{"id":19881,"date":"2018-07-16T14:33:26","date_gmt":"2018-07-16T10:33:26","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=19881"},"modified":"2018-07-16T14:37:25","modified_gmt":"2018-07-16T10:37:25","slug":"david-hilbert-v%c9%99-onun-23-problemi-iii-hiss%c9%99","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2018\/07\/16\/david-hilbert-v%c9%99-onun-23-problemi-iii-hiss%c9%99\/","title":{"rendered":"DAV\u0130D H\u0130LBERT\u00a0 v\u0259 onun 23 problemi (III hiss\u0259)"},"content":{"rendered":"

\"\"<\/a><\/p>\n

David Hilbetrin 1-ci problemi<\/strong>: Kontinuum hipoteza<\/em> \u2013 Bu problem 1877-ci ild\u0259 \u00e7oxluqlar n\u0259z\u0259riyy\u0259sinin banisi Georq Kontor t\u0259r\u0259find\u0259n ir\u0259li s\u00fcr\u00fclm\u00fc\u015fd\u00fcr. Problemi v\u0259 onun h\u0259llini ayd\u0131nla\u015fd\u0131rmaq \u00fc\u00e7\u00fcn b\u0259zi anlay\u0131\u015flara m\u00fcraci\u0259t ed\u0259k.<\/p>\n

Ekvivalentlik (y\u0259ni qar\u015f\u0131l\u0131ql\u0131 \u2013 birqiym\u0259tli uy\u011funluq) d\u0259qiqliyi il\u0259 yaln\u0131z iki c\u00fcr sonsuz \u0259d\u0259di \u00e7oxluq var: Hesabi \u00e7oxluq – N natural \u0259d\u0259dl\u0259r \u00e7oxlu\u011fu il\u0259 eynig\u00fccl\u00fc (ekvivalent) \u00e7oxluq v\u0259 kontiniuum \u00e7oxluq – R h\u0259qiqi \u0259d\u0259dl\u0259r \u00e7oxlu\u011fu il\u0259 eynig\u00fccl\u00fc olan \u00e7oxluq. Kontiniuum g\u00fccl\u00fc \u00e7oxlu\u011fun ist\u0259nil\u0259n alt \u00e7oxlu\u011fu ya hesabi, ya da kontiniuum g\u00fccl\u00fc alt \u00e7oxluqdur. Dem\u0259li, ekvivalentlik bax\u0131m\u0131ndan hesabi \u00e7oxlu\u011fun (N) g\u00fccl\u00fc kontiniuum (R)) \u00e7oxlu\u011fun g\u00fcc\u00fcnd\u0259n azd\u0131r. (N\u2282R) Problem bel\u0259 qoyulur:
\nKontiniuum hipoteza: Hesabi v\u0259 kontiniuum g\u00fccl\u0259r aras\u0131nda aral\u0131q g\u00fcc varm\u0131? Ba\u015fqa s\u00f6zl\u0259 N\u2282T\u2282R \u015f\u0259rtini \u00f6d\u0259y\u0259n, n\u0259 N n\u0259 d\u0259 R \u00e7oxlu\u011funa ekvivalent olmayan \u00e7oxluq varm\u0131?<\/p>\n

Problemin h\u0259llini anlamaq \u00fc\u00e7\u00fcn riyazi m\u0259ntiqd\u0259n K.H\u00f6ydelin (Avstriya) qeyri taml\u0131q teoreminin populyar ifad\u0259sini qeyd ed\u0259k: \u0130st\u0259nil\u0259n sonlu sayda aksiom v\u0259 anlay\u0131\u015flar vasit\u0259sil\u0259 qurulmu\u015f kifay\u0259t q\u0259d\u0259r m\u00fck\u0259mm\u0259l n\u0259z\u0259riyy\u0259d\u0259 bu n\u0259z\u0259riyy\u0259nin n\u0259 t\u0259sdiq, n\u0259 d\u0259 inkar ed\u0259 bilm\u0259diyi t\u0259klif (formula) var.<\/p>\n

