\uc774 \uae00\uc740 \ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774, \uadf8 \ubca1\ud130\uacf5\uac04\uc758 \uae30\uc800\uc758 \uae30\uc218(cardinal number)\ub85c\uc11c \uc798 \uc815\uc758\ub428\uc744 \uc0b4\ud3b4\ubcf4\ub294 \uae00\uc774\ub2e4. \uc720\ud55c\uc9d1\ud569\uc73c\ub85c \uc0dd\uc131\ub418\ub294 \ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774 \uc798 \uc815\uc758\ub41c\ub2e4\ub294 \uac83\uc740 \ubcf4\ud1b5\uc758 \uc120\ud615\ub300\uc218\ud559 \uad50\uc7ac\uc5d0 \uc544\uc8fc \uc798 \uc18c\uac1c\ub418\uc5b4 \uc788\uc73c\ubbc0\ub85c \uc5ec\uae30\uc11c\ub294 \uc0dd\ub7b5\ud558\uace0, \uc774 \uae00\uc5d0\uc11c\ub294 \uc720\ud55c\uc9d1\ud569\uc73c\ub85c \uc0dd\uc131\ub418\uc9c0 \uc54a\ub294 \ubca1\ud130\uacf5\uac04, \uc989 \ubb34\ud55c\ucc28\uc6d0\ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774 \uc798 \uc815\uc758\ub418\ub294 \uac83\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \uc774 \uae00\uc740 \ucc38\uace0\ubb38\ud5cc [1]\uc758 \uc81c9\uc7a5 2\uc808\uc758 \ub0b4\uc6a9\uc744 \ubc14\ud0d5\uc73c\ub85c \uc791\uc131\ud558\uc600\ub2e4. <\/p>\n
\n\uccb4 \\(\\mathbb{F}\\) \uc704\uc758 \ubca1\ud130\uacf5\uac04 \\(V\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, (\uc120\ud0dd\uacf5\ub9ac\ub97c \uac00\uc815\ud588\uc744 \ub54c) \\(V\\)\uc758 \uae30\uc800\uac00 \uc874\uc7ac\ud568\uc744 \uc54c\uace0 \uc788\ub2e4. \uc5ec\uae30\uc11c\ub294
\n\\(\\mathcal{B}\\)\uc640 \\(\\mathcal{C}\\)\uac00 \ubaa8\ub450 \\(V\\)\uc758 \uae30\uc800\uc77c \ub54c, \\(\\mathcal{B}\\)\uc640 \\(\\mathcal{C}\\) \uc0ac\uc774\uc5d0\ub294 \uc77c\ub300\uc77c \ub300\uc751\uc774 \ubc18\ub4dc\uc2dc
\n\uc874\uc7ac\ud568\uc744 \ud655\uc778\ud568\uc73c\ub85c\uc368 [\\(V\\)\uc758 \ucc28\uc6d0]\uc744 \\(V\\)\uc758 \uae30\uc800\uc758 \uae30\uc218\ub85c \uc815\uc758\ud560 \uc218 \uc788\ub2e4\ub294 \uac83\uc744 \ubcf4\uc774\uace0\uc790 \ud55c\ub2e4.\n<\/p>\n
\n\uc774\ub97c \uc704\ud574 \\(\\mathcal{B}=\\{v_i\\mid i\\in I\\}, \\mathcal{C}=\\{w_j\\mid j\\in J\\}\\)\ub85c \ub450\uace0, (\\(I\\) \ud639\uc740 \\(J\\)\uac00 \uc720\ud55c\uc9d1\ud569\uc778 \uacbd\uc6b0\ub294 \\(V\\)\uac00 \uc720\ud55c\uc9d1\ud569\uc73c\ub85c \uc0dd\uc131\ub418\ub294 \uacbd\uc6b0\uc774\ubbc0\ub85c) \\(I\\)\uc640 \\(J\\)\uac00 \ubaa8\ub450 \ubb34\ud55c\uc9d1\ud569\uc784\uc744 \uac00\uc815\ud558\uace0, \\(\\mathcal{B}\\)\uc640 \\(\\mathcal{C}\\) \uc0ac\uc774\uc5d0 \uc77c\ub300\uc77c \ub300\uc751\uc774 \uc874\uc7ac\ud568\uc744 \ubcf4\uc774\uc790.\n<\/p>\n
