨⌊◊© | ⌊ ∑ ⟨⌊◊© ⟩ ⟩∫ ∑ ⟩|∑™ ∫®⟩∑®◊ ∑⟩® ⟨ ™ ∑®ð∑ ∇∫◊ð◊⌈∫∑⟩ ∫◊| ∑ ∑ ∑⟨ ⌊∫◊∫ | ∫∑⌊∑
⊕⌉∑ ™ ◊ð∑| ∑ ™◊ ∑™∑⌊◊⌈∫∑ð◊⟩| ⟩◊ ∑⟩⌊ | ∑⟩∫| ⇑∫ ©⌊ ⟨⌋⟩™∑⌊◊∫ ®◊ ∑®⌋ ⟩ ⌈∈⟩∫◊® ∫∑ ◊⟩∫ ™ ∑® © ®ð∑ ∑ ∑ð◊⟩| ⟩◊ ⌈ ∫ ⟨⌋| ∫◊∫ ∫™ ∫ ® ©™◊|⟩∫◊∫ ⟩⌊ ◊⌈ ◊ | ∑ ◊ ∑⟩ ð®∑∫®◊ |⌊◊ ⌋| ⌊ ⟩∫ |◊||ð ⟩⌊ | |⌊ ∫ ð◊⟩| ⟩◊ ©™∑ ™ ™∑⌊ ⟩⌊∑™ ∑∫ ◊™ð © ⊕⟩⌊ ∑®⌋ ®⟩∫® ∑∫∑ ∫ ⟨∑ ⟩∫◊⌊ ⌊ ∑ ∫™ ∫∑™◊ ∑∑⟩⌊ ®◊ |⌊◊ ∫ © ∑ ∑⌊⊆◊⟩®∑ © ⌊ ® | ⟩∫ ™◊ ∑ ∑ð∑ ™∑ ®⌋⟩™∑⌊◊∑∫∑© ð◊ ™ ⟨ ⌊ ∑ ð◊⟨ ∫ ®⌋| ⌊ ∫∑⌊ ∑∈ ∑ © ®ð∑ ∑ ∫ ◊∑∫™ ð ©◊ ◊ð◊⟨ ∫ ⟨ð◊∫ ⟩ ⟨∑ ®⟨ ⌊ © ð ™◊ ℜ ∑⟩∫ ∫ © ∫ ⟨⌋ð◊ ©◊™⌋®◊∫ |ð ⟩⟩® ð™®⌋ ∑∫∑|ð ⟩ ∫ð∑∫ ∑⟨ ⌊ ⌈ ∫ ∑∫ ⌊ ◊| ∫ ∑ ⟨ ™ ∑⟨ ð ◊ ℜ™ ð ©∑ |ð ™ ◊∫ |⌊◊ ◊⟩⌊∑™ ⌉ ⌈™∑ ◊®∑ ∑ð |ð ⟩∫ ◊| ⟩◊∫ ∑© ∫ ∫ ® ∑ ∫ ⟩ ∫⟩ | ™◊ | © ∫ ⌊ ∑© ∫ ⟩∫ ® ∑ð∑™
⊆◊ ◊⌈∫∑™∑ ®⟩∑©™◊⟩⟩◊ © ®◊ © ∪ ◊⌈∫∑ ™ |ð∑ ⟩|∑®◊ ⌉ ⌈ ∑⌊ ®∑| ∑ ⟨ ∑⌊⟩ ⟨∑ ∫ © ∫ ⟨⌋ ◊ ∫ ⟩ |⌊◊ ð ®◊∫ ⟩® ∑®ð∑ ∇ ⟩∫◊® ®ð◊⟩| ⟩◊ ∑ð◊⟨ ∫◊⌈∫∑⟩ ℜ⌋ ∑ð| ®◊⌈∫∑∫ ∫ ∑⟩™∑⌊◊ ◊ ∑ ⌈∫∑|ð ∑ ⟨ ™ ⟩∫ ™ ™∑⌈⟩∫® ∑™ð © ⊆∑⟩∫ ∫®|⌊ ◊∫ ®⟩| ⟩ | ⟨⌋ ⌋∑™∑⌊◊®|⌊ ◊⌈∫∑∫ ⌊ | ∫∑ ∫ ∑ ∫™⌊ ®◊⟩⟨ ⌊ ∑ ◊ ∑ ∑ © ∫ ⟩∫◊∫ ⟩ ∑⟩™∑⌊◊ ⌋ ∑⟩⌊ ⟩∫◊ ∫⟩ ⟨∑ | ∫ð ⌊ ⟩®◊ ∑⌈⟩∫ ð ⌋⊕⟩⌊ ®⟩| ⟩|∑ © ™∑⌊ ◊ð◊ ∑∑ |ð∑™∑⌊ ∫∑|◊| ∑ ®⟩∑∫◊| ⟨ ™∑∫|ð ∑ ⟨ ™ ⟩∫ ∫⌊ ∫ — ∫ ™∑⌊◊ ⟨⌋ ∫ ⟩ ∫⟩ |∫ð∑∫ ∑⌈©ð ||∑∉ð |⌊◊ ð ®◊ ®◊ ◊ ∑⟩ |ð ∫∑⌊ ◊ | ⟨∑™◊| ©™◊®⌋| | ◊ ™ ⟨∑ ⟩ ⌊ð ∑∫∑ ◊™ ®◊ ◊|⌊◊ ∑ð ◊ ◊|∫ ® ◊ ™∑ ∫∑⌊ ⟩∫ | ∫ ð◊ | ® ⌊ ∫®◊ ™® ©◊∫ ⟩ ®|∑ð∑™ ™ ⟩∫ ©◊∫ ◊ ∑ ∑ ⌋ ∑⌊∑⌈
ℜ⌋™∑⌊ ∫∑®⟩| ⟩|∑ ™ ™®◊™∑⌊◊| ∫ ð⌋∑®∑™ ∫®◊⟩| ⟩|∑ | ⌊ ∫∑⌊ ⌋ ∑ ∑ ® ⟩| ∑ ∫ð ð ⌈∫∑⟩ ◊ ⊆∑® ∫∑®™∑⌊◊ | ∫ ð⌋∑ ∑|ð ⟩ ∫| ⌊ ∫∑⌊ ⌋ ð∑ ⌊ ∫◊∫ ®⊆∑| ™ ∑ ⌈∫∑™∑⌊◊|∑ð® ⌈©ð ||⌋| ∫ ð⌋∑⟨∑ ⟩⌊ ® ⟨ ⌊∑∑⟩⌊ ⌋ ∫ð∑⟨ ∫⟨ ⌊ ∑© ® ◊ ™∑⌊◊ ®∫ ð ⌈ ∫ð∑∫ ∑⌈©ð ||
⊕⟩⌊ ®◊⟩®™ð © ®◊∫⌋®◊∑∫ ∫|◊ ⌊∑ ⌊ ⟩ ∑ ∑⟩|◊ ∫∑⟩∑⟨∑ ∫ ®⌋ ™∑⌊ ∫∑ ∑ ⟨ ™ ™∑⌈⟩∫® ®⟩∑© ∫ ∑∫∑ ◊®∑⟩∫ ⟨ ™ ⌊ |∩◊ ◊⟩∫ ∑ ∫ ∫| ©◊ ∫®∫ ∫ ⟩ ®ð◊⟨ ∫ ⊕⟩∫ ∑⌉∑ ™ ⟩| ⟩ ⟨ ◊⟩∫◊® ∫ ⟩∑⟨ ð◊⟨ ∫◊∫ ∇ ™ ∫∑ ∑© ∑™∑⌊◊⌈∫∑∇ ®⟩∑ ∑© ∉ ⟩∫ ™ ∫®ð∑ ∇| ⌊ | ®⌋∫◊||ð ⟩ ™ ∫∑— ∫?ℜð∑ ⌊ ∫◊∫∑®◊⟩ ◊ ◊∑∫⌊ ⟨ ⟩ ®∑⟩∫ ⌊ ⟨ ⟩| |◊
ℜ∫∑ ∑ ∑™ ®⟩∑®ð∑ ◊™◊®◊⌈∫∑⟩∑⟨∑® |ð ⟩↔⊇◊| © | ∫ð◊∫ ∫ ⟩∑⌈ ◊⟩®ð∑ ⟩ ◊ ⟨ ⌊ ∑⌈™⌊ ∑ | ⌊ ⌈?≈∇™∑⌊◊⌈∫∑ ∫ ∫® |ð ⟩|ð ®⌋ | ⌈⊕⟩⌊ ®⌋⟩∫ ∫∑|∑ð∑™®⌋⟨ ð ∑ ™ ™® ™∑⌊◊ ∫®∑∫ ◊ ∫ ∫® |ð ⟩| ∑∫®◊ ®∑ð ⟩ ð ∑ ∫ ð ®◊∫ ⟩
∉∑ð∑ ∫◊®©⌊◊® ⟨ ◊ð ⌊◊∑∑⟩⌊ | ∑⟩∫| ⌈⊗∑⌈⟩∫® ∫∑⌊ ∑⟩⌊ ∫ ∑↔® |ð ⟩ ⟩ ∑ð∫ ≈—®ð ™⌊ ↔⟩ ®⌋≈ ◊ ∫|∑ð∑™∑⌊⌋®◊∫ ⟩ ®↔ ◊® ð | ®≈⊆ ®◊ | ⟩∫ ™◊ ∑ ◊®ð∑ ⟨∑™ ∫ ⟩ ®⟩® ∑⌈⟩| ⟩ ⟨ ⟩∫ |ð◊®⌊ ∫ ⟩® ⟩ ð◊⟩| ð ™| ™ ∉ |ð ⟨ ®◊®®⌋ ⟨∑™ ∫∑⟩ ∫ ∑∫∑ ∑ ∫ ⟩® ∫ ⌊ | ⟩ ⌊ ∑ ® ⌊ ↔ ∑⟩™® ©◊ © ð≈—◊ ∫ | ®∑ð ∫∑™⌊ ®◊ ∑© | ™⟩ ◊ ®∑ð∑ ⟩∫ ®∑ð⌋®⟩∑⟨ —|ð ⟩∫ ⟨∑⟩ ∑ ⌋⌈| ™◊ð |

⊗⊕⊆⇐℘∪
ℑ∑™ ⟩∫ ∑™ ⟨ð ™∑∫∑⌊ ⇑∫ ⟨ ⌊∑ ⟩ ◊ ®◊ ⟩⌊∑™ ∑∫ ∑ ∑™⌊∑ ®⌋⌊∑ ∫ ⟩ ∫ ∫ © ∑ ∫◊⌊ © | ⌊ |∫◊ ⌊ ◊⟨ ⌊∑®◊ ℜ⌋ð ™∑ ⌋™⌊ ∫ © ∫ ⟨⌋®⌊◊™∑∫ ®⟩∑ ⟨⌊◊©◊
⊗ ⊂∑ð