M\u00fcasir \u00e7oxluqlar n\u0259z\u0259riyy\u0259sinin formal aksiomalar\u0131 olaraq Zermolo \u2013 Frenkel (ZFC) aksiomlar\u0131 g\u00f6t\u00fcr\u00fcl\u00fcr.<\/p>\n

1940-c\u0131 ild\u0259 Avstriya riyaziyat\u00e7\u0131s\u0131 Kurt H\u00f6ydel isbat etdi ki, kontiniuum hipotezan ZFC \u00e7oxluqlar n\u0259z\u0259riyy\u0259si \u00e7\u0259r\u00e7iv\u0259sind\u0259 inkar etm\u0259k olmaz. 1963-c\u00fc ild\u0259 is\u0259 amerika riyaziyyat\u00e7\u0131s\u0131 Pol Koen h\u0259min n\u0259z\u0259riyy\u0259d\u0259 bu hipotezan\u0131n do\u011frulu\u011funu isbat\u0131n\u0131n qeyri-m\u00fcmk\u00fcn oldu\u011funu g\u00f6st\u0259rdi.<\/p>\n

Bel\u0259likl\u0259, kontiniuum hipoteza \u00e7oxluqlar\u0131n ZFC n\u0259z\u0259riyy\u0259sind\u0259n as\u0131l\u0131 deyil, H\u00f6ydelin qeyri-taml\u0131q teoremind\u0259 g\u00f6st\u0259rildiyi kimi, bu n\u0259z\u0259riyy\u0259 daxilind\u0259 h\u0259min hipotezan\u0131 n\u0259 isbat, n\u0259 d\u0259 inkar etm\u0259k olmaz. Kontiniuum hipotezan\u0131 ZFC n\u0259z\u0259riyy\u0259sin\u0259 \u0259lav\u0259 ets\u0259k he\u00e7 bir ziddiy\u0259t al\u0131nmaz. Qeyd ed\u0259k ki, bu hipotezan\u0131n do\u011frulu\u011funun q\u0259bul edilm\u0259si hesab\u0131 v\u0259 kontiniuum g\u00fccl\u0259r aras\u0131nda sonsuz sayda m\u00fcxt\u0259lif g\u00fccl\u0259rin varl\u0131\u011f\u0131na g\u0259tirib \u00e7\u0131xar\u0131r.<\/p>\n