\n\\(\\mathcal{C}\\)\uac00 \\(V\\)\uc758 \uae30\uc800\uc774\ubbc0\ub85c, \\(\\mathcal{B}\\)\uc758 \uac01\uac01\uc758 \uc6d0\uc18c \\(v_i\\)\ub97c \\(\\mathcal{C}\\)\uc758 \uc77c\ucc28\uacb0\ud569\uc778
\n \\[
\n v_i=\\alpha_1 w_{k_1}+\\cdots + \\alpha_m w_{k_m}\\quad (\\alpha_k\\neq 0)
\n \\]
\n \uaf34\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uc77c\ucc28\uacb0\ud569 \uc804\uccb4\ub97c \uc0dd\uac01\ud574\ubcfc \ub54c, \\(\\mathcal{C}\\)\uc758 \uc784\uc758\uc758 \uc6d0\uc18c\ub294 \uc774 \uc77c\ucc28\uacb0\ud569\ub4e4 \uc911\uc5d0 \uc801\uc5b4\ub3c4 \ud55c \ubc88\uc740
\n \ub098\ud0c0\ub098\uc57c\ub9cc\ud55c\ub2e4. \uc65c\ub0d0\ud558\uba74, \ub9cc\uc77c \uc774\ub7ec\ud55c \uc77c\ucc28\uacb0\ud569 \uc911\uc5d0 \ud55c \ubc88\ub3c4 \ub098\ud0c0\ub098\uc9c0 \uc54a\ub294 \\(w_{j_0}\\)\uac00 \uc788\ub2e4\uba74, \\(\\mathcal{B}\\)\ub3c4
\n \uae30\uc800\uc774\ubbc0\ub85c \\(w_{j_0}\\)\ub97c \\(v_i\\)\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uace0, \uc774\ub54c\uc758 \ubaa8\ub4e0 \\(v_i\\)\ub294 \ub2e4\uc2dc (\\(w_{j_0}\\)\ub294 \uc544\ub2cc) \\(w_j\\)\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub2e4\uc2dc \uc4f8 \uc218
\n \uc788\uac8c\ub418\ub294\ub370 \uc774\ub294 \uace7 \\(w_{j_0}\\)\ub97c \ub2e4\ub978 \\(w_j\\)\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4\ub294 \ub73b\uc774\ub418\uc5b4 \\(\\mathcal{C}\\)\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc778 \uac83\uc5d0
\n \ubaa8\uc21c\uc774 \ub418\uae30 \ub54c\ubb38\uc774\ub2e4.\n<\/p>\n
\n \uc774\uc81c \\(\\mathcal{C}\\)\uc5d0\uc11c \\(\\mathcal{B}\\)\ub85c\uc758 \ud568\uc218 \\(\\varphi\\)\ub97c \uc815\uc758\ud574\ubcf4\uc790. \uac01 \\(w_j\\in\\mathcal{C}\\)\ub294 \\(\\mathcal{B}\\)\uc758 \uc5b4\ub5a4 \uc6d0\uc18c\ub97c
\n \ud45c\ud604\ud558\ub294 \uc77c\ucc28\uacb0\ud569\uc5d0 \uc801\uc5b4\ub3c4 \ud55c \ubc88\uc740 \ub098\ud0c0\ub098\ub294\ub370, \uadf8 \uc77c\ucc28\uacb0\ud569\uc774 \ub098\ud0c0\ub0b4\ub294 \\(v_i\\)\ub97c \ud558\ub098 \ud0dd\ud558\uc5ec \uc774\ub97c \\(\\varphi(w_j)\\)\uc758