∇® ⌈ð◊ © ® ð ™∑ ©◊ ∑ ∑∫⟩ ◊ ◊∫ ⟩ ™ ⌈ ∑ ð◊⟩|ð ⟩∫ð◊ ∑ ⌈ ⟨| ⟩ ◊ ∑| ∫ ð ⌈®∑™∑∫|⟨⌊◊© ⟩ ⟩∫ ⇑∫◊ ⟨|◊—|ð∑ ð∑ ∑|™∑ ©◊ ∫ ∑ ∑| |◊|| ⌊ ⟩∫ | ®⟩∑ ⟨∑™ℵ| ∑ ∑⟨⌊◊©?⊆ |∫ ∑ ∑ ◊∑∫ | ∫ð∑⟨⌊ ∫ ™∑ © ⟩ ©ð ⌈| ⌊ ⌈|◊|™⌊ ⟩∑⟨ ∫◊| ™⌊ |ð ◊ ⌉ ⊆∑ ∑⌊ ®⌋®⟩∑ð ∑ | ⌊◊©◊∑∫∑ ∫ ™ ⟨ð ™∑∫∑⌊ ® ◊∫ ⌊ | ®⟨∑™ ⟩∫ ?ℜ⌋—⟨ ©◊∫⌋⌈ ⟩ ◊⟩∫⌊ ®⌋⌈— ∑∫∑|ð ∑⟩∫ |ð ◊ ⌉ © ð◊ ™ ⟨ ⌊ ∑™ ⟨ð◊ ∑ ⟩™∑⌊◊∑∫∑|ð |ð⌋® ⟩ ◊ ◊⟩∫ ⌈™ ⟨ð ™∑∫∑⌊ ∑™®◊⟩® ™ | ⌋⟩| ◊ ⊗ð © ∑™∑⌊ ∑⟩⌊ ®◊⟩™∑⌈⟩∫® ∫∑⌊ ∑∫ð∑® ∫®◊ ∑ ◊∫∑ð ◊⌊ ∑| ⌊ ∑ ∑ ⟨∑™ ⟩∫ ∑ ∑ ◊∑∫®◊ ∑ ©◊ð ⟩ ⌉∑⟩∫® ®◊ ℜ⌋®|ð◊®∑⟩™∑⌊◊∫ ∫ ∫®⌋⟨ ð
∉ ∫ ® ∑ ∫®∑ð ™∑ ∑↔⇓⌊ ⟨⌊ ∑ ®◊ ◊ ™∑ © ≈™ ⌊ ⟩∫◊∫ ™⌊ ®◊⟩|⌊ ∑®⌋ ◊|◊ ™⌋⌈™∑ ℜ◊ ◊ ◊™◊ ◊— ∑ ⟩∫◊ ® ◊∫ | ™⟩ ◊ ™∑ ⟨ ©◊∫⟩∫®∑
∪ ∑ ⟩ ™∑ ◊ ◊∑∫⟩ | ∫ ⌊ ⟨ ∑⟨ ©◊∫⟩∫® ∪™∑ ð ð ∑∫® ⟨ð◊ ∑ ∑∉ ⟩∫◊ð◊⌈∫∑⟩ ⟩⌊∑™ ®◊∫ ®∑⌊∑ ⟩∑ð™ ◊◊ ∑ð◊ ◊| ∫ ð⌋⌈ ∑ ⌊ ⟨ ∫ ◊ ∑|∫⌋®◊∫ ∫ ∑© ∑®⌋⌈™∑∫
ℑ ™ ∫∑ ◊⟩∫ ⌈ ®⌋™ ⟨ ®◊ ⟩ ⟩® ∑© ∈∫®◊⟩∫ð∑⟨ ∑∫⟩ ∑|ð ⟩∫ ∫ð ™◊ ©ð ∑ ∑⌊◊ ∑|ð ®⌊∑ ®⟩® ⟩|∑ ⟨ ©◊∫⟩∫® ℜ⌋™ ⌊ ⌋ ∑∫| |ð∑™⟩∫◊®⌊ ∫ ⟩| ⌊ | ®◊ ™∑ ∑© ◊ ∫ ∫ ©™◊ |ð ™ ∫∈|ð∑™∑⌊ ∫∑⟩ð || ©™◊®◊ ∑ ⟨ ™ ⟩∫◊∫ ⟨⌊◊™◊∫∑⌊∑ |ð∑™∑⌊∑ ⌈⟩ ⌋™∑ ∑© ◊ |⟩ ð ⌈∫∑ ∫ ™◊∫ ◊⟨ ◊©∑⊕ ∑™ ∑® ∫ð ®∑ ∑ð ®⌋ ⌋®◊⌈∫∑ ⟨ð◊ ™∑ ∑©| ∫ ð⌋∑®⌋ ◊|◊ ◊⌊ |ð∑™⟩∫◊®⌊ ⌈∫∑ ◊ ∫ ®⌋ ∫ð◊∫ ∫∑ ⌊ ® ∫ ®|⌊◊™⌋®◊∑∫∑
ℵ⟩∑⌈ ◊⟩ ◊| ∫ ®◊ ™ ⟩ ® ⌋ ◊| ® ↔⊂⌋™ ⌊ ⌋™◊®◊∫ ∫ ⟨⌋| ⌊ ∫ ≈∈™ ◊ |ð ⟨∑™ ⟩∫ ⟩ ⟩∫ ∫®∫ ∫ ⌊ ™ ◊™∑ ∫⟩ | ⌊ ∫ ∑© ∑™◊®◊ ® ◊ ∑ ℜ⌋ ∑⟩ ∑∫∑®⟩∫ | ∫ ®| ∫◊|∫⟩ ∑ð© ∑⌈⌊ ⟨® ⟨ ⌊ ™ ∫∑ | ð| |◊ ∑ ◊ ∫∑⟩ ∫™◊®◊∫ ∪ ∑⟩∫ ∫™⌊ ∫ © ™ ™◊∫ ⟩ | |◊®⌋ð◊ ⟨ ©◊∫∑∑∫∑ℜ◊ ™◊ð ∑ ⟨ ◊∫∑⌊ ™ ⌊ ∑ ⟨⌋∫ ◊∫∑ð ◊⌊ ⌋ ∫ ∑∫⟨⌋∫ |ð ⟩∫ ⟩⌊ ©◊⟨∑ ð◊⟩ ∑∫◊| ⌊ ∫ ∫ ∫ ® ◊ ∑ ®◊ ∑⟩ ®⟩∫® ∑⌊ ⟨ ® ·∑ ⌉∑™ð∑∑®⌋⟨ ™∑∫∑∫∑ ⟩| ð∑∑|ð ∫ ∑∫∑®⟩® ™∑ ©
∇⌊∑™ ∑∫∫◊| ∑| ∫ ∫ ∑⟩⌊ ™∑ © ⟩∫◊ ∫∑™ ⟩∫®∑ ⌈ ∑⌊ ®◊ ∑⌈ ∫ ®⌋ ∑ ⟩| ð | ⌈ ∑∫∑|◊| ∑⟩∫ | ⟨⌊ ⟩ ⊕⟩⌊ ∑ ◊| ∫ |™ ⟩∫ ∑ ⟨ ©◊∫⟩∫®◊®⌋⟩ ∑∑∫∑ð∑◊⌊ ®◊∫ ⟩® ® ⟩∫ ◊⌈™∑∫∑®ð∑ ™⌊ ⌊ ⟨® ™ð ⟨⌋∫ ® ∑⟩∫∑⟩⟨ ©◊∫⟩∫® ⟨ð∑∫∑∫∑| | ⌈ ™ ð ® ∑ ð◊™ ⟩∫ ∑ ⟩ ◊ ∑⟩® ∑© ⟩∫ © |ð∑™ ◊ ◊ ∑
ℵ∫∑|∑ð | © ® ð ⟨ ∑ |ð◊® ⌊ ∫ð◊∫ ∫ ⟩⟨∑ð∑©◊∫ ™∑ ©
↔∇⟨∑ð∑ ∑ ∑™∑ ∑©—™∑⌊ |ð ®⌋ | ≈⊕⟩⌊ ®⌋ ∫ ∫∑ ◊ ⟩ ® ⌈ ∑ ◊® ⟩ ⟩∫ ®◊ ◊|ð ®⌋ |◊ð◊⟩ ™ ®◊∫ ™∑ © ™ ⌊ ◊⟩ ∑ ∫ ⟩ |ð ®⌋ | ⌈ ∫|⌊◊™⌋®◊∫ ⊆◊| ∫ ⟩|∑ ◊⌊ ⟨ ⌈ ∑∫⟩| ∫| ∫ ⟩ |◊⟩∫ ⟨ ™∑∫ ◊⌊ ∑⟩⌊ ∑⌊ ®∑| ∑⟩ ∑∫| ™ ∫ ⟩ | ™ ⌈∑™ ⟩∫®∑ ⌈|ð ∑— ◊ ∫⟩ ∫⟩∫® ∑ ⟨ ™ ⌈⟩ ⌋™∑ ∑©® ∑ ∫ ∑ © |ð ⟩◊∉ð ⟨ð∑∫ |ð ®⌋ | ⟩⟨∑ð∑©◊∫ ™∑ © ®⌋ ◊⌈™∑∫∑∑∑ ∑ ∑ ∑∑|ð ®⌊∑|◊∫∑⌊ ⌈ ∑ |ð ®⌋ | ∫ð◊∫ ∫ ℜ⌋ ⟨ð∑∫∑∫∑⟩◊ ®◊ ∑ ∑ ®∑ð∑ ⟩∫ ®⟩∑⟨∑ ◊ ⟩ ® ∑ ◊® ⟩ ⟩∫ | ∫ ð◊ ⟩® ⟨ ™ ∫®◊⟩ ∫⟩∫ð◊ ◊ ⌉∑∫⌋ ™ © ⟩◊ ⌋ ð◊ ð ∫∑⌊ ⌋ ⟩∫ð◊ ®® ∑⌊ ®∑|◊
⊇◊| ∑ ⟨ð◊ ⌊ ∑| ∫ð◊∫ ∫ ◊ð◊⟨ ∫◊ ⌋∑™∑ © ?∉ |ð ⟨ ⌈∫∑∫◊| ⟩ ∑
∫⌊ ∫∑ ◊
— ∫ ®◊ ⟩⟨∑ð∑ ∑
| ∫ð◊∫ ∫∑ ◊ ⟨ð◊ ®◊ ∑®◊ ∑ ⌊ ®◊ ™∑∫∑⌈
— ◊ ∫™⌋
⟩| ⌊ ⌈∫∑®⟨⌊◊© ∫® ð ∫∑⌊ ⌋ ∑⌊
⊇ ∑ | ™ ⟨ ∑ð◊⟩|ð∑™∑⌊∑ ∑ ◊ ⟩ ® ∑ ⟩⌊ ® ∑∫| ⟩⌊ ∫ ⟩ ® ⌈™⌊ ®◊ ∑© ⟩ ⟨⟩∫®∑ © |⌊◊ ð ®◊ ð◊⟩ ™ ®
∪ ◊| ∫ ∫ ©⌊◊® ∑⟨⌋ ∫∑⌊ ⟩ ⟩⌊ ®◊ ⊗ ∑ ◊⊂∑ð ↔⇓∑™ ⟩⟨∑⟩| ∑ ⌋ ⟨ ©◊∫⟩∫®◊ ⟩® ∑© | ™⟩ ◊∫∑⌊ © ð◊ ◊ℑ⌋∫ ⟨ ©◊∫⌋ ⟩ ◊⟩∫⌊ ®⌋ |ð∑ ⟩|∑®◊ ⌉ — ∑ ∑ ∫|∑ ⌊∑ ∑|ð◊® ⊗∑ © ∫∑| ∫| ∑⟩® ⟨ ™ ⌉∑™ð ⟨∑⟩| ∑ ⇓| ⟩∫ ⟩ ◊ ⟩® | ™⌊ ◊ ⟩∫ ⊂ ⌈∫◊⌊◊ ∫ ∑ ⟩∫◊ ð◊⟨ ∫◊∑∫ ◊⟨⌊◊© ®⟩∑ ⌊ ™∑⌈ ∑ ∑∫ |◊| ◊ ⟩ ®⌋ |ð ⟨⌊∑ ⇑∫ ™∑⟩ ⇓⌊ ⟨⌊ ™∑ © ⇓ ⟩| ⌊ | ⟩∫ð |∫ ® ð◊⟩⟩ ™ ∫∑⌊ ⇓⟩ð◊™ ⟩∫ ð◊⟩⟩∫◊ ⟩ ⟩ ® ®ð◊⌉◊ ∫⟩ | ∑®∫⌋⟩ ∑|ð◊∫ ð◊ ∑ð∑≈
⊂ | ™ð ©◊|◊|∫ ⟩|ð ⟩ ⌊◊ ∑ | ∑ ◊| ⟩∫ ™ ◊∑∫ ™∑ ©◊ ∑ ∫◊∑∫ ∫ ∑∑⟨ ™∑∫ © ⟨∑ ð∑ ⌊ ∫◊∫ ?⇓ ∫®∑∫ ⌊◊∑⌈ ∫ ◊ ∫ ∑∫™∑ ∑©⟨ ⌊ ∑ ∑ ∑∑∫⟩∑⌈ ◊⟩ ∑© ®⟩® ∑⌈ ∑ ∫ ∑ ∑∫ℑ ⌊ ∑™∑ © ™ ⌊ ⌋⟩ ∫®∑∫⟩∫® ®◊∫ ⟨ ⌊∑∑®⌋⟩ | ⟩ ◊⌊ ⟩∫◊∫ ⟩ ⌊ ⟨ ⌊ ∑⌈◊|∫ ® ⟩∫ ◊®∑ð ∑∑ ∫ ™ð © ® ∑⟩∫∑ℵ∫◊| ð◊⟨ ∫◊∫ ◊∫ð∑ ð◊⟨ ∫◊ ® ∫∫ ⌊ | |∑ —™® ð | ⌊ ð◊ | ?⊆ ®⌋⌈⟩∫◊∫ ⟩— ∫ ⟩ ⌉∑⟩∫® ®⟩® ∑ ∫ ⟩∫◊∫ ⟩ |∑ð|ð ∑⟩⟩ ◊⌊ | ∫ ð |ð ™ ⌊ | ⟩|∑ ∑⟩∫◊ ⌈ð◊ |⌊◊∫ ∫⟨ ⌊ ∑ ∑ ™ ð∑|∫ ð ∑⟨ ⌊ ⌈ ð ⌋↔ℜ ◊⌊∑ | ⌈| ∑⌊∑|⟨ ⌊ ∑™∑ © ∑®⌊∑ ∫≈∉ ∑ ∫ ∑|⌊ ⌈⌊ ©™⌊ ◊ ◊⌊◊∪®∫ ð ⌈ ∑ ®◊ ⌋⌈ ∑ ∫| | ® ™ ∑ ∑ ⌉ ⟩ ™∑ ∑©®⟩∑©™◊®®⌋ ©ð⌋ ∑ |◊ ⌋®◊∑∫⟩ ∫ ∫ ∑⌊ ®∑||∫ ∑|ð ⟩∫ ∫ð◊∫ ∫™∑ © |◊| ∫ ◊⟩∫ ®|⌊◊™⌋®◊∑∫®⟨ ∑⟩ ⌊ ®⟩◊ ⟨ð◊ ®◊ ∑⟨ ™ ∫ | | ∫∑ð ◊ ©ð◊ ∫ ⟩∫ ⟩∫ð◊ ⌋∑ ⌋| ⌊ ® ™ ∫∑⌊ ⟩| ∑|ð◊®◊—®⟩∑ ™ ◊| ® ð ∈⟨⌋ ∑ ∫◊| ∑®⌊ ∑ ® ®ð◊⌉◊ ∫⟩ ⟩∫ ð ∑⌈

∇®∠ℵ∏—⇑®∈ℜ∇⊕℘∈⊄∪¬⇐⊂⇔∇⊄⇐

℘ ⟩| ™ ™◊ð ®◊⌊ ∑⟩| | ⌈⟩∫® ∑|ð ◊∫ ®∑⌉ | ∫ ð⌋∑ ∑ © ∑ ∫ ∫®◊© ∑ ∫ ®∑⌉ | ∫ ð⌋∑ ⟩| ⟩ ⟨∑ ∑ ∫ ™ð ⟩∫ ∫ ⟨⌋ð◊ ⌊ ◊∫ ∑ ™ ⟩ ⟨ ⌈
™ð◊ ⟩|ℵ⟩⟩ ⟩| ⌈