Davam\u0131 var…<\/p>\n

\u018fd\u0259biyyat<\/p>\n

1. D.Hilbert Vortrag gehalten auf dem internationalen Matematiker-Kongrez zu Pariz. 1900.
\n2. D.Hilbert Mathematische Probleme. Archiv f. Math. u. Phys, III s. 1 (1901) 44-63.
\n3. \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0413\u0438\u043b\u0431\u0435\u0440\u0442\u0430, \u0421\u0431\u043e\u0440\u043d\u0438\u043a \u043f\u043e\u0434 \u0440\u0435\u0434\u0430\u043a\u0446\u0438\u0439 \u041f. \u0421. \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u043e\u0432\u0430, \u041c., \u041d\u0430\u0443\u043a\u0430 1969 \u0433. 240 \u0441.
\n4. \u0411\u043e\u043b\u0438\u0431\u0440\u0443\u0445 \u0410. \u0410. \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0413\u0438\u043b\u0431\u0435\u0440\u0442\u0430 (100 \u043b\u0435\u0442 \u0441\u043f\u0443\u0441\u0442\u044f) \u2013 \u041c\u0426\u041d\u041c\u041e, 1999, \u0442-2, 24\u0441.
\n5. \u0414\u0435\u043c\u0438\u0434\u043e\u0432 \u0421.\u0421. \u041a \u0438\u0441\u0442\u043e\u0440\u0438\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442\u0430 \/\/ \u0418\u0441\u0442\u043e\u0440\u0438\u043a\u0430 \u2013 \u043c\u0430\u0442. \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u2013 \u041c., \u041d\u0430\u0443\u043a\u0430, 1966 – \u211617 \u2013 91-122 \u0441.
\n6. \u041b\u044f\u0448\u043a\u043e \u0421.\u0418., \u041d\u043e\u043c\u0438\u0440\u043e\u0432\u0441\u043a\u0438\u0439 \u0414. \u0410., \u041f\u0435\u0442\u0443\u043d\u0438\u043d \u042e. \u0418., \u0421\u0435\u043c\u0435\u043d\u043e\u0432 \u0412.\u0412. \u0414\u0432\u0430\u0434\u0446\u0430\u0442\u0430\u044f \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442\u0430 \u00ab\u0414\u0438\u0430\u043b\u0435\u043a\u0442\u0438\u043a\u0430\u00bb, 2009-192 \u0441.
\n7. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442 \u0414. \u0418\u0437\u0431\u0440\u0430\u043d\u043d\u044b\u0435 \u0442\u0440\u0443\u0434\u044b \u0432. 2. \u0422 \/\/ \u041f\u043e\u0434 \u0420\u0435\u0434\u0430\u043a\u0446\u0438\u0438 \u2013 \u041c, \u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b, 1998.
\n\u2022 \u0422.1. \u0422\u0435\u043e\u0440\u0438\u044f \u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432, \u0422\u0435\u043e\u0440\u0438\u044f \u0447\u0438\u0441\u0435\u043b. \u0410\u043b\u0433\u0435\u0431\u0440\u0430. \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f. \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u2013 575 \u0441.
\n\u2022 \u0422.2. \u0410\u043d\u0430\u043b\u0438\u0437. \u0424\u0438\u0437\u0438\u043a\u0430. \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442\u0430 \u2013 607 \u0441.
\n8. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u041c.-\u041b.: \u0413\u043e\u0441\u0442\u0435\u0445\u0438\u0437\u0434\u0430\u0442, 1948-\u0421\u0435\u0440\u0438\u044f: \u041a\u043b\u0430\u0441\u0441\u0438\u043a\u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u043e\u0437\u043d\u0430\u043d\u0438\u044f.
\n9. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u0410\u043a\u043a\u0435\u0440\u043c\u0430\u043d. \u0412. \u041e\u0441\u043d\u043e\u0432\u044b \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043b\u043e\u0433\u0438\u043a\u0438.\u041c.: \u0418\u0437\u0434\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0430\u044f \u0433\u0440\u0443\u043f\u043f\u0430 URSS, 2010, 304 \u0441.
\n10. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u0411\u0435\u0440\u043d\u0430\u0439\u0441 \u041f. \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438. \u041c.: \u041d\u0430\u0443\u043a\u0430 \u0422\u043e\u043c I 1979, 560 \u0441.
\n11. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u0411\u0435\u0440\u043d\u0430\u0439\u0441 \u041f. \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438. \u0422.2. 1982. 656 \u0441.
\n12. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u041a\u043e\u043d-\u0424\u043e\u0441\u0441\u0435\u043d \u0421. \u041d\u0430\u0433\u043b\u044f\u0434\u043d\u0430\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u041c.-\u041b.: \u0413\u043e\u0441\u0442\u0435\u0445\u0438\u0437\u0434\u0430\u0442 (1951).
\n13. \u041a\u0443\u0440\u0430\u043d\u0442 \u0420. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442. \u0414. \u041c\u0435\u0442\u043e\u0434\u044b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438. \u0422\u043e\u043c I 1933.
\n14. \u0412\u0435\u0439\u043b\u044c. \u0413. \u0414\u0430\u0432\u0438\u0434 \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442 \u0438 \u0435\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0442\u0432\u043e\u0440\u0447\u0435\u0441\u0442\u0432\u043e \/\/ \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u0435 \u2013 \u041c.: \u041d\u0430\u0443\u043a\u0430, 1989 \u2013 \u0441 214-256.
\n15. \u041a\u043e\u043d\u0441\u0442\u0430\u043d\u0441 \u0420\u0438\u0434. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442 – \u041c.: \u041d\u0430\u0443\u043a\u0430 1977 \u0433.
\n16. \u041f\u0430\u0440\u0448\u0438\u043d \u0410.\u041d. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442 \u0438 \u0442\u0435\u043e\u0440\u0438\u044f \u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432 \/\/ \u0418\u0441\u0442\u043e\u0440\u0438\u043a\u043e- \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f – \u041c.: \u041d\u0430\u0443\u043a\u0430 1975 \u0433. \u2116 20 \u0441 171-197.
\n17. \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432. \u0410.\u041d. \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442 \u0414\u0430\u0432\u0438\u0434 \/\/ \u0411\u043e\u043b\u044c\u0448\u0430\u044f \u0441\u043e\u0432\u0435\u0442\u0441\u043a\u0430\u044f \u044d\u043d\u0446\u0438\u043a\u043b\u043e\u043f\u0435\u0434\u0438\u044f \/\/, 1969.
\n18. \u0410.\u0412.\u041f\u043e\u0433\u043e\u0440\u0435\u043b\u043e\u0432. \u0427\u0435\u0442\u0432\u0435\u0440\u0442\u0430\u044f \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442\u0430. \u041c\u043e\u0441\u043a\u0432\u0430. \u041d\u0430\u0443\u043a\u0430. 1974. 80 \u0441.
\n19. \u042e.\u0412. \u041c\u0430\u0442\u0438\u044f\u0441\u0435\u0432\u0438\u0447. \u0414\u0435\u0441\u044f\u0442\u0430\u044f \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0413\u0438\u043b\u044c\u0431\u0435\u0440\u0442\u0430 \u2013 \u041c. \u041d\u0430\u0443\u043a\u0430. \u0424\u0438\u0437\u0438\u043a\u043e-\u043c\u0430\u0442., \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430. 1993-223 \u0441.
\n20. Q.\u015eubert Kalk\u00fcl der abz\u00e4hlenden Geometric, 1879.<\/p>\n

