Tr\u00ean \u0111\u00e2y ch\u00fang ta v\u1eeba nghi\u00ean c\u1ee9u t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c c\u00f3 c\u01a1 s\u1ed1 kh\u00f4ng ph\u1ea3i l\u00e0 X0. \u0110\u1ec3 \u0111\u01b0a ra k\u1ebft lu\u1eadn n\u00e0y, \u0111i\u1ec3m ch\u1ee7 y\u1ebfu l\u00e0 kh\u00f4ng th\u1ec3 s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 th\u1ef1c theo b\u1ea5t k\u00ec th\u1ee9 t\u1ef1 n\u00e0o. Th\u1eadm ch\u00ed ta kh\u00f4ng th\u1ec3 s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 th\u1ef1c trong kho\u1ea3ng 0 v\u00e0 1 theo th\u1ee9 t\u1ef1. Ta c\u00f3 th\u1ec3 d\u00f9ng ph\u1ea3n ch\u1ee9ng \u0111\u1ec3 ch\u1ee9ng minh k\u1ebft lu\u1eadn n\u00e0y. Gi\u1ea3 s\u1eed ta c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 th\u1ef1c t\u1eeb 0 – 1 th\u00e0nh d\u00e3y v\u00e0 ghi \u0111\u01b0\u1ee3c: xi = 0, ai1 ai2 ai3 ai4\u2026 trong \u0111\u00f3 aij l\u00e0 s\u1ed1 l\u1ebb th\u1eadp ph\u00e2n \u1edf v\u1ecb tr\u00ed j, \u0111\u01b0\u01a1ng nhi\u00ean l\u00e0 aij l\u1ea5y c\u00e1c gi\u00e1 tr\u1ecb t\u1eeb 0 \u0111\u1ebfn 9 l\u00e0 10 s\u1ed1.<\/p>\n\n\n\n
Gi\u1ea3 s\u1eed ta l\u1ea1i ch\u1ecdn s\u1ed1 y = 0, b1b2b3b4\u2026v\u00e0 bi \u2260 ai (vi\u1ec7c n\u00e0y d\u1ec5 d\u00e0ng th\u1ef1c hi\u1ec7n) b\u1edfi v\u00ec ch\u1ec9 c\u1ea7n l\u1ea5y m\u1ed9t s\u1ed1 l\u1ebb \u1edf y kh\u00e1c v\u1edbi xi l\u00e0 ta c\u00f3 y \u2260 xi v\u00e0 do \u0111\u00f3 y s\u1ebd kh\u00f4ng thu\u1ed9c nh\u00f3m s\u1ed1 \u0111\u00e3 s\u1eafp x\u1ebfp (t\u1ee9c nh\u00f3m xy). T\u1eeb m\u00e2u thu\u1eabn n\u00e0y ta th\u1ea5y kh\u00f4ng th\u1ec3 d\u00f9ng b\u1ea5t k\u00ec c\u00e1ch n\u00e0o \u0111\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c s\u1ef1 \u0111\u1ed1i \u1ee9ng 1 – 1 gi\u1eefa c\u00e1c s\u1ed1 xy v\u1edbi t\u1eadp h\u1ee3p s\u1ed1 t\u1ef1 nhi\u00ean.<\/p>\n\n\n\n
C\u01a1 s\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c l\u00e0 X1. Nh\u01b0 v\u1eady li\u1ec7u c\u00f3 c\u00f2n c\u01a1 s\u1ed1 n\u00e0o trung gian gi\u1eefa A0 v\u00e0 X1? Theo Canter, ng\u01b0\u1eddi s\u00e1ng l\u1eadp l\u00ed thuy\u1ebft t\u1eadp h\u1ee3p kh\u00f4ng c\u00f3 c\u01a1 s\u1ed1 n\u00e0o kh\u00e1c X0 v\u00e0 X1\u01a1, n\u00f3i c\u00e1ch kh\u00e1c t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n c\u00e1c s\u1ed1 th\u1ef1c ch\u1ec9 c\u00f3 th\u1ec3 l\u00e0 X0 v\u00e0 X1. \u0110\u00f3 ch\u00ednh l\u00e0 v\u1ea5n \u0111\u1ec1 \u201ch\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c\u201d. (Ng\u01b0\u1eddi ta xem t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c c\u0169ng nh\u01b0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 \u201ch\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c\u201d, \u0111\u00f3 ch\u00ednh l\u00e0 v\u1ea5n \u0111\u1ec1 \u201ch\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c\u201d).<\/p>\n\n\n\n
V\u1ea5n \u0111\u1ec1 h\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c c\u00f3 \u00fd ngh\u0129a quan tr\u1ecdng trong nhi\u1ec1u ng\u00e0nh to\u00e1n h\u1ecdc. T\u1eeb khi v\u1ea5n \u0111\u1ec1 h\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c \u0111\u01b0a ra, nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc h\u1ebft s\u1ee9c c\u1ed1 g\u1eafng \u0111\u1ec3 ch\u1ee9ng minh ho\u1eb7c ph\u1ee7 \u0111\u1ecbnh n\u00f3. T\u1ea1i h\u1ed9i ngh\u1ecb to\u00e1n h\u1ecdc qu\u1ed1c t\u1ebf n\u0103m 1900, nh\u00e0 