∇∫ð◊ ™®∑∑© ⟨⌊ ◊⌈ ∑| ™ð © —⟩ ∑ ∑ ∑ð∑ ∫∑⌊ ⟩∫ — ◊| ⌋|◊ ™ ∠◊⟨ ∫◊ ◊™⟩ ⟨ ⌈ ◊™ ⌊ ∑ ∑ ⟩® ∑⌈ ®| ∑ ⟩⌊ ◊∑ ∑⟩∫ ∫ ∑™ ∑ ®◊∫ ®⌊ ∑ ◊⟩ ™ ⟨ ∑⌊ ®∑|◊∪⟨ ∫◊∫ð ◊⟩| ⟩ ⟨ ◊ ⟨ ∫ ⌊ ⟨⌋∑ ∑ ∫⌋ ⟩∫◊ ® ∫ ®◊⟩ ◊| ∫ |⟩◊ ⌈⟨⌊◊© ð ™ ⌈ ∑⌊
∇∫ð◊ — ∫ ®⟩∑© ⌊ ⌋⟩⌊ ℜ⌋™ ⌊ ⌋ ∑⟨ ∫ ⟩ ⟩ ⟨⟩∫®∑ ⌋ ⌋⟩⌊∑⌈◊| ∫ ∫ ⌋⟩⌊ ⟩ ™◊∫∑⌊ ◊ ◊ ∫ ⟩ ◊ ∑ ∫ ∑©◊∫ ® ⌋⟩⌊ | ⌊ ∫∑⌊ ⌈⟩∫ð◊ — ®∑ð∑ ⟩∫ ⊗ ◊⌈∫∑ ™ ⟨ð∑ ∫ ⟨⌋↔∫ ∑© ⟨ ⌊⟩ ≈ ∑|ð ⌊ |®◊
⊆∏ ⌊⌊®⌋™∑⌊ ◊ ⟨ ⌊∑∑ð◊⟩|ð ⟩∫ð◊ ∑ ⌋ ® ™ ®⟩∫ð◊ ◊⟩∫ð◊ ⟩ ∑ð∫ ⟩∫◊ð ⟩∫ ⟨ ⌊∑ ⌉∑∫⌋⌊ ⟨ ® © ð◊ ◊ð ®◊ |ð ∫ | —| ∑∫
↔∇ ◊⟩∫⌊ ®∫ ∫|∫ ∑⟩∫ð◊™◊⌊ ∫®⟩∑ ∑⟩∫ ∇∫ð◊ |◊ð◊⌊ ∑∫ð◊ ð◊ ð ◊∑∫® ⟨ð◊ ∑ ∑ ⟨ ®◊∑∫⟩◊ ®∑ð∑ ⟩∫ | ™ð⌋®◊∑∫ ∫ ◊ ⌊◊ ™◊∑∫ ◊∫ ® ð◊ ⌋®◊∑∫ ∑⌊ ™∑⌊◊∑∫ ∑® ⌋ ⟩◊ | ∫ð ⌊ ∈ ⟩® ™ ∫ ◊ ∑∫ ◊ð ®◊ ∑⌊ ⟩∫ ð◊⟩⟩∫ð◊ ®◊∑∫ ∑∫| ⟩∫ ⌋ ⌊∑ |ð∑| ∫⟩∫® ∑∫| ∑ ∫ð◊ ⟩ ⌊ ⌈∈ ⌊ ◊∑∫ ◊⟩∫ ⌈ ® ⟩∫ |ð∑®ð◊⌉◊∑∫⟩ ⌊ ®⟨∑⟩⟩ ⌊ ∑ ∑© ∑™∑⌊◊ ∫ ◊∑∫◊ ⟨ ⟩ ◊∑∫|◊ ∫ |ð ∫ © ®◊∑∫ ∑ ™◊ ∈ ™ ◊∑∫⌊ ⟨ ® ◊⟩ ⌊ ∑∫⌊ ∑ ®⟩∫®◊™ | ⌋|◊ ™ð ⟨ ⌈ |ð ®⌊∑|◊ ∑⟩ ◊⟩∫ ®∑™∑∫|⟨∑⟩⟩ ∑∫ ⟩|∑ |∑ ◊⌊ ≈
⊆∑⟩ ⌉∑⟩∫® ∑∫ ∑⌊ ®∑|◊⟩® ⟨ ™ © ∫⟩∫ð◊ ® ® ® ⟩| ∫◊∫ ⟩® ∑⟩ ◊ ∑ ◊ ∫ ⟩ | ∫ð ⌊ ð ®◊∫ ⌋⟩⌊ ∫∑⌊ ⌋⌈|ð ∑⟩⟩ |ð◊®⌊ ∫ ⟩∫ð◊
∪®⟩∑∫◊| ⟩∫ð◊ ⟩∫◊∑∫⟩ ⟩∫ð◊ ∫ ⌊ | ™ ∫∑ | ð| |◊®⌋| ∑ ∑|ð | ⟩ ∑∫∑⟩ ∪⟨ ∑⟩∫ ® ◊⟩ ◊ ⟩ ⌊◊| ∫ ð◊ ◊⟩∫◊®⌊ ∑∫ ◊⟩| ð ⌈ ◊ ð ®©⌊◊ ◊ ◊∫◊ ®™⌋ ◊ ∑ ◊©◊∫ ®∑⌉∑ ∑ ®∑™◊ ™ ⟩∑⌊∑ð∑◊⌊ ⟩∫ ∫ ⟨⌋| ⌊ ∫ ®⌋⌈ |⌋∫◊| ð ⌈ ® ⟩∫ ð© ∫ ®⌋ ®|∑ ◊∫⌊∑ ⌈ℜ⟩| ∫∑⟩ ⟨⌋∫ ⟩® ∑⌈ ®⌋| ⌈ ∑∫∑ ∫ ∑ð◊ |ð |◊⟩◊⌊ ⟩ |⟩∫ð◊ ð◊⟩∫® ð ⌊ ∑© ∫ ⟨⌋| ⌊ ∫ ∑ ∫ ∑ ∑ð ⟨ ⌊ ∑∑∪ ∫ | ◊⟩∫ ⌉∑ ™ ⟩∫ ⌈ ⌋∑ ◊© ⌊ ⟨ © ™ ⌉∑© |
ℜ ◊|⌊ ∑ ∑ ∫∑⌊ ⟩ ⟨⌋|ð ®∑⟩∫ ™ ⟨ð⌋⌈⟩ ®∑∫⊗ ∑ ◊⊂∑ð ↔ℑ ⟩ ∑ ™◊ ™ ◊⌈∫∑ ⟨ ⟩|∑ ∑ℑ ⟩ ⟨ ⌊∑ ™ ◊⌈∫∑ | ⌊ ™ ð ® ∑ℑ ⟩ ∑⟩ ◊⟩∫ © ⟩⌊ ◊ ™ ◊⌈∫∑ ℑ ∑⌈ ◊⌉ ∫∑ ◊⟩∫◊®⌊∑ ℑ ⟩ ⟩ ∑ð∫ ð◊ ⌋ ⌊ ⌈∫∑ ®∑ ⌈ ℑ ©∑⟩∫ ∫ ®◊ ◊⟩∑© ™ ≈