M\u0259nb\u0259:\u00a0Misir M\u0259rdanov, Vidadi Mirz\u0259yev \u201cDavid Hilbert v\u0259 onun 23 problemi\u201d , Az\u0259rbaycan Milli Elml\u0259r Akademiyas\u0131 X\u0259b\u0259rl\u0259r M\u0259cmu\u0259si, Cild 4, \u21164, Dekabr 2017-ci il. s\u0259hif\u0259 9-18.<\/em><\/strong><\/p>\n

\u00a9 B\u00fct\u00fcn h\u00fcquqlar qorunur. X\u0259b\u0259rl\u0259rd\u0259n istifad\u0259 ed\u0259rk\u0259n www.imm.az sayt\u0131na istinad z\u0259ruridir.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

David Hilbetrin 1-ci problemi: Kontinuum hipoteza \u2013 Bu problem 1877-ci ild\u0259 \u00e7oxluqlar n\u0259z\u0259riyy\u0259sinin banisi Georq Kontor t\u0259r\u0259find\u0259n ir\u0259li s\u00fcr\u00fclm\u00fc\u015fd\u00fcr. Problemi v\u0259 onun h\u0259llini ayd\u0131nla\u015fd\u0131rmaq \u00fc\u00e7\u00fcn b\u0259zi anlay\u0131\u015flara m\u00fcraci\u0259t ed\u0259k. Ekvivalentlik (y\u0259ni qar\u015f\u0131l\u0131ql\u0131 \u2013 birqiym\u0259tli uy\u011funluq) d\u0259qiqliyi il\u0259 yaln\u0131z iki c\u00fcr sonsuz \u0259d\u0259di \u00e7oxluq var: Hesabi \u00e7oxluq – N natural \u0259d\u0259dl\u0259r \u00e7oxlu\u011fu il\u0259 eynig\u00fccl\u00fc (ekvivalent) \u00e7oxluq […]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[77],"tags":[],"_links":{"self":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/19881"}],"collection":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/comments?post=19881"}],"version-history":[{"count":1,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/19881\/revisions"}],"predecessor-version":[{"id":19882,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/19881\/revisions\/19882"}],"wp:attachment":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media?parent=19881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/categories?post=19881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/tags?post=19881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}