to\u00e1n h\u1ecdc n\u1ed5i ti\u1ebfng Bordad \u0111\u01b0a ra 23 b\u00e0i to\u00e1n \u0111\u01b0\u1ee3c s\u1ef1 ch\u00fa \u00fd c\u1ee7a nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc \u0111\u01b0\u01a1ng th\u1eddi, trong \u0111\u00f3 b\u00e0i to\u00e1n h\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c l\u00e0 m\u1ed9t trong c\u00e1c b\u00e0i to\u00e1n \u0111\u00f3. Th\u1ebf nh\u01b0ng c\u0169ng gi\u1ed1ng nh\u01b0 ti\u00ean \u0111\u1ec1 song song trong h\u00ecnh h\u1ecdc Euclide, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc ph\u00e1t hi\u1ec7n kh\u00f4ng c\u00f3 c\u01a1 s\u1edf \u0111\u1ec3 b\u00e1c b\u1ecf n\u00f3, c\u0169ng kh\u00f4ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c n\u00f3. Cho \u0111\u1ebfn n\u0103m 1938, Cadel ch\u1ee9ng minh h\u1ec7 ti\u00ean \u0111\u1ec1 ZF c\u1ee7a l\u00ed thuy\u1ebft t\u1eadp h\u1ee3p thu\u1ed9c v\u1ea5n \u0111\u1ec1 h\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c l\u00e0 kh\u00f4ng th\u1ec3 ph\u1ee7 \u0111\u1ecbnh. 25 n\u0103m sau, Cohen l\u1ea1i ch\u1ee9ng minh h\u1ec7 ti\u00ean \u0111\u1ec1 ZF thu\u1ed9c h\u1ec7 th\u1ed1ng v\u1ea5n \u0111\u1ec1 li\u00ean t\u1ee5c l\u00e0 kh\u00f4ng th\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c. Th\u00e0nh t\u1ef1u c\u1ee7a Cadel v\u00e0 Cohen \u0111\u01b0\u1ee3c xem l\u00e0 hai th\u00e0nh t\u1ef1u l\u1edbn trong c\u00f4ng t\u00e1c nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc c\u1ee7a th\u1ebf k\u1ec9 XX. N\u00f3 c\u0169ng b\u00e0y t\u1ecf h\u1ec7 ti\u00ean \u0111\u1ec1 ZF v\u00e0 v\u1ea5n \u0111\u1ec1 \u201ch\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c\u201d l\u00e0 \u0111\u1ed9c l\u1eadp v\u1edbi nhau v\u00e0 bi\u1ebfn \u201cv\u1ea5n \u0111\u1ec1 li\u00ean t\u1ee5c\u201d th\u00e0nh \u201cgi\u1ea3 thi\u1ebft li\u00ean t\u1ee5c\u201d. C\u0169ng c\u00f3 nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc c\u00f2n ch\u01b0a y\u00ean l\u00f2ng v\u1edbi \u201cgi\u1ea3 thi\u1ebft li\u00ean t\u1ee5c\u201d v\u00e0 h\u1ebft s\u1ee9c t\u00ecm c\u00e1c ti\u00ean \u0111\u1ec1 m\u1edbi \u0111\u1ec3 thay th\u1ebf. Hi\u1ec7n nay m\u1ecdi ng\u01b0\u1eddi \u0111ang h\u1ebft s\u1ee9c c\u1ed1 g\u1eafng trong c\u00f4ng cu\u1ed9c t\u00ecm t\u00f2i \u0111\u00f3.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: T\u1eadp h\u1ee3p; C\u01a1 s\u1ed1; Gi\u1ea3 thi\u1ebft h\u1ec7 th\u1ed1ng li\u00ean t\u1ee5c.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Tr\u00ean \u0111\u00e2y ch\u00fang ta v\u1eeba nghi\u00ean c\u1ee9u t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c c\u00f3 c\u01a1 s\u1ed1 kh\u00f4ng ph\u1ea3i l\u00e0 X0. \u0110\u1ec3 \u0111\u01b0a ra k\u1ebft lu\u1eadn n\u00e0y, \u0111i\u1ec3m ch\u1ee7 y\u1ebfu l\u00e0 kh\u00f4ng th\u1ec3 s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 th\u1ef1c theo b\u1ea5t k\u00ec th\u1ee9 t\u1ef1 n\u00e0o. Th\u1eadm ch\u00ed ta kh\u00f4ng th\u1ec3 s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 th\u1ef1c trong kho\u1ea3ng 0 v\u00e0 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7686","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7686","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7686"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7686\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7686"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}