∉∠∪ℜ⇔·⊇ℵ—∏ℵ∠ℵ⊇®⊕∠—∇©⊗⇐ℑℵ

⊂ ⌊⌊ ⌋⌊ ™∑⌈®⟩ ® ∫®⟨∑™ ⟩∫ ™∑| ⟩| ⌊ | ∑∫◊|® ⟩| ⌊ ®◊⌊ ⟩ ⟩ ⌊ ⌈|ð ®⌋ |
⊆∏ ⌊⌊

©™◊ ◊— ∫ ð∑ ⌊ ∫◊∫|ð ®⌋ | ·∫ ⟨⌋®◊ ◊ ⟩∫◊⌊◊™ð © ⌈®⌋⟩◊ ™ ⌊ ⌋ ∑ ∫ ⟩ ℵ™⌊ ∫ © ∑ ⟨ ™ |∑ð∑⟩ ∫ð∑∫ ⟩® |ð ®⌋ | ⟨ð◊ |ð ∑ ∑∇ ⌊◊|ð ®⌋ | ©ð ◊| ∫ ⟩∫ ∫® ∫ ∑∑|⟩∑⟨∑ ◊⟩⌊ ⟨ ℜ⌋™◊ ∑ ∑ ◊ ∑ ◊∑∫∑|◊|®◊ ◊⌊ ⟩∫ ð ð ∑∫⟩ | ⟩◊ ⟨⌋| ®∑ ∩◊| ∉ð ®⌋ | ⊇◊|∫ ⌊ | ®⌋ ∫ ∫ ◊| ⟩ ◊∑∫∑ ⟩|∑ ®◊ ©◊ð◊ ∫ ð ®◊ ⊆◊|ð ∑ð∑⟩⌊ ®⌋⟩ ð ð ∑∫∑|ð ®⌋ | ™ ◊∫ © ® ð ∫ |ð ®∑∫◊ ⟨ ⌊ ™ ð ® ∑ ™◊ ∑— ∫◊|ð ®⌋ |◊⟩∫◊ ∑∫®◊ ∑⟩∫∑⟩∫®∑ ⌋ |ð ™ ⌊ ∑ ∑ |ð ∫ ∑∫®®◊ ∫◊| ∑® ⟩∫ ∑ ™◊ ⌋∑|⌊◊ ⌋ | ∫ ð⌋ ⟩∑© ™ ®⌋ | ™ ◊∫ ∑⟩ ∑∑∫∑ℵ®⌋ð◊⟨ ∫◊∫ ∫ |ð ®⌋ | ®⌋⟩ ∑∫∑⟩| ⌉ ⟩◊ ® ∑ ∫◊||◊| ∑ ™ ⟩◊ ® ∑ ∑ |ð ®⌋ | ⌈⟩ ⌉∑⟩∫® ∑∫⟩◊ ◊ ∫∑⟩ ◊ ⟩® ⊄ ⟨ |ð ®⌋ | ⟩ ð ð ®◊∫ ⟩| ⌉ ⟩◊ ® ∑ ð∑© ⌊ ð | ®∫ ð ⌉∑© ⟩ ™∑⌈⟩∫® ↔∇ ◊⟩∫ ∑— ∫ ∫ ∑|ð ®⌋ |◊≈∇™∑⌊◊⌈∫∑⟩ ◊⟩∫ ∑ ⟨ð◊ ⟩® ∑⌈ ⊇◊ ™ ∑ ∫ð |ð ⟩ ® ⟩ ∑ ∫|ð⌋®◊ ©⌊◊ © ® ð ∫∑⟩∑⟨∑↔∇∑© ™ ⟩◊ ⌋⌈⟩ ◊⟩∫⌊ ®⌋⌈™∑ ∑⌈ ⇓|ð ®⌊∑|◊ ®⟩® ∫ ⌊ | ™ ⟨ð ⟨⌊◊© | ⌊ ∑|ð ®∑∫◊ ∑ ⟩|∑ ™ ð ® ∑≈
∠◊⟨ ∫◊ ◊™| ⌊ ∫∑⌊ ⌋ ∑ ∑ ⟩® ∑⌈ ⟨ ™ ∫∑ ∑ ® ◊∫∑⌊ ⌋| |ð ∑ ℜ◊ ∫ð ™ ⟨ ™∑∫ ™∑ð ®◊∫ | ⌊ ∫∑⌊ ⌋⌈ ◊⟩∫ð ⌈⟩ ™◊ ⌋⌈⟩| ⌉ | ∫ ® ⌋ ⟩∫◊ ® |∑ ∑™ ∑® © ∫ð∑ ©◊∑⟩⌊ ⌊ ™ ® |ð ©®◊⟩⟩∫◊ ∫| ™⟨ð◊⟩⌋®◊∫ ®◊ ∑©◊∫ ® ⌋⌈ ◊∫∑ð ◊⌊™⌊ ð◊ ⌋ ⌊∑ ⌈⊕⟩⌊ ⌋⟩⌊ ®◊ ™ð ∑⌈ ◊| ⌋ ∑©◊∫ ® ⌋ ⟨ ™ ∫∫◊| ∑ ◊ð◊ ∫∑⌊ ⌋|◊| |⌊ ◊ |ð ®⌋ |◊↔∇|∑ | ®∑™∑ ⟩ ∫∫ © ◊⟨∑ð∑ ⟩ ≈∈|ð ∑ ∑™ ⌊ | ©◊∫ ◊ ∑ ∑ ◊∫ ®◊ ∑ |ð ™® ∑ |⟨⌊◊© | ⌊ ⌊ ⟨ ⌈ | ⟩∫◊®⌊∑ ⌋ ®◊ ∑⌊∑⌈
⊇ ∑ |ð∑ ™∑ ∑ ®⌋ ∑ ∫∑⟩® ⟩|⌊ ⟩∫ |ð ®⌋ | ®◊ |ð ™∑∫⟩ ⟩∫ ⌊| ∫ ⟩ ⟩ |ð∑™∑⌊∑ ⌋ ∫ð ™ ⟩∫ ð◊⌊ © |⟩ ⌊ © ∑⟩| © ◊ð◊|∫∑ð◊∪ |ð∑ ™ ⌊∑ ∑—®◊ ◊|⌊◊∫◊ ◊® ™® ð ⟩|∑ ◊∉ð∑ ⟨ð◊ ®⟩® ∑⟩ ◊ ∑ ∑ ® ∑©◊∫ ® ∑ ⌋ ⌊∑ ∑ ◊| ∫ ® ∑®⌋⟨ ™∑∫∑⟩ ◊⟩∫⌊ ®⌋ℜ◊ ∑ ∑|ð ™∑∫⟩ ◊|ð ©◊∫ ⟩ |ð ⌊◊©◊∫ ⟩ ⌊ |◊ ™ ⟩∑| ™ | ∫ð ⌊ ð ⟩∑⟨ ©®◊⟩®⟩∑⟨ ™∑∫| ⌊ ◊∫ ⟩ ∑⟩∫∑⟩∫®∑ ⊆ ®|∑ð ™⟩∫◊ ®⌊∑ ◊| ∫ | ⟩|∑ ®◊ |ð ™∑∫⟩ |ð ® ∫ | ⌊ ⟩⟩◊⌊ ◊⟩∫ ⌈ ® ⟩∫ ∫∑ð|∑ ∑
∉ ∑ ®⟩∑∫◊| © ∑⌊ ™ ∑© ∑™ ⟨ ⌊ ⟩ ® ?⊗◊|ð ⟩∫ | ∫ ∫ ∑© ⟩ ⟨∑ © | ©™◊ ∑ ∑⌊◊⌊ ℵ ∫ ∑ |◊ ⌋®◊∑∫ ◊ ∫⟩ ∫⟩∫® ∑ ∑⟩∫ ⌊ ⟨ ∫ ⌈ ∑ð∫⌋ ◊ð◊|∫∑ð◊⟨∑ | ∫ ð ⌈ ⟩|∑ ∑® ⌈™∑∫® ∉ ®ð◊ ® ∫ ∑⟩∫ ⌊ ⟨ ∑⌊◊ ⟩| ⟩ ⟨ ® ⟨ð◊ ∑ ∑⊆∑ ⟩∫◊ ® ⟨ð◊ ◊ ⟩® ∑⟨ ™ ⌉∑∑®⟩∑⟩® ® ⟩∫ ™ ⟩∫ ∑ ∫ ◊∫∑ð ◊⌊ ∑⟨⌊◊© | ⌊ ∑| ∫ ð © ®⌋⟩ ∑∫∑™ ⟩∫ ®⌋®ð∑ ⌊ ∫◊∫∑|ð ⟨ ∑∫∑⟩∫∑ ⟩ ⟨⟩∫®∑ © ð◊® ™ ™∑⌈⟩∫® ∫∑⌊ ∑© ∫ ⟩ ⌊ ◊ ∫ ∫∑
©®∑ð∑ ⟩∫ ®⟩∑⟨∑| ® ⌊ ∫™ ®∑⟩∫ ™∑⌊ ™ | ◊⊆ ∫ ⟨⌋|ð∑ ⟨ð◊ ®◊∫ ◊⟩∫ ⌈ ® ⟩∫ ® ®∑ð∑ ⟩∫ ®⌋™ ⌊ ⌋| ®∑ð ∫ ®⟩∑⟨ ℵ ∫ ® ∫ ⌊ | ®∫ ⟩⌊ ◊∑∑⟩⌊ ®⌋™ |◊ ∑∫∑⟩◊ ⟩∑⟨∑ ∑© ⟩∫ ∫∑∉ ∫ ∑ ⟨ ™ ∑|ð ⟩∫ ⟩ ◊∫ ®⟩∑⟩® ⟩⌊◊⟨ ⟩∫ ◊⌈∫ ∑⟩∫® ⟨◊® ∫ ⟩ ∫ ∈™ ◊| ∫ © ◊⌊ ⊆ ™ ®ð∑ ∑ ð◊ ® ®◊∫ ∫∑™ ⟨ð ™∑∫∑⌊ | ∫ ð⌋∑ ⟩ ⟨∑ ®◊ ⌋™⌊ ®◊⟩ ◊| ∫ | ⟩|∑ ⊗⌊ ∫ © ® ⟩| ⌊ ®◊∫ ⟩ ð ⌊ ⌈ ⟩|∑ ◊ℑ∑ ™ ◊ ◊™ð◊ |⌊ ◊⟩ ⟩∫◊® ∫∑⟩| ⟩ |∫∑ ™ ⟨ð ™∑∫∑⌊∑⌈| ∫ ð⌋∑™⌊ ®◊⟩⟩∑© ™ ◊ ⟨ ⌊∑∑®◊ ⌋⊆ ∑ |∑ð∑ ⟩⌊ ™ ⟨ð ™∑∫∑⌊∑⌈ℑ™ð◊ |⌊ ◊ | ∑© ⟩| ⟩ ⟨ð◊⟨ ∫⌋ ◊™ ◊ ◊∫∑ ⟩™∑⌊◊ ◊| ∑ ∫ ◊∫∑ |ð ®⌋ |◊ | ∫ ð⌋∑ ◊ ⌈® ©⌊ ™⟩⌊∑™ ∑∫|ð ⟨ð∑⟩∫ ®|∑ð® ∑ð∑™ | ∫ ð⌋∑™ | ⌊ ∫|ð∑|ð◊⟩ ⌋⌈⟩| ⟩ |ℑ™ð◊ |⌊ ◊∉ð ®∑™∑ ⌋∑ ∑| |∫ ®|∑ ◊∫◊ ∫⟩ ⟨∑ ∑ ∑ ⌈ | ©
⊆∏ ⌊⌊⊇∇∫ ⊗ ⟨∑⌈⟩ ⟩|∑ ◊⟩| ⌉ | ∫ ® © ð ® ⟩|ð ∫ ⊂ ⟩|↔∉ | ðð ≈
© ∑ð∑ ⟩∫ ∑⟩∫ ∑™ ⟩ ⌈ ™ ð | ∫ ∑™ | ∫∑ð | ∫ð ⌊
⊂ ⌊ ◊⌊ ® ⟩∫ © ® ð ∫ ∫ ⌊ | ∫ ∫ |ð ⟩ ∫| ⌊ ∫∑⟨∑ ™ð © ⟨∑©◊∫ | ⟩∫⌋ ð◊ © ® ð ®
∉ ð ™ ||◊ ™◊ ®∑⌉ ™ ⌊ ◊ ◊ ™ ∫ ⟩ ◊⟩® ∑ ∑⟩∫∑|◊ ™ ∑™∑⌊ ™ ⌊ ®⌋| ⌊ ∫ ⟩ ®⟩® ∑®ð∑
∠∑ ∫∑⌊ ⟩∫ |ð ◊∫ ð∑ ∑ ∑ ®⌋| ⌊ ∫ ∫ ∫ ⟩ ∫◊∑∫∑ ⌋ ⟨ ◊∫∑⌊ ◊®∑ð ◊∫ ∫ ∫ ð∑ ⌊ ⟩ ⌉∑⟩∫® ∫
ℑ∑ð∑ ⌊ ® ⟩∫ ∫ð◊∫ ∫ ∫ ⌊ | ◊⟨⌊◊© ™ð © ⟩◊ © ⟩∑⟨ ™ð © ⟩⌊ ®◊ ∑∫ð◊∫ ∫ ⟩ð∑™⟩∫®◊| | ⟩∫
©⟩∑ð™ ∑ ∑∫∑ð ∫ ®ð∑ ∑ ®⟩∑®ð∑ ◊ ◊∫ ⟩ ∑ ⟨ ™ | ⌊∑ ⌋ ∫|◊ ◊∫ ⟩ ∫®⟩∑ ⟩ ∑∫ ⌋ ™∑⌊
∪⟩|ð∑ ⟩∫ ⟩| ð∑ ∫ ®⟩∑⟨∑ ∫ð ⟩∫ | ®◊ð⟩∫® ⌋⟩⌊ ™ ⌊ ⌋⟨⌋∫ ⟩∫⌋ ⟩|ð◊®∑™⌊ ®⌋ —∫◊| ∑™ ⌊ ⌋⟨⌋∫ ⟩⌊ ®◊
∇|ð◊®∑™⌊ ® ⟩∫ ∑®ð∑™ ∫ ⟨⌊ ∑ ∑⟩|ð◊®∑™⌊ ®⌋ ™∑⌈⟩∫® ∑⌊ ◊∫ ∑© ⟨⌊◊© ∑®⌋| ⌊ ⟩® ⟨ ◊ ⟩∫
∇™∑ð ◊ ⟩∫ ⟨∑©◊∫ |ð◊⌈ ⟩∫∑⌈⟩™∑ð ®◊∫ © ∑®™◊ ∑∑⟩⌊ ⟩|ð◊®∑™⌊ ®
· ⟩∫ ∫◊ ∑∫∑ð|∑∫ ∑ |ð ∫ ⟩∫ ∫∑⌊◊ ™∑ ™⌋|ð ®⌋ ∑|
∇| | ⌈⟩∫® ∑ ∑ð◊⟩⟩∫ð◊ ®◊∫ ⟩ | | ⟩∫ |◊ ⌊ ⟨ | | ® ™ ∑|ð ∫ ⟩∫∑⌈| ∫ ð⌋ ∫ð ™ ⌊ ∑® ⟨∑ ◊∫
ℜ ™∑ð ◊ ⟩∫ ∑|ð∑™◊®◊∫ ⟩ ⟩⌊◊™ ⟩∫ð◊⟩∫ |ð ∑|◊|™⌊ ™ ð ® ⌊ |ð ™ ⌊ ∑ ð ™◊ | ©™◊ ∑ ◊ ◊∫ ⟩ ∫ ™ ⟩ ⟩∫ ® ⌊ ⟩∫ ⌊ ⟩⌊◊⟨ ⟩∫ ⌊ | ©™◊ ∫ ©ð ◊∑∫ ∑ ⌊ ⟨ ⟩| | ⌈⟩∫® ⌊ ð∑| ∫◊
∇ ð∑ ∑| ™ð◊ ◊∫ ®⟩® ∑ | ®∑™∑ ∪ ⟩ ⟩ ∇ |ð◊∫
⊗◊⌊∑∑ℑ™ð◊ |⌊ ð◊⟨ ∫◊⌊ ◊™ ∫ ™ ⟨ð ™∑∫∑⌊ ⟩⌊∑™ ⌉ ⟨ð◊ ∈ ⟩ ⟩∫◊®⌊ ⌊∫◊⟨⌊ ®| ∫ ð ®|⌊ ◊⌊®⟩∑™ ⟨ð ™∑∫∑⌊∑⌈®∑™ ⌉ ∑© | ⟩|∑ ®∫∑ ∑ ∑ ™ ⌈ ∑™∑⌊ | ∑ ∫ð ð ®◊⌊® ◊ ∑ ◊ ™ |ð |∑ℜ∫∑ ∑ ∑⟩⌊∑™ ⌉∑⌈ ∑™∑⌊ |⟩ ð ®◊⌊® ◊ ∑ ◊®∫ ð |ð |∑ ∫™◊®◊ |∑ð®⌋⌈®ð◊⟩| ð ∑ ∑| ™⟩ ◊ ⊗ ⌈™ ™ | ◊⟩| ⟩|◊™ ⟨ð ™∑∫∑⌊∑⌈ ◊ ◊⌊®⟩∑⟩ ◊ ◊⌊◊∪ ◊© ™| ®∫ ð ⌊ð◊ ◊| ⌊ ⌋⌈ |⌊
∇ ⟩® ∑⌈⟩∫ ð ⌋ ∑⟨⌋ ∫∑⌊ ⟩ ⟨ð◊∫ ∫ ®◊ ∑® ◊ ∑ ◊⟩⌊∑™ ⌉ |ð ∑ ™◊ © ∑⟩ ◊⟩∫⌊ ® ∑® ∫|⌊◊™⌋®◊⌊ ◊ ◊®∫ð◊∫ ∫ ⟩™∑⌊◊∫ ⟩∑© ™ ∉ð ®⌋ |◊®⟩∑ ∫|⌊◊™⌋®◊∫ ◊| ∫ ◊| ◊ © ⌊ ™ ℑ⌊◊© ™◊ð ∑⌈ ◊ ◊⟩∫ | ⟩|◊ ∫⟩ ® ⟩∫ | ∫ ð⌋∑ ©⌊ ⟨⌋ ∑ ∫ |⌊ ∑ ®⟩ ↔⇓⟩™∑⌊◊ ∫ ⟩∑⌈ ◊⟩≈™ ⌊ ⟩∫◊∫ ™∑® ®⟩∑⌈®◊ ∑⌈ ↔∇∑⌈ ◊⟩≈— ∑ ⟨⌋⟩∫ð ∫∑ ℜ◊ ®◊∫ ∫ ∑© ∑™◊∫ |ð∑®ð◊∫ ∫ ⟩ ® ↔® ∑ð◊—| ©™◊ ©⟨⌋≈∉ð∑®ð◊∫ ∫∑™ ®∑™∑ ∑™∑⌊◊™ | ◊⟨∑ |ð ∑™⌊∑ ®|ð ®⌋ | | ∫ ð◊ |◊|®⌋ ◊∑∫∑®⌋ð◊⟨◊∫⌋®◊∑∫⟩ | ∫∑ | ®∫ ð∑ ·∫ ⟨⌋™ ®∑⟩∫ ™∑⌊ ™ | ◊ |ð∑ ™∑®⟩∑© ™∑⌈⟩∫® ®◊∫ ∉⌊◊ ð |◊ ™⌋⌈⟩® ⌈™∑ ™ ⟨ ®◊⌈∫∑⟩ ®⌋| ⌊ ∑ |◊ ™ ⌈ ◊ ∑ ∑ ⌈ ∑⌊ ℜ⌋ð◊⟨ ∫◊⌈∫∑⟩ © ◊⌊®® ™∑ ⌋⟩⌊∑ © |ð |◊ ◊↔⇓⟩™∑⌊◊ ∫ ⟩∑⌈ ◊⟩≈ ⟩ð◊ ∑| ⟩⌊∑|ð ∑⟩∑ ∫ ⟩⌊ ®|ð ⟩∫ | ∫∑|™∑⌊ ⊕⟩⌊ ®⌋⟨ ™∑∫∑™∑⌊◊∫ ∫ ð∑© ⌊ ð ®◊⟩| ® ∫⟩ ⟩® ∑© ð ™◊ð∑ ⌊∑|⟩®⌋ ◊ ∑∫∑™∑⌈⟩∫® ®◊∫ ⟨∑ |ð ∑™⌊∑ ⊆ ®| ∑ ⟩⌊ ◊∑ ∑|ð ⟩ ∫∑↔⇓⟩™∑⌊◊ ∫ ⟩∑⌈ ◊⟩≈∑⟩⌊ ®⌋ ∑|ð ⟩∫ | ∫∑|™∑⌈⟩∫® ⟩ð◊ ∑| ⟩⌊∑ ∫ ⟩⌊ ®®∫ ∑ ∫
⊆◊ |ð © ® ð ∫∑ ∑ ∑ ∑∑ð◊ ↔∩◊®∫ð◊ ⟩™∑⌊◊ ®⟩∑ ∫ ◊|⌊◊ ð ®◊⌊⟩™∑⌊◊ ∫◊||◊| ™◊ ∑ ◊ © ⌊ ∑⊂ ∑ ð◊® ∫⟩ ◊ ◊∫ ™ ® ™ ∫ ™∑⌊ ™ | ◊⇓ ∑ ∫|⌊◊™⌋®◊ ™∑⌊ ®™ ⌊© ⌈ ⌉ |◊⟩ð◊ |ð ⟩∫ |◊ |∑© ð∑◊⌊ ◊ ⇓⟩™∑⌊◊ ®◊ ð◊⟨ ∫ ®|∑ð® ∑ð∑™ ®⟩∑©™◊© ∫ ®© ∫ ®◊|™∑⌈⟩∫® ≈
∏ ⟨ð◊∫ ∫ ®◊ ∑® ◊ ∑ ◊| ⟩∫ ∑® ⌊ ∑⟨ ⌋⌈|⌊ | ⟩|∑ — ◊| ∑ ∫ð◊ —↔⟩| ⟩ ⟨ ⟩∫ ®ð∑ ⌊ ∫◊∫∑|ð ⟨ð∑∫∑ ⌈|ð ®⌋ | ™ ⌊© ⌈|ð◊|∫ | ◊™∑ð ®◊∫ ® ◊ ∑ ◊ ™ ∑™ ⟩∫®∑ |ð∑™ ∑∫∑™ | ⌊ © ◊| ⌊∑ ⟩ ®⌊◊™∑ ⊇ ∑ ∫ð◊ ◊ ◊∑∫⟩| ⟩ ⟨ ⟩∫ ™∑ð ◊∫ | ™| ∫ð ⌊∑ ⟩® ∑® ◊ ∑ | ⟩ ð ®◊∫ ∑© ◊™◊ ⌈|ð ⟨⌊∑ ∑| |◊ ◊ ∑⟨ ™∑∫ð∑ ∑ ◊⊇ ∑ ∫ð◊ ◊ ◊∑∫⟩| ⟩ ⟨ ⟩∫ ⟨◊®⌊ ∫ ⟩ ∫| ⟩⌊∑™⟩∫® ⌈™ ð ⌋ |ð ®⌋ ∑| ® ⟩∫ |ð ⟨ð∑∫∑ ®⌋ ð |ð ®⌋ ∑|∈ ◊ ◊ ◊∑∫| ⌊ ∑®⌊◊™∑ ∑⟩ ⟨ ⌈≈
⇐® ð |ð ®⌋ |◊ ◊| ®◊ ®∑⟩∫ ∑ ð∑ ∑ ∑↔∉ ⟩∑ ®™∑⌈⟩∫® ∑| ∑∫∑|ð ®⌋ | | ⟩∑ ®|ð ®⌋ | | ∑∫∑ ◊ð◊|∫∑ð| ⟩∑ ® ◊ð◊|∫∑ð| ∑∫∑⟩ ™ ⟨ ≈∏◊ð◊|∫∑ð ©ð◊∑∫ ©ð ð ⌊ ®™ ⟩∫ ∑ ⟩|∑ ◊∪ ◊™ ∑ ⟨ ™ ð◊⟨ ∫◊∫ ⟩| ⌉ |◊|| ∫ ® ⌋ ⟩∫◊ ® |∑ ∑™ ∑® © ∫ð∑ ©◊∫◊| ◊|∫ ® © ™∑⌈⟩∫® ⊇|ð ∑ð ð◊⟨⌋|ð ®⌋ ∑| ⌋⌊∑©| ⟩⌊∑™ ∑ ◊®∑™∑ | ð ™| | ∫ ð⌋⌈⟩™∑ð ®◊∑∫ ◊⟩ ∑™◊∑∫®⌋ð®◊∫ ⟩ ⟨⌋™∑ ⟩∫ ∇◊ ∑ð◊ ∑—⌊ ◊∫ ⟩ ⟨⟩∫®∑ ⌋∑|ð ®⌋ | ⊇◊|∫ ⌊ | ®⌋ ∑ ∫∑⟩® |ð ®⌋ |◊ |◊|∫ ⌊ | ◊ ∑∫∑ ∫ð◊⟨◊∫⌋®◊∫ ∫∑ ∑ð∫⌋ ◊ð◊|∫∑ð◊| ∫ ð⌋∑ ∑ ∑ ®∑™ ∫| ⟩|∑ ®◊ ◊ ∑ ∫⟩ ™ ∑ ◊®◊∑ ⟩∫ ∉ ® ∫⟩ ∑∫ ⌊ | ◊⟩⟩◊ ™∑⌈ ð∑◊⌊ ⌋∑ ◊ ⟩⌋ ð∑◊⌊ ◊ ⊆ ∑ ◊⟨ ™ ∫∑|ð ∫∑ð|∑ ∑| ∫ ð ∑™ ⌊ ⟨⌋∫ |ð∑ ™∑®⟩∑© ◊|∫ ® ◊ ∑|◊⟩⟩ ® ◊| ∫ |®◊ ∑⌈ ∑⌊ ◊∫∑ ⟨ ⌊∑∑|ð ®∑ð

ℜ⊕∠ℵ®ℜ∈∠⇓∧ℵ⇓·©⊗⊕∇ℵ

⊗ ⟨ ∑ ⟩ ∑⟩⌊ ®∑ð ∫ ⟩ ∑
⊆∏ ⌊⌊
℘™∑®∑ð◊∫◊ |◊||ð◊® ⌊ ⟩∫ ◊
⊇⊆

ℜ∑ð◊— ™ ©⌊◊® ⌋ |ð | ® ⟩|∑ ◊↔∉ ®∑ð∑®◊ ∑⌈® ™◊∑∫⟩ ®◊ ≈™ ⌊ ⟩∫◊∫ ⌊ ∫⌋ |ð◊® ⌊ ®◊ ∑⌈ ⊂ © ∑|ð |∑ð® ⌈ ∑ ∑ ™◊ ∑∫∑ð ∫®∑ð ℵ®∑™ |∑ð®⌋∑ ◊© ◊ ◊⟩∫ ⟨⌋⌊ ⟩™∑⌊◊ ⌋|ð◊® ⌊ ® ◊|ð◊®⌊∑ |ð ⟩∫ ⟨⌋⌊ ◊⟨ð◊∫ ⟩ ∫∑ð|∑ | ®∑ð ∫ ®⟩® ⟩ ⌊⌋⊆ | ©™◊ ∑⟩ ∑®◊⌈∫∑⟩ ∫ ◊⌈™∑∫∑| ∫ |™ ⟩∫ ∑ ∑⌊ | ⌊ ∫∑ ⌋⌈ð∑ ⌊ ∫◊∫® ∑®ð∑ ℜ⟩∑ ⌋⟩⌊ ◊ ∑ ◊ ⌋∑ ◊®∑ð∑ð∑◊⌊ ®⌋®◊ ∫⟩ |ð∑| ∫⟩∫® ∑⟨⌋®◊ ∫∫ ⌊ | ∫∑| ∫ ð⌋∑®⌋⟩◊ ®⌋™ ⌋®◊∑∫∑ ⌊ |ð ◊∑∫∑ℜ⟩∑©™◊| ∫∑↔⊂⌋⟩⌊ ⟨∑ ®∑ð⌋ ∑ð∫®◊∑⟩∫ ≈® ⌊ | ®∑ð◊⟩| ⟩ ⟨ ◊|ð ∫ ® ⟩∫ ∫ ∑ ™◊ ◊ ⊇ ©™◊®∑ð ∫ ∫ð ™ ◊| ⌉ |ð ™ ∫⟩◊ ® ∑ ∑⟩| ⌉ | ∫ ð © ð∑◊⌊ |ð∑| ∫ ®∑ð ⟩ ⟨∑ ∫ ©™◊| ©™◊ ◊ ◊∑∫|◊ ◊∫ ⟩ ∫ ®⟩∑| ∑ ℜ∑™ ⟩|∑ — ∫ ™∑⌈⟩∫® ∑∫⌉◊∫∑⌊ ⟩|⌊◊ ð ®◊ ∑ ◊⟩∫ ⌈ ® ⟩ ⌉∑⟩∫®⌊ ∑ ∑⟩®∑ð ⌈® ⟩|∑ ∇⌊∑™ ∑∫| ∫ ∫ ∑⟩⌊ ®⌋© ® ð ∫∑® ®ð∑ ⟩◊ ® ∑ ↔⇓⟨ ©◊∫⌋⌈◊ ™◊ ⌊ ®⌋⌈◊ ⟩|∑ |ð ®∑∫◊ ∑⟩ | ∫⟩∫® ∫ ∑≈◊®©⌊ ⟨ ∑™ ⟩ ™ ∫⟩ ∑ ∑↔⊗◊ ®⟩∑ ∫ ∫◊|⟨⌋®⟩∑⟨ ©◊∫⌋ ⟩∫◊⌊ ≈—∫ ®◊ ∑⟩ ◊ ∑|◊⟩ ∑∫|∑ð∑™⟩ ∑ ®⟩| ⟩ ⟨ ⟩∫ | ⌊ ∫ ∑⌊◊∑ ∑⇑∫ ⟩ ∑ ∑⟩|ð ∫◊ ∑©⌊ ⟨ | ® ∫ð ®◊⟩|◊| ⟩∫ð◊ © ð◊ ™ ⟩ ⌊ ∑∑©ð | ⟩⌊ ®| ∫ ð⌋∑®⌋⟨ ™∑∫∑| ®∫ ð ∫ |◊ ™ ∑ ∫ð ◊|ð◊®⌊∑ ⌋ ◊®◊ ∑⟨⌊◊© | ⌊ ∑∪®◊ ∑| ™⟩ ◊ ∑|ð ∑∫∫ ∫ ®⌊ ∑∫⟩ ™ ◊ ∫ ⌈®™◊ ⟩⌊ ◊∑—®◊ ∑⟩ ∑ ∑∪| |◊®⌋|◊|ð∑⟨∑ | ∑| ®∑ð ∫∑®ð∑◊⌊ ⟩∫ ⟩ ⌉∑⟩∫®⌊∑ ⌊ ⟨ ⌈®◊ ∑⌈ ∑ ∫⌋ ⟩∫◊ ∫⟩ ∑ ∫◊ ↔ℜ⟩∑ ∑© ⟨ ™∑∫∑|ð ⟩ ∫ ® ⌊ ∫®∑⟩® ∑⌈®∑ð ∫∑ ∫ | ⌊ ⌊ — ⟨ ™∑∫®◊ ≈∪ ∑ | ⌊ ⌊ ◊ ∑| ⌊ ∫∑⇑∫ ®◊ ∪ ™ ◊ ∫ ∑| ∫ ð⌋∑⌊ ™ ⟩⌊∑™ |◊| ⌈⌊ ⟨ ∑∫ ™ |∑ ∑™ ⟩∫ ©◊ ∫ © ð∑ ⌊ ∫◊∫◊⟨⌊◊© ™◊ð ∫⟩ ∫⟩∫® ™∑∫⟩| ⌈ ◊ ® ⌈®∑ð⌋® ™ ∈ |ð ⟩∫ ∑ ⟩ ◊ ∫®∑⌊ ◊⌈ ∑⌈⟩ ⌊⌋ ◊⌊ ∑ ⌈®®∑ð∑∉ ®∑ð ∫∑®⟩∑⟨ ®⟩® ® ⟩∫ ℵ|ð◊|∫ ∑⟩| | ⌉ ®◊ |◊ ∑∫∫ð∑ © ΙΙ ◊⟩∫ | ©

∉∠∈℘∠ℵ⊂⊂ℵℑ⊄ℵ℘∈∇∈∇®∈⇓⊆∪⇓
∇⊗⊕⊄ℵ⊕®ℜℵ∇∩⊗∈∠∈ℜ⇔⊂∪

ℜð◊ ⟨ð◊⟨◊∫⌋®◊∑∫ð◊ ◊ℑ ©∑∑⌊∑ ∫
⊄ ⟨◊ ⟨ ⌊∑ ® |◊∑∫®⟩ ◊ ◊ ◊ ∫∑™ ⟩∫®∑ ⌈ ⟩ ∑⌊ ⌉∑⌈⟩ ⌊ ⌈⟩∫◊ ® ∫⟩ ®◊ ∑⟩ ⟨⟩∫®∑ ∑| ™⟩ ◊ ∑∇ ⌊◊®◊ ∑⌈ ⌋⟩⌊ ™ ð ® ∑| ™|ð∑|⌊∑ ◊ ®∑ð ⌈®⟩ ⟨⟩∫®∑ ∑ ⟩ ∑⌊∑ ∑⟩| ⟩ ⟨ ◊ ⌊∑ ∫ ⌊ ⟨ ∑ ◊⟨ ⌊∑®◊ ∑
√∑⌊ | © |ð∑™⌊ ∑ ⌈® ∑⌈|ð ©ð◊ ⌋ ⟩|∑ ◊ ®⌊ ∑∫⟩ ® ⟩| ∫◊ ∑⟩ ◊ ® ∑⌊ ∈ ⟩∫ ®⟩® ⌈ð◊ ∫ ∑©◊∫ ® ⌋ ⌋⟩⌊∑⌈®⌋®∑ð ∑∫∑ ™ ð ® ∑®◊ ∑ ∫∑⌊ ⟨ ™∑∫∑⟩| ⟩ ⟨ ⌋⟩|ð◊® ∫ ⟩ ⟩⌊ ⟨ ⌈⟨ ⌊∑ ∉ð∑|ð◊⌉◊ ð◊ © ® ð⌋ ∑™ ©◊ |ð∑|ð◊⌉◊ ™ ◊∫ ®⟩| ◊∫ ®⌋∫∑ ⟩◊ ⌋ ⌊ ∫∑ ⟩∫ |◊| ∫◊ ◊ ∑ ⟩∫ð◊ ◊|∑ð∑™ ∇⌊ ®◊∑ ∑™ ∑® © ⟩◊ ® ∑ ↔⊂ ∑ ð ⟩|◊ ™⌋ ™ ∑ ⟩∫◊ ® ∫⟩ ®⟩∑⌊ ∑ ⌊ ∑|◊ ™◊ |⌊∑∫ |◊ ∑© ∫∑⌊◊® ⟩⟩∫◊ ◊®⌊ ®◊∑∫⟩ ≈— ∑| ⟩∫ ⌈ ® |◊ð∑◊⌊ ⌋∑⟩∑ ∑ ◊®◊ ∑© ™ ð ® ⟨⌊◊© | ⌊ ⊆ ∑⟩∑© ™ ∑™ ™◊ ⟩ ◊ ◊⌊◊ ◊ ∫ ⌈ ∑ ◊⟨ ™ ∫∑|∑ð∑™⟩ |ð ∑⟩∫ ↔⊇◊ ™◊ |⌊∑∫ |◊ ∑© ð©◊ ◊⟩∑⌈ ◊⟩® ⟩⟩ ™◊∑∫⟩ ⌉◊∑∫⟩ ®⌋ ™ ð◊®⌊ ®◊∑∫ℜ⟩∑ ∑∫∑⌊ —®|ð ∑⟩⟩∑® ⟩⟩∫◊ ®⌊∑ ™ ð ® ©◊ð ≈
⊇ ©™◊®⌋ ⟩|⌋∫⌋®◊∑∫∑⟨ ⌊ ⌊ ⟨ © | ð ™|◊| |ð ⟨ ⌈∫∑|ð∑ ⟨ð◊ ®⌋®◊∫ ∑∑® ∑ð© ⟩ ∑⌊∑ ® ◊ ⟩∑⟨∑↔⇑ ∑ð© ⟩ ∑⌊∑ ◊| ⌊ ∑∫≈ ◊ ® ∫∑∫ ∫ ð©◊ | ∫ ð⌋⌈⟩® ∑⌈⟨ ⌊ ⟨∑⟩| | ∫®◊⟩∉ ®∫ ð ⌈∫∑ ∫ ð◊ ⟩∫ ⌊ | ⟩| ⌊ | ⟩ ∫∑∫∑ ⌋ | ∫∑ ⟩ ⌊∑®∑ð⌋ ⌊ ⟨®
∩◊⟨ ∫ ⟩ ∑ ∑™ ∑® ⟩® ∑ ∫∑⌊∑®⌋|ð ® ∫∑∫∑ ⟩◊ ⌋ ⟩® ⌊ ⟨ ® | ∑ ⊇◊ ™◊ |⌊∑∫ |◊®◊ ∑© ð©◊ ◊ ∫ ®∑∫⟩ ◊ ◊⟨ ∫ ∑ ∉ ∫ ∑⟩⌊ |ð∑™⌊ ∑ ⌋⌈®| ©∑∫ð∑ ©®⌋™ | ⌊ ∫∑ ∑⟩| |ð◊ ∑ | ∫ð◊⟩∫ ⌋ ™ ∑ |ð◊® ⌊ ⌋ | ∫◊ ∑ ®⌋ ⟩ ⌊ ∫∑ ⟩| ð ∫∑™∑⌈⟩∫® ∑|ð∑™⌊ ∑ ⌈®◊ ∑ ® ◊ |ð ©ð◊ ⌋∩◊⟨ ∫ ⟩ ⟩∑⟨∑ ◊ ∫∑⟩ |ð◊® ⌊ ⟩ ∑∫◊∫ ð◊⟨ ∫ ⟩ ∫™⌋ ◊| ⌊ ∫∑ ð◊ ⟨ð◊ ∑ ∉ ∫∑ ∫ ↔∑⟩⌊ | ⟩∫ ™∑ð ◊∫ ⌊ |∫ © ◊∫ ∫⌋ ⟩⌊ ◊∑∫⟩ ≈
∩◊ ◊ ⟩ ∑ ∑™ ∑® ⌋ ∫ð∑ © ®⌋® ™ |ð∑|ð◊⟩ ⌋⌈™∑ ®⟩| ∫∑ ⟩® ∑⌈ |◊⌊ ⟩∫ ∫ ∫ ∑∫∑⟩™∑⌊◊∫ ®⟩∑ ∫ ◊ ∫ ∫∑ℜ⌋ ◊ ∫∑⟩ ⟩ ®◊⌊ ⟨ ∫ ⟩∑⟨ |ð ⌉◊∫ ◊⟨ ∫ ∫ ⟩ ⟩∑⟨∑ℜ◊ ∑|ð ⌊ ∑ð◊⟩∫◊∑∫|◊|™⌋ ℜ⌋®⟩∑©™◊⟨ ™∑∫∑ ™∑⟩ ⟩∑⌈ ◊⟩®| ⌊ | ð ™|∑ ™ð◊® ⟩| ⟩ ⟨ ⌋∑ ∑ ∫ ⟩® | ⟩ ⟨⟩∫®∑ ∑⌊◊ ⟩ ⌊ ⌈®◊ ∑⌈ ⌋⟩⌊ | ∫ ð◊ ⟩∫◊ ∑∫®∑ð ⌈ ⟩ ⌊ ⌈ |ð◊®⌊ ∑ ◊ ∫ð∑ ð ∑ ◊ ®◊

·◊⟩∫ ΙΙ
∉ð◊|∫ ∑⟩| ⌈∫ð∑ ©↔ℜ ⟩| ∫◊ ∑⟩ ◊ ⌊
∇◊ ⌋⌈| ð ∫| ⌈| ∫ |⟨⌊◊© ⟩ ⟩∫ ≈

⊆⊕©∉∠ℵℜ⊄⇓⊕⊂∈℘∈©∇∉⊕∏ℵ⊆⊕ℑ⇔ℜℵ⊕®

∇ ◊ ∑— ∫ ∑ð© ⌋ ∑ ∑ ® ™∑∫ ∑∑ ð ∑ ⌉ ∫ ∫ ∑∑⊂ © |ð◊∫ | ®∫ ð ∑ ◊ ⌋⟩⌊ ⟨ð∑∫◊∑∫⟨ ⌊ ⟩ ⌊ ®∑ð∑ ⟩∫ ®⌋ð◊ ∫ ⟩ ⊕™ ◊ ⌋⟩⌊ ∫◊| ⌈⟩ ⌊ ⌈ ∑ ⟨⌊◊™◊∑∫⊇ ∑ ∫ð ð ⌋⟩⌊ ®⌋∫∑ ⟩◊ ⌋ ®∑⌊ ®◊∑∫∑ | ∫∑ ◊⌊∇ |ð∑™∑⌊∑ ⌈™ ⌊∑⌈⟩| ⟩ ⟨ ⟩∫ ™◊ ∑ ∫®∑ð ™◊∫ ∫ ™∑⌈⟩∫® ∫∑⌊ ⟩∫ | ∫ ð◊ ®◊⟩ |ð ◊∑∫⟩ ™◊ ◊®◊ © ∪ ∑ ⟩ ◊ ∑®⌋◊®∫ ◊∫ ∑⟩| ∑ ∑∫∑ ð® |ð ©⟩∑⟨ ∪ ∑ ð∑© ⌊ ð ∑| ®∫ ð∑ ∑ ⌋ | ⌊ ∫∑⌊ ⌋ ⟩∫◊ ® | ∫⌊ ◊∑∫®◊ ∑⌊◊ ∫| ⟩∫⌋ ◊ ∫◊ ⌈
ℜ◊ ∑ ∑™ ∑® ⌋⌈∫ð∑ ©⟨ ™∑∫⟩ |ð ® ™◊∫ ⟩ ð◊ ⌈↔⊇◊ ™⌋⌈™∑ ®⟩∫® ⟩∑⟨ ⌊ ∑ ⌊ ∑≈⊕⌉∑® ◊ ◊⌊∑®∑|◊⟩ ⌊ ∫ ⟩⌊ ® ∫|ð⌋⌊⇑ ⌊ ⊇ | ∫ ð⌋⌈| © ⌊∑ ∫ ⟩ ∑ © ⌊ ™ ∪ ®∑⟩∫ ⌋⌈®⟩∑ ð |∑®∑ ⊗ ⊄∑ ◊⌊ | ⌊ ⟩⟩◊⌊ ⌈⟩ ⌊∑ ∑⌊ ®∑ ∑⟩| © ©◊⟩| ⟩ ⟨ © ð ð ®◊∫ ⌊ ⟨⌋∑⟩ ⟨⌋∫ ® © ∑© ∑⟩∫ |∑⟩ ©™∑ | ∑∫↔∉ð∑ ™∑ ∑ ⟩ ∫ |ð ∑⟩ | ð ∫| ⌊ ∫® ⊇◊ ™⌋⌈™∑ ®⟩∫® ⟩∑⟨ ⌊ ∑ ⌊ ∑≈
©⟩∫◊ ®⌊∑ ∑| ∫ð ⌊ ◊™ ⌋⟩⌊ ∫ð∑⟨ ∑∫∑ ∑™ ∑® ⌈|ð◊|∫ | ⊆ ◊ ∫ ⟩ ®⌋ð◊⟨◊∫⌋®◊∫ ⌋⟩⌊ | ⟩® ∑ ∑⌊◊ ∫⟨ð◊⟩⌋®◊∫ ∫∑| ∫ ð⌋∑ð◊ ð ∫∑⌊ ® ™∑⌈⟩∫® ∫ ◊®◊ ∉∑ð®⌋∑®◊ | |⌋∫| ∑ ∫ ⟩® ∑ ⌋ ⌊∑ ∑⟨ ™ ∫®⟩∫ð∑ ∑ ⌋ ð ⟩∫ ⌋ ⟩ |ð ∫ ®⌊∑ ∑ ⟩ ⟨∑ | ⟩∫∑ ∑ ∑⟩| ⌊ | ™ ∑⌈∫ð∑ ð ® || ©™◊®◊ ∑⟩ ◊ ∑| ⌈ ∑∫ ∫ ∫ ∑ ©ð◊⊆◊⟨∑ð ∫∑⟩ ∑⟩∫®◊|ð ™ ⌊ ∫ ◊ ∫ ®⌋⟨ ™∑∫∑| ð◊ ∑ ⌋ ∑ ∑ | ∫ ð⌋∑| ⟩⌊∑™ ∫ ◊ ∫ ⊗ ®∑ð ∫∑⟩ ⟩ ⌊∑® ∫ð ®◊⟩ℜ⌋ ® ™ ∫∑|◊| ◊ ∫® |◊∫ | |ð∑∫ ⌋∑|⌊◊ ⌋™∑⌈⟩∫® ⌈|ð ð◊⟨ ∫∑ ◊™⟩ ⟨ ⌈·∫ ⟨⌋ ®⌋∑ ⟨∑ ™∑ | ð∑ ⌊ ⟩ ®®◊ ∑ ⟩ ◊ ™ ⌊ |ð ⌈∫ ∫™ ∑⟩ ∑®∉ð ® ∫∑ ◊⟨ ∫ ®◊ ∑⌈ ™∑∑ ∑ ∫ ⟩∑⟨ ◊ ◊ ∫⟩ ⟨⟩∫®∑ ®⌊ ⟩∫ ð | ™™∑ð ®◊⌈∫∑ ∫ ™∑ ™ ∫∑ | ð| |◊ ◊ ∑| ⟩∫ ∫| ð ∑ ◊ð◊⟨ ∫◊∑∫
∠◊⟨ ∫◊ ◊™ ∑ ∑ ∑ ⟩ ◊ ®◊ |ð ™∑∫⟩ |∑ð∑ ∫ |∑ð ™| ©™◊®⌋ ∑ ∫ ⌈™∑∫∑ ∫⟩∫◊ð © ⌋ ⌊∑ ® ® ∫ ∑ |™∑⌈⟩∫® ∫∑⌊ ⟩∫ ∑⌉∑ ∑ ◊|ð∑| ∫∑⟩ ℜ ∫ ∫ ∑ ∫ ∑ ⌊∑©| ⟩®◊⌊ ∫ ⟩ ◊ ◊™∫∑ ⟨ ⌊∑∑ ∫ ⟩ ◊ ∑⟨ ™∑∫ ◊ ∑|∫⌋®◊∫ ®◊ ∫ ®⟩∑⟨∑⟩| ⌊∑ ∑© ∑|ð ⌈™∑∫∩◊⟩∫◊® ∫∑⟩∑⟨ |ð ™ ⌊ ◊∫ ∑ ∑™ ∑® ⌋⌈∫ð∑ ©⊆◊⟨∑ð ∫∑⟩ ∫∑ð|∑ ⊕⟩⌊ ⟩∑© ™ ®◊⟩ ∑∫ð◊⟨ ∫⌋™∑ ∑©⟩∑ |ð ∑© — ∫ ®◊ ◊ð∑◊⌊ ⟩∫ ⊆ ®ð∑ ∫ ⟨⌋∑∑ ∑ ∫ ⊆∑ ∑∫◊∫ ⟩ ® ∫ð ⟩∑⟨ | ◊™◊®◊ ⟨∑⟩| ∑ ⌋∑↔⊇◊|?≈↔℘™∑?≈↔⊇ ©™◊?≈∉ð ⟩∫ ∫ð∑ ©⊕ ∑™ ∑® ⌋⌈∪∑⟩⌊ ◊|∫ ® ◊ ®◊ ® ⟩∫∑⌈®⟩ð∑™ ∑ ð◊⟩⟩ ∫◊ ◊ ◊ ∑⟩ ◊∫ ⟩ ® ⌈⟩ð |™◊⌈∫∑⟩∑⟨∑© ™∇∫◊® ∫∑ð∑◊⌊ ⌋∑ ∑⌊ ℜ⌋ ∑ ◊⌈™∑∫∑ ∑ ™◊ ◊⟩™∑ ©◊ ∑⟩∫◊ ∑∫∑ |ð∑ ™∑ ∫ | ⟩ ◊®∫ ◊© ™ ◊ ⟩ ® ∑ ◊® ⟩ ⟩∫ ⟨ð∑⟩∫ ⟩ ∑∫∑ℜ◊ ∑| ™⟩ ◊ ∑| ◊⟨ ∫ ∫⟩ | ∫ ™ ⟩∫ ∑ ∫ ⌈ ∑⌊ ∉ ⌊ ◊⌈∫∑ ™ ® ⌊ ⟩∫® ∑ ∫∫ð∑ ©◊ ⟨ ™ ∫∑ ®∑ð∑ ⌋®◊ ◊ ∑ ∫⟩ ∑ ◊®◊∑ ®⌊ ⟩∫ ð
⊆∑|ð | ⟩|◊⌈∫∑ ™ © ™ ∫ð∑ ð ®| ∫ ®◊ ∈∫ ∑ ◊⌈∫∑⌊ ⟨ ∑⟩◊ ∑ ◊⌊∑ | ∑| ⌊ ∫∑⌊ ∑ ∑ ∑ ∑® | ®∑ð ∫∑ ® ®⟩∑ ∑⟩⌊ ◊⌈ — ∫ ð∑ ⌊ ∫◊∫®◊ ∑⌈ð◊⟨ ∫⌋ ◊™⟩ ⟨ ⌈∈∫|ð ⌈∫∑™®∑ð ⟩|◊ ∫∑ ↔⊗◊ |ð ◊ ∫∑⟨ ™ ®∑ð ∫∑⟨∑≈∪| ©™◊|®◊ |ð ™ ∫⟨ ⌊ ∑™∑ © ⟩|∑ ®⌋⟩ ™ ®⌊∑ ∑ ⟩|ð ⟩ ∫∑⟩∑⟨ ∫ ⌊ | ⟨ ™ —©™∑ ⟨⌋⌊ ð◊ ∑?
∇∫ð∑ ⌊∑ ∑| ⟩|∑ | ⟩∫◊ ®|◊ ð∑◊⌊ ◊ ∑⌊∑⌈ð◊⟨ ∫◊ ◊™⟩ ◊ ∑ ð ð ®◊ ∑ ◊ð◊|∫∑ð◊™ ⌊ ⌋⟩∫◊∫ ⟨ð◊ ℜ⌋™ ⌊ ⌋| ®⟩∫® ®◊∫ ◊ ◊ð∫™® ©◊ ⟩ ® ◊|ð◊®⌊∑ ⟩|∑ ◊◊ ∑ ⟩|⌋∫⌋®◊∫ ∑ ∑™ ∑® ∫ ⟩| ∫|ð∑™⟩∫ ⌉∑⌈ð◊⟨ ∫⌋ ◊™⟩ ⟨ ⌈ ® ⟨⌊◊© ⟩∑⟨∑⊇ð ∑∫ © ∫ ⟨⌋ ◊⌈∫ ⟩® ⌈| ∫ ®⌋ð◊ ∫ ⟩∑⟨ |ð ⟨⌊ ∫ ⟩ | ◊ ∑ ∑ ⌋ ∑⌊ ∑ ⟨ ™ ◊ ∑∫ ⌊ | ∑ ∑™ ∑® ◊ ð◊⟨ ∫◊ ◊™⟩ ⟨ ⌈ ⟩∫ð∑ ⌊∑ ∑|| ⌊ ∑ ®⟩∑ ®⌋ ®⌋ ◊ ⌈⊆ ◊ ∫ ⟩ ◊ ◊⌊ ð ®◊∫ ⟨ð∑∫∑ ⌋⌈ |⌋∫ ⟨⌋∫ © ∫ ®⌋ | ∑ ∑ ∑⟩⌊ ®◊ ð ◊ | ⟨ ™◊∑∫®◊⟩| ∫ ⊆◊ ∫∑⟩ ∫⌊ ◊∫ ®◊ ⌋∑⟩®∑™∑ ∫ ∑ ◊ ∫∑⌊ ⌋ ◊|∫⌋— ∫®⌋™ |ℵ™⌊ ∫ © ∫ð∑⟨ ∑∫⟩ ∫◊∫ ⌊ ∫∑ð◊∫ ð ◊ ∫∑ð∑⟩ ⌉ ®◊⟩∫∑ ∈∫ ∑⟩ ∫∑⟩ ® ◊∫∑⌊ || ©◊ ◊|ð◊®⌊∑ ⌋ ◊∫ ∫ ⟨⌋ ∫◊ ⌉ ⌈ ∑⌊ ®∑|®⟩∫◊⌊ ◊| ∫ ⟩|∑ ◊
⊆◊∩◊|◊™∑ © ∑⌊ ™ ◊ ◊⌊ ∫⟩ ∑∫⟩® ⟩|∑ ®⟩∫ © ∑ ∫◊|◊|| ◊| ⌊ ⟩ ⟩| ©◊ | ⟩◊ ⟩ ®∑ð ∑ ⟩∫® ®◊ ⊆∑⟩∫ ∫ ∑™ ∑ ®◊∫ | ™ ⟨ ⌊ ∫∑ð◊∫ ð ◊ ∑∫ ∑|ð ⟩∫ ®™ ® ∫ ®◊⟩ ™◊∫ ⌉ ⌋⌈∫ ⌊ ||ð∑◊⌊ ◊ ∑| ⌈⟩ ∑⌊ ⌈ ™∑ | ∫ ð◊ ⟨ |®◊⌊ |∑ð∑®∑ð ∑∫®◊ · ∫◊ ®⌋| ⟩∫ ⟨ ™∑∫∑ ◊ ™ ∫ ⟩ ®◊∫ ⟩ ∑ð∑ ™◊ ⟨⌊◊© | ⌊ ∑ ©⌊ ⟨ ∑®⌋| ©ð ∫∑⟩ ® ∑∑∫∑ ⟩ ⌊ ∑∑|ð ® ∫⟩ ®◊ ∑ ∑⌊◊ ∑®⌋ð®◊∫ ⟩ ®|∑ð∑™⊆◊⟩∫ | ∫ ∑ ∫| ©™◊ ™ ◊ ∫◊| | ©∫ ⌊| ∑∫®◊⟩ ◊| ∫ ⟩|∑ ◊ℜ⟩∑ ∫ ⟩∫◊ ® ∫⟩ ® ⌋ ⟨⌊◊© ™◊ð ⟩® ∑© ð ™◊® ∑ | ∫ ð ∑ ∑ ð |ð |◊∑∫®®◊⟩⟩| ⌋ ⟩∫ð◊ ⊆ ◊ ∫ ⟨⌋◊|∫ ® ð ®◊∫ ® ∑ ∑| ∫ ð ∑®◊⟩ ⟩∫ð◊ ®◊∑∫ ◊|ð∑|⌊ ⌈∫∑∑© ⟩| ⌉ ∑ ∑™ ∑® © ⟩◊ ® ∑ ⇓ ∑ ∑| ◊|◊| ⌈| ⟩ ∑∫ | ©∑ ™ | ◊ ⟩ ◊⌊◊ð∑◊⌊ ⟩∫ | ∫ |⟨⌊◊© | ⌊ ⊆ ◊ ∫ | ©◊™⌊ | © ∫ ⟩∫◊ ∑∫∫∑ ⟩◊ ⌋ ∫ ⌊ | |™∑⌈⟩∫® | ∫ ð © ∑ ∑ ®◊∫◊⌊ ⊄ ⟨ ◊⟩∫◊ ∑∫∫∑ |∑ð®⌋ ⟩∑ ∑ ∑ ™◊ ⟨⌊◊© | ⌊ | ∫ ð ∑⟩ ®ð∑ ∑ ∑ |ð ð◊⟩∫∑∫ ™◊⟩∫®⟩ ™⌋ℜ⌊ ⟨ ⟩⌊ ◊∑ ∑ ⟩∫◊ ◊®⌊ ®◊⌈∫∑⟩ ∉ ∫∑ ∑ |ð◊®⌊ ∑ © ⟩|∑ ◊ ∑⟨⌋®◊∑∫⊂ ð ∫∑ð∑⟩∑ ∫ ⌊ | ⟩|∑ ◊ ∑®◊ ↔∑⟩⌊ ⟨⌋≈∫ ∑⟩∫ |ð◊®™◊ ⟨∑ ™∑⌈⟩∫® ℜ◊ ∑↔∑⟩⌊ ⟨⌋≈™ ⌊ |ð∑ ⟨ð◊ ®◊∫ ⟩ ®↔∑⟩⌊ ⟩∑© ™ ◊ ð◊⟨ ∫◊∫ ◊™⟩ ⟨ ⌈® ∑⟩∫ ⟩◊ ⟨ ∑®◊ ⟩◊ |ð ⌉∑ ⟩ © |ð◊®⌊ ∫ ⟩ ◊ ∑ ◊ ◊ ∫® ∫ | ™| ∫ð ⌊ ®⟩ ⟩® ™ ⟨ ∫ ⟩ ⟩|∑ ◊≈ℜð∑ ∑|ð ⟩∫ ∫®◊ ∑ð∑ ∫∑⌊ ⟩∫ ℜ ®⌋™ ◊∑∫∑ ∫ ®◊ ∑| ™ ∫ ⌊ ⟨ |ð∑™|ð ∫ ◊∫∑ ⟨ ⌊∑∑ ∑ ∫ ⟩∑⟨ ?® ©™◊|ð∑™⟩∫◊® ∫∑⟩∑⟨ ∑ð∑ ⌊∑∫ ⟨ ™∑∫|ð ™ ⌊ ◊∫ ⟩ ◊®⌋—⟩© ð∑ ™ ◊∫ | ∫∑ð ⌋ © ™◊ | ©™◊®⟩∑∑⌉∑ ⟨⌋⌊ ∑ ∫ ∉ ∫ ◊ ∫∑⟩∑© ™ ⊆◊ ∫∑⟩∫∑ ∫ ∑∑∫∑ ◊| ∫ | ∑⌊ ®⌋ ◊⌉ |◊∑∫∑ ∑™ ⟩∫◊ ⌉ ∑ ®∑ ® ∑| ð∑ ∑ |ð ⟨⌊∑ ⌋
ℑ ™ ∫∑ ®∑ð∑ ⌋®⟩∑⟨∑∈∫|◊ ∫∑⟩ ∫⟩⌊ ®◊↔ ∑® ≈ℑ ™ ∫∑ ®∑ð∑ ⌋® ∑ ⟩∫ ⟩⌊ © ™∑⌈ ⌊ ∫ ®◊ð ®| ∫ ð⌋∑®⌋|ð∑™⌊◊©◊∑∫∑⊗ ◊⌈∫∑®⟩∑®ð∑ ⟩® ™ ⟩∫ ∑ ∉∑ð∑ ⟩⌊ ∫∑ ◊⌊ ⟩∫|∑⟨ ◊© | ◊⌉∑|∑ð∑ ∫⌋®◊⌈∫∑⟩® ◊| ⟩ ⊆∑ ◊⌊ ⌈∫∑⟩® ⟩|∑ ®⟩® ∑⌈ ◊ ⟩∫ ℜ⌋⟩™∑⌊◊⌊ ® © ð◊ ™ ⟨ ⌊ ∑ ∑ ™ ◊∑∫∑|ð ⟩∫ ™ ⟨ð ⌈| ⌊ ® ∑ ∫ © ◊⟨⌋⌊ ◊| ™⟩ ∑∫ ∑ ™◊
∠◊ ® ®◊⌈∫∑®⟩∑⟨∑|ð ®⌋ | ®∑™ ⌉ ∑| ⟩|∑ ⊆◊ ∫∑⟩|ð ®⌋ | |◊ ™ ∑ ∫ð ð◊⟨ ∫◊∫ ◊™ ð ð ®◊ ∑ | ∫ ® ⌋ ⌋⟩⌊∑⌈∉ð ®⌋ | ⟩ ™◊ ∫⟩ ® ⌊∑⌈ℜ ⌊ ∫ð∑ ð ∑∫⟩ ↔∇™∑⌊◊⌈ ∫ ⟩∑⌈ ◊⟩≈∪™∑⌊◊⌈∫∑¬◊© ◊ ◊© ®⌋⟨ ™∑∫∑ ™∫ |®∑ð ∑∪ ∑ ⟨⌊ ∑®⌋| ∑⌈| ™⟨∑ð∑∫∑⟩ ∫∑ ⟨ ⌊ ∑®⟩∫ð∑∫ ∫∑ ∑⌊◊ ⌉ | ®◊
©⟩|∑ |ð ∫ © ®◊∑∫∑⌉∑⟨ ⌊ ⌈ ⟩|∑ ⊆ ∑ ◊⟨⌋®◊⌈∫∑ ∫ ®⟩∑™◊ð ®◊ ∑®◊ ◊⌊ ⟨ ð ® ∑ ◊∫∑ð ◊⌊ ⌊ ™ ® ™ ⌊ ⟨⌋∫ ⟩| ⌊ ®◊ ⌊ ®⌋ ∫ | ∫∑ð ∑∫∑
⊆∑⟨ ⌈∫∑⟩ ⟨◊∫ ⟩ ⊆∑∫ð◊∫ ∫∑®ð∑ ◊ð◊ ™ ⌋®◊ ∑ ⌊ ⌋∑⟩∫ð◊™◊ ⊗∑⌊ ∫∑ð◊™ ⟩∫ ⟨ ©◊∫⟩∫® ⟩™ð © ⌊ ™ | ©◊ ™ð © ®⌋| ©◊∑∫∑⟩∑⟨∑⊗ ◊ ™ð © ®⌋™ ◊∑∫∑ ⟩∑⟨∑ |ð ®⌊∑|◊∑∫∑®⟩® ∫ ⌊ | ∫∑ ⌊ ™∑⌈ ∑⌈ ◊ð◊|∫∑ð©◊ð ð ∑∫⟩®◊ ⊕⟩⌊ ®⌋ ∫ ∫∑ ∫ ⟨⌋®®◊ ∑⌈ | ® ⌊ ⟩ ™ ⟨ð⌋∑ ∫| ∑⌉∑™ð⌋∑⟩ ⟩∫ ∫∑⌊ ⌋∑⌊ ™ ⟩∫◊ ∫∑∫◊| ⟩◊
∉ð ⟩∫ |◊ ||ð◊|∫ ∑⟩| ®⌊◊™∑ |ð∑™⌊◊©◊∑ ⌈|ð ©ð◊ ⌈®⟩∑®ð∑ | ∫∑⟩⌊ ®◊⊂◊ð|◊ℵ®ð∑⌊ ↔·∑⌊ ®∑ ∑⟩|◊ — ∫ ∫ ∫ ∑⌊ ®∑| ∑⌈™ ◊∑∫≈

∈ℑ∧∪⊕∩ℵ⊂⊕·ℵ⊆∪⇓⊇∉∠ℵ⊇®∪·⊕∇⊇∪⊂∩ℵ⊆⇓®∪⇓⊂
∉ð∑ ™∑ ∑ ®⌋|∑ð∑⌈™∑∫∑ ∑| ⟩ð∑™⟩∫®∑ ||ð◊|∫ ∑⟩| ◊ ∫ ⟩|◊ ◊∫ ∑⟩| ⌊ | ⟩⌊ ® ∫ |◊| ∑∫∑ | ◊⌊ ∑ ⌋® ⟩ ® |ð ©ð◊ ⌋ ⟩™∑⌊◊∫ ∑⟨ ⌊ ⌈ ⟨ ð|◊ ™ ⌈

⊂∑∫ ™∏ ∑∇ ⌊ ®⌋
ℜ ⟩ ® |ð ©ð◊ ⌋| ⌊ ∑ ∑∫ ™∏ ∑∇ ⌊ ®⌋⇑∫ ∫ ∑∫ ™| ©◊∑∫ ∑|∫ ® ⟩| ⌊ ®◊∫ | ∫◊|∫⟩™ð © ⌈⟩∫ ð ⌈ | ⌊ ◊∫ ð∑◊⌊ | ⌉ ⊆∑® ∫ |ð∑™∑⌊ ∫ ®⌋® ⌊ ⌋ ◊ ⌋®◊∫ ∫ ⟩∫ ð ℑ © ℜ⌋⟩ ð◊ ∇ ™◊∫∑⌊∑ —⟩ ∫ ∑® ∫ ∇ ∫ ®∫ ∫ ∫ð∑ ©| ∑∫ ™ ∇ ⌊ ®⌋™◊∑∫® ⟩∫ ◊|∫ ® ð ®◊∫ ð◊⟨ ∫ |ð◊® © | ⌊ ◊ð © ⌊ ® © ©◊ ∫∑ ⟩◊ ⌋ ® ⟩⟩∫◊ ® ∫ ⟩® ⟩™ð © ⌈⟩∫ ð ⌈™⌊ | ⌊ ∑ ⌊ ⟨ ⌈ð∑◊⌊ ⌈| ⌉ ↔∉ð ∑ ™∑⟩ |ð◊® ∑| ⌊ ◊ð ∑?≈—⟩|ð ⟩ ∫∑®⌋⊗∑⌊ ®∫ ∫ ∑ |ð◊® ∑| ⌊ ◊ð ∑ ©◊ ®⌊ ∑∫⟩ ◊ |ð ® ™ | ® ð⟩ ™◊ ® ð©™∑ ⌋ ð ð ®◊⌊ ⟩ ð⌊∑ ◊⌉ ⌈ ◊|ð∑™∑⌊◊ ∑⟩| © ⟩ ⌉∑⟩∫® ®◊ ®| ∫ ð © ⟩| ™⟩∫® ∑∫⌊∑® ∑⌊ © ∑⟩| ∑| ⌊ ◊ð ∑ ©◊◊ð ⌊ |ð◊® © | ⌊ ◊ð ∫ ™ ∫ ◊ ◊™ ⌈|⌊◊ ℵ|∫ ® ð ®◊®|ð◊® ∑| ⌊ ◊ð ∑®⌋◊®∫ ◊∫ ∑⟩| ⟩® ⌋®◊∑∫∑⟩ ⟩™ð © ⌈⟩∫ ð ⌈ ∫◊⟩® ◊ ◊∑∫ð◊⟨ ∫◊∫ ◊®◊⟩ ® ⟨⌊◊© ®◊ ℜ⌋⟩ ∑∫∑™ ⟨ ∫ ⟩ ⌊ ⟨ ⌈ ∑⌊ | ∫ ð | ⟩∫◊® ∫∑|∑ð∑™⟩ ⟨ ⌈ð∑◊⌊ ®◊∫ ⌊ ⟨ ∑ ∑⌊◊ ∑ ® |⌊ ∫ ∫ ® ⟩◊ ∑®∑ð ∫ ∑ ∫ ∉ ⌉ ◊ ∑∫|ð ™ ∫ ®®◊ ∫ ®⟩ ™ ⟩◊ ⌋ ∑ ™◊ ⌋ ⟩| ⟩ ⟨ ⊕⟩⌊ ∫ ∫ ∫ ®⌋™ ⟩ | ð ⟩|◊⌊ ®◊ |ð ⟩∫ ◊ ∫ ⟩ ∑ ∑™ ∑® ⌋ ∫ð∑ © | |ð∑™⌊◊©◊∑ ⌈ ∑|ð ©ð◊ ∑
∩◊⟩ ∑∫ ∑© |ð ⟩ ™ ∫◊|∫ ® ◊ |ð◊® © | ⌊ ◊ð ?↔⊂ ©⟩ð∑™ ∑© ∑⌊ ®∑|◊ | ð ∑∫® ◊⟩∫ ∫ ™ ◊|◊ ∑ ∫™ |⌊ ®®⟩∑| ™
|⌊ ®®⟨ ™ð ⟩ ⟩∫ ∫© ™ © |⌊ ®® ⟩ ∑ |ð◊⌈ ∑ð∑™| ◊|ð ∑ ∫ ⌋ ◊⟩∫ ∫◊ ∫ ⌊ | |ð ◊⟩⌋|◊ |ð ⟨ ™∑ ∈™ ◊| ∑ |ð ∑ ∫ ⌋∑ ◊⟩∫ ∫⌋ ⟨∑⟩|∑ ®◊ ∫⟩ ◊∫∑⌊ ∑ ⟩| ⌊ ®◊ ∑|ð◊® © | ⌊ ◊ð ©◊ ◊ ∑⌈™ ® ⌈⟩® ∪™∑◊⌊ ◊ ™⌊ ⌋ ⌊∑ ◊⟩∫ ∫◊ ◊ ™ ∫⟩ ® ∑ ∫ð∑ ◊⟩∫ ∫ © ⟩|∑|∫ð◊ ⟩ ⟩∫◊®⌊ ∑∫ |⌊ ®®⟩∑| ™ ∪ ∑ ∫ ®∑⌊ ∑ ⌋∑ ∑ ∫◊⌊ ◊ ð ® ∑ ≈ℜ⟩| ∫∑ ⌋© ® ð ⌊ ∫ ∫ ®ð∑ |ð ◊⟩⌋|◊ |ð ⟨ ™∑ — ∫ ®ð∑ ð◊⟨ ∫⌋ ◊ ∑© | ™⟩ ◊ | ©™◊®⌋ ∑∫∑| ð ∫ ∑ ⌊ ⟨ |ð ⟨⌊∑ ◊⟩ ®ð∑ ∑ ∑ ⟨ ™∑∫ð∑ ∑ ◊⇑∫ ∑⟩∫ ◊⌊ ◊ ð ®∑ ⊆ ™⌊ ∫ © ∫ ⟨⌋®⌋⌈∫ ◊◊⌊ ◊ ð ®∑ ® ®⟩∑ ∑ ⟨ ◊∫∑⌊ ™ ™◊∫ ⟩ | ©™◊®⌋⌊ ∑∫∑⟩|◊∫ ∇| ⌉ |ð∑™⌊◊©◊∑ ⌈|ð ©ð◊ ⌋®⌋ ◊ ∫∑⟩ ⟩⌊∑©| ⟩∫ ®⌋ ™ ∫ ◊◊⌊ ◊ ð ®∑ ®⌊ ⟨ ∑®ð∑ ™ ð∑ ◊ ⌊ ⟨⌋∑ ◊⟩ ⌉ ⌋∑|ð ⟨⌊∑ ⌋⊆ ™⌊ ◊ ◊⌊◊®◊ ⟨ ™∑∫ ◊ ∫ ⟩ ð◊⟩⟩⌊◊⟨⌊ ∫ ⟩ ∫◊||◊| ∑ |ð ð◊⟩⟩⌊◊⟨⌊∑ ◊⟩∫ ∫◊ © ®⌋ ® ⌊ ◊ ∑™⌊ ∑∫⟩ ∫™ | ⌊∑⟨◊ ⌈®⟩∑| ™ ∪ ∑ ◊ ∫ ⌈ ◊⟩∫ ∫∑ © ®⌋ ® ⌊ |ð◊® ∑ ⌊∑® ∑| ⌊ ◊ð ©◊ ◊ ◊ ∫ð◊⟨ ∫◊∫ ⟩ ® ∑⟩∫
↔⊇ ©™◊ ⟨∑| ⌊ ® ⌋ ©◊◊|∫ ® ⌋ð◊ |∑ð∑|ð ©ð◊ ð ®◊∫ ⟩ ◊∫∑⌊ ⌋ ∑⌊∑ ◊|ð◊®⌊∑ ⌋ ⟨ð◊ ⟩ ®⟩∑ |◊|| | ∫∑ð⊗⌊ |ð ©ð◊ ð ®◊ ⟩® ∑© | | ∫∑ð◊ |ð◊®⌊∑ ð◊ ®⌋| ⌊ ∑∫∑⟩ ⟩⌊ ®◊ ⌊ ⌋⟩⌊∑ ⌋ ⟨ð◊ ◊ ∇ ™◊ ∑ ⌋⟩⌊∑ ⌋ ⟨ð◊ ®—|ð | ⌉ ® ⟨ð◊ ∑ ® ◊⌊ ◊ — ∫ ð◊⟨ ∫◊|ð◊® © | ⌊ ◊ð ∇® ⌋®◊∑∫⟩ ⟩∫ ⌈⟩∫ ð ⌈∩◊∫∑ ®◊ ∑ ∫◊⌊ ⌋⌈| | ∫∑ð® ™ ∫®| ∫◊|∫⟩∫◊| ◊ ⌋®◊∑ ⌋ ℑ ⌊ | | ∫∑ð ◊®◊ ◊| ∫ð∑⟨ ⟩∫ ©⟩⌊⌋ ◊ ◊® ⟩|ð ∫◊ ®⌋⟩ ⇓∪⌊ ®⌋⟩ ∫∑⌊⌊∑|∫ ⌊ ∪⟩∫ | ⌊ ℑ © ®◊ ◊| ∫ð∑⟨ ⟩∫ ™ ®⌊∑∫® ð ∑∫⟩ ≈®◊| ∫ ð◊⟨ ∫◊⌊ ®⟩∑©™◊|ð ⟩∫ ®|◊| ⌈∫ |∑ð ™⟩® ∑© ð◊ ® ∫ ∑⌊ ®∑| ◊⟨⌋⌊ ∫ |ð ⟩∫ ð ⌊ ⟩∫◊ ®⌊∑ | ∫◊|∫◊⟩™ð © ⌈⟩∫ ð ⌈⟩∑© ™ ∑⟩| ⌉ ∑∫ ™◊∇ ⌊ ®⌋⌊ ⟨ ⌈ ◊⟩⟩| ⟩ ⟨∑ ® ⟨ ® ∫ ∫ ⟩®
ℜ⌋⌈™ ◊◊⌊ ◊ ð ®∑ ®⌋| |◊™∑∫∑®™ð © ⌈ ð ð©™∑ ∑∫ ®ð∑ ∑ ⌋ |ð ⟩∫ð◊ ⟩∫®∑ ⌋ |◊| ™ð © ⟨◊ð ∑ð ®∪ ∑ ◊◊⌊ ◊ ð ® ∑®ð◊⟨ ∫ ®|⌊ ◊ ∫⟩ ∫ |⟩∫ð◊⟩∑ ⟩ ð ∑® ⟩|ð ∫ ∑ℜ⌋|∑ð∑ ™ ∫∑ ® ∑ ∑© ð ® ⟩ ◊ ® ® ∫ð∑ ⌈⇑∫ ∫® ∫ð∑ ⌈ ð ®∑ ∑⟩∫ ∫ ⟩◊ ∑| ™⟩ ◊ ∑ ð ⌊ | ∫ ð © ® ◊ ∑⌈ ⌋ ∑© ® ð ⌊ ◊⟩∫ð◊ ◊ ∫ ⌈| ©
∉ð ∑ ∑∫ ™∇ ⌊ ®⌋®⌋ ◊ ∫∑⟩ | ∫ð ⌊ ð ®◊∫ ⟩® ⌈ð◊ ◊⟩∫◊® ∫∑®|⌊ ◊∫ ⟩ ∫® ð ∑⟩| ∑ð© ⟩® ∑© ↔⇓≈∪®⟩∑ ∫ ◊⟩ ∑∫|ð ⟩∫ © ◊|∑ð®⌋⌈® ©⌊ ™ð◊⟩⟩⌊◊⟨⌊∑ ∫∑⌊◊ ð◊ ◊| ∫ ð ∑ ®| ∑ ⟩⌊ ◊∑ ∑⟩∫ ∫ ∑™ ∑ ®◊∫ ∫◊||◊| ∑ ⟨∑⟩|∑ ∫®◊ ⟩® ⟩™ð © ⌈⟩∫ ð ⌈∠∑⌊◊|⟩◊ ∫◊| ∑ ∑ ⟨ ™ ◊ ∑⌊ ®∑| |◊|® ™
∪®⟩∑ ∑ ∑⟩ ∫ð ◊⟨ ⌊ ⟩ ∑⟩∫ ∑∫ ™∇ ⌊ ®⌋ ∫⌊ ◊∑∫⟩ ∫∫ð◊™ ⌈|◊⟩⟩ ® ⌈ ∑™ ∫◊ |ð◊|∫ | ∑ ⌈⌈ ©◊ ⊂∑∫ ™∇ ⌊ ®⌋◊|∫ ®∑ ∫◊◊|∫ ® ◊ ∑™ ∫◊ ®∑™∑∫ ∑| ∫⟩ ∫⟩∫® ⌋ ⌊∑ ◊|| ⌊ ∫∑ ⌋ ⌊∑ ∉ð ∑ ∑∫ ™∇ ⌊ ®⌋®⌋ ◊⟩∫◊®⌊ ∑∫∑⟩® ⌈ð◊ ð◊⟨ ∫◊∫ ⟨ ⌊∑∑|ð ™ |∫ ® | ⌊ ◊∑∫∑® ⟩∫ |ð◊®⌊ ∫
⊗∑⌈⟩∫® | |ð∑™⌊◊©◊∑ ⌈ ∑∫ ™ |∑®⌋ð◊⟩⟩⌊◊⟨ ®∫∑⌊ ð◊ ◊ ∑∫∑ ⌋⟩⌊∑ ® ⟩|ð ® ™ ∫ ∑⌊◊∑ ⌋∑|∑ð∑ ∑ ⌋®⟩® ∑⌈ ∪⟩| ⌊ ∑ ∑ ∑⌊◊ ⌈|ð ™◊⟩∫®◊ ®∑ð∑ ⟩∫ | ⌉ð ∫|™◊⌊ ∑⌈ ⌊ ∑
∇◊ ⌋ ®◊ ⌋ ⟩ ⟩∫◊®⌊ ⌉ ⟩|∑ ◊ ™∑⟩ ⟩∫◊ ® ∫⟩ ™◊ ∑ ®∑ð◊∈∫⟩ ∫⟩∫® ∑®∑ð⌋— ∫ ð∑ ⌊ ∫◊∫◊|∫ ® ⌈ð◊⟨ ∫⌋⌊∑® © | ⌊ ◊ð | ∫ ð ∑© ® ð ∫®◊ ∫ ®◊ ◊ ◊ ⌈ ∑© ∑®⌋⌈™∑∫® ⌊ | | ⟩ð∑™⟩∫® ∑ ∑™ ∑® ⌋ ∫ð∑ ð ® |◊|∫ ® ð |ð◊® ∑| ⌊ ◊ð ∑®⌋| ™ ∑∫∑⟩ ◊™⌊ © ∑⟩| ©ð◊ ∑ ⌊∑® © | ⌊ ◊ð ™ ⟩∫ © ∑∫∑ ∑⌊ ◊⌊◊™ ∫∑⟩® ⟩™ð © ⌈⟩∫ ð ⌈™⌊ | ⌊ ∑ ∑ ⟨ ™ ⌈| ⌉ ⊆∑∫ð◊∫ ∫∑™ð◊© ∑ ∑®ð∑ ®◊ ∑⌈ ™® ©◊ ⟩ ® | ™◊ð∑◊⌊ ⌈∫∑®⟩∑ ◊⌊ ∑ ⌋∑®®◊⟩⟩| ⟩ ⟨ ⟩∫ ⟩| ⌉ |ð∑™⌊ ∑ ⌈ ∑|ð ©ð◊ ⌋
®ð∑ ©| ⟩ ⟩∫∑ ∑⊆
⊂∑∫ ™∇ ⌊ ®⌋®|ð ©ð◊ ∑™ | ⌊ ∑∫ ™ ∑™ ⟩∫®∑ ∑ |ð◊ ∑ ∑ ⟩ ⟩∫∑ ⌋⊆ ©|ð◊ ∑ ∑™⌊ ⟩| ⌋ ® ∫◊⟩ |ð ® ™◊∑∫⟩ ð ⌊◊ ⟩◊ ® ∑ ∇| ⌉ ∫ © |ð◊ ∑ ®⌋| |ð◊® ∫∑⟩® ∑ ™ ð ® ∑↔ ⟩∫◊ ® ∫∑| ⟩⌊ ∫ ⌉∑⌊ ∑ð◊® ®∑⟩ ∑ ⌊ ∫∑ ð| ⌊ |ð ® ⟩ ð◊ ∫∑ | ∑ð ∑ ∫ ®™ ⟩∫ © ∑∫∑ ⌊ © ∑⟩| ⌈ð∑© ⌊ ð ®| ∑⟩| © ⟩ ⟩∫ ◊⌊◊™ ∫∑| ð™ ◊ ð◊⟨ ∫⌋ ©◊® ∑ ∑⌈ ® ∫ð∑ ∑⌈ ∑ð® ⌋ ⟩ ⟩∫∑ ⊇ð ∑∫ © ⟨⌊◊© ™◊ð ∫ |ð◊ ∑ ⟩ ™◊∑∫⟩ ™ ® ◊ ⟩ ⌊◊ ð©◊ ◊ ∫⌊◊ ®◊∑∫⟩ ð◊⟨ ∫◊ ∑ð® ® ⌋ |ð ®∑ ⟩ ⌋ ⟩ ⟩ ™ ®® ®⟩∑ ð©◊ ∑≈⇑∫ |ð◊ ∑ ∑™ | ⌊ ∑ ∑| ⌊ ∫∑⌊ ⌋ ⟩∫◊ ®|◊ ∑ ⟨⌋⟩∫ð ®⌋®∑™∑∫®◊⟩ ◊™ ð © ⟩|∑ ◊∇◊ ⊇⊆ | ⟩◊⌊↔©™◊ ⌊ | ð◊ ∑ |ð ™ ∫ ∑⟩ð◊ ·∑⌊ ®∑|⟩ ™◊ ∫ © ∑ ™ ◊⌊ ∫ ™∑⌊◊⌊®|ð ⌊ ∑ ™ ◊∑∫® ∫ ®∑ð ∫ |◊|™∑⌈⟩∫® ∑∫⟩∑⌈ ◊⟩—®⟩∑ ∫ ∫ð◊ ∫⟩ ◊∑© ⟨ ™ ⌉∑ ⊗ð © ⟩⌊ ®◊ |ð ⌊⌋∑ ⌋⟩⌊ ®∑ð◊ ∫®∑ð™ ∫®◊⟩®∫ ∫ ⟨ ™∑∫⟩®◊ ®⟨ ™ ⌉∑ ⊇◊|® ™◊ ∑ ∑∫⟩® ð ®⟩ ∫®∑∫⟩∫® ⟩⟩ ⟩ ™ ∫◊| ⌊∑| ⌊⌋®◊ |⌊∑∫ || ∑ ∫⟩® ∑| ⌊ ∑ ∑⟩ð◊ | ⌊ ⟩∫ ⟩ ©⌊◊⟩ ®◊ ∑⌈®∑ð∑℘™∑®∑ð◊∫◊ |◊||ð◊® ⌊ ⟩∫ ◊≈
∈⟨|∑™ ∫∑™®◊ ⌉ ⌋ ∑∫ ™◊Ξ∇ ⌊ ®⌋ ⊇⊆ |ð ™ |∫ ® ⟩∫ ®◊ ◊ ∫ ⌈® ð◊⟩∫∑∫ © |ð◊∫
⊂∑∫ ™ℑ ™∑ ◊
·◊ð⌊ ℑ ™∑ |⟩ ∫∑ð◊|∑®∫ ◊ ⌋⌈™ ð∑|∫ ð⊆ ® ⌈¬| ⌊⌋∪⟩ ∑⌊∑ |ð ∑⟩⟩ ð ð◊ ⟩| © ⟩∫ ∫ ∫◊ ∑ ∠ ⟩⟩ ∑⌉∑® ◊ ◊⌊∑ΞΞ®∑|◊⟩ ð ⌊ ð ®◊⌊⟩® ∫∑ ð ⟩⌊∑™ ⌉ ⟨ð◊ ↔·∫ ⟨⌋⌊∑© ∑® ™∑⌈⟩∫® ®◊∫ ◊| ™⟩ ◊ ∑ ∑ ⟨ ™ ⟩| ∑ ∫ð ð ®◊∫ ⌋⟩⌊ ®⌊ ⌉ ⟩ ⟨|∑|∫ ® ∑ ⟩ |ð◊∫ ∫ ∑∑™ | ð ∫| ⌈ ð◊ ⌋| ∫ ð◊ ∑∫⟨⌋∫ ⌊∑©| ◊|∑ ◊∫⌊∑ ◊®|◊ ∫ | ®∫ ð ∫ ∑∑⟩ ®◊ ⟩ ®◊|◊|| ⌊⌋⟨∑⌊ |∑⟩ ≈ℑ ™∑ |ð∑™⌊◊©◊⌊® ™∑⌈⟩∫® ®◊∫ ◊| ™⟩ ◊ ∑®| ⌊ ⟩ ⟩ ⟩∫ ∫ ∑⟩∫ ® ⟩| ⌊ ®◊∫ ⟩ ®ð∑ ∑ ∑ |∑ð∑™ ◊⟩⌋|◊ ∑ |ð ⟨ ™∑ ∑ | ©™◊®⟩∑ ⌋⟩⌊ ∫∑⌊ ⌋∑|ð ∑⟩⟩⌋⟩®∑™∑ ⌋| | ∫ ®◊ ™∑ ⟨ ™∑∫ ◊ ◊∫ ⟩ ◊|◊ ®◊∫ ⟩ ⟩| ð ∫| ð ⌊⟩◊ ® ∑ | ∫ ð⌋∑ð∑◊⌊ ⟩ © ∫ ∑ ∫ ®◊ ®⌊ ⟩∫ ð


⊆◊ |◊⟩◊ ◊
∇ ∑™ ®| ð ∫| ð ⌊ ð ®| ↔ℑ ©◊∫⟩∫® ©⟩|∑ ∩™ ð ® ∑≈⟩⌈ © ®⟩| |ð◊ ∑ ∑ ⊆◊ |◊⟩◊ ◊| ∫ ð ∑™⌊ ∫⟩ ∫®⌋ © |ð◊∫ ⟩ ⌊ ∫∑™∑⌈⟩∫® ∑ ð ⌊ ð ®| | ∫ ð◊ ⟩◊ ◊| ⟩∑⟨∑ ⌉ ® ™∑⌈⟩∫® ∑∫ ◊ ◊ ∑⟩ ◊ ∑
⊇◊| ∫ ð◊⟨ ∫◊∑∫?©|ð◊ ∑ ∑⊆◊ |◊⟩◊ ◊ ◊|ð◊®⌊∑ ◊ |ð∑|⌊∑ ∑ ⌋ ® ∫◊ℜ⌋| ⌊ ∑© |◊ ™⌋⌈ð◊ ◊ ∑ ◊⌊◊∫∑|⌊ ® ⟨⌊◊⟩∫ ⟩ ⌊ ∑ © ⟩|⌊∑∫∑ ∇ ⌊ ∑ ∑⟩|⌊∑∫∑ ∑ ◊ ⌋®◊ ∫⟨ð ⌋ ð◊ ∇ ∫◊∑∫⟩ ∫ ∫ ∑⟩∫ ®⌊ ∑∫⟩ ↔|◊ ◊⌊ ™⌊ ®⟩∑ ∑ ∫◊⌊ ⌋ ™∑⌈⟩∫® ⌈⟨∑⟩⟩ ◊∫∑⌊ | ™™∑ð ®◊ ⌉ ∑ ⌋∑ | ∫∑⌊◊≈ℜ⌋| ⌊ ⊆◊ |◊⟩◊ ⟩| ⌊ ð ⌊ ⟩◊ ® ∑ ◊|ð◊®⌊∑ ◊ ⟩|∑ ®⌋™ ⟨ ∑∫∑⟩ ®∑⌊ | ⌊∑| ⌋ ð∑ ⌊ ∫◊∫ ®◊ ◊ ™ |ð∑| ∫∑ ⌋ ⌋ ® ∫◊
®∑ |◊ð◊⟨ ∫⌋⟩ ð ⌊◊ ⟩◊ ® ∑
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