\n \uac12\uc73c\ub85c \uc815\ud558\uc790. \uc989, \uac01 \\(j\\in J\\)\uc5d0 \ub300\ud558\uc5ec \uc9d1\ud569 \\(S_j\\)\ub97c \\(\\mathcal{B}\\)\uc758 \uc6d0\uc18c \uc911\uc5d0 \\(w_j\\)\ub97c \ud3ec\ud568\ud55c \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ud45c\ud604\ub418\ub294 \uc6d0\uc18c\ub97c \ubaa8\ub450 \ubaa8\uc544 \ub193\uc740 \uc9d1\ud569\uc73c\ub85c
\n \uc815\uc758\ud558\uba74, (\uc55e\uc11c \uc0b4\ud3b4\ubcf8 \ubc14\uc640 \uac19\uc774) \\(S_j\\)\ub294 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\ub2e4. \ub530\ub77c\uc11c (\uc120\ud0dd\uacf5\ub9ac\ub97c \uac00\uc815\ud558\uba74) \ubaa8\ub4e0 \\(j\\in J\\)\ub9c8\ub2e4 \\(S_j\\)\uc758 \ud55c \uc6d0\uc18c\ub97c \ud0dd\ud560 \uc218
\n \uc788\uace0, \uadf8 \ud0dd\ud55c \uc6d0\uc18c\ub97c \\(\\varphi(w_j)\\)\ub85c \ub450\uba74, \\(\\varphi: \\mathcal{C}\\to\\mathcal{B}\\)\ub294 \uc798 \uc815\uc758\ub41c \ud568\uc218\uc774\ub2e4.\n<\/p>\n
\n \uc774\uc81c \\(\\varphi\\)\uc758 \uce58\uc5ed\uc744 \\(\\mathcal{B}’\\)\uc73c\ub85c \ub450\uc790. \uc989 \\(\\varphi(\\mathcal{C})=\\mathcal{B}’\\)\ub77c \ud558\uc790. \ub9cc\uc77c \\(v_{i_0}\\in
\n \\mathcal{B}’\\)\ub77c\uba74, \\(v_{i_0}\\)\uc758 \\(\\varphi\\)\uc5d0 \ub300\ud55c \uc5ed\uc0c1, \uc989 \\(\\varphi^{-1}(\\{v_{i_0}\\})\\)\uc758 \uc6d0\uc18c\ub4e4\uc740 \\(v_{i_0}\\)\ub97c \\(\\mathcal{C}\\)\uc758
\n \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \ub54c \ub4f1\uc7a5\ud55c \\(w_j\\)\ub4e4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\ubbc0\ub85c \\(\\varphi^{-1}(\\{v_{i_0}\\})\\)\ub294 \ubc18\ub4dc\uc2dc \uc720\ud55c\uc9d1\ud569\uc774\ub2e4.\n<\/p>\n
\n \uc774\uc81c \uc9d1\ud569\uc871 \\(\\mathcal{F}=\\{\\varphi^{-1}(\\{v_{i_0}\\})\\mid v_{i_0}\\in\\mathcal{B}’ \\}\\)\ub97c \uc0dd\uac01\ud558\uc790. \\(\\mathcal{F}\\)\uc640 \n\ub530\ub77c\uc11c \\(\\mathcal{B}’\\)\uc758 \uae30\uc218\ub294 \\(\\mathcal{C}\\)\uc758 \uae30\uc218\uc640 \uac19\uc73c\uba70 \uc774\ub294 \\(\\mathcal{B}’\\)\uc744 \ubd80\ubd84\uc9d1\ud569\uc73c\ub85c \uac16\ub294 \uc9d1\ud569\uc778 \\(\\mathcal{B}\\)\uc758 \uae30\uc218\ub294 \\(\\mathcal{C}\\)\uc758 \uae30\uc218\ubcf4\ub2e4 \uc774 \uae00\uc740 \ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774, \uadf8 \ubca1\ud130\uacf5\uac04\uc758 \uae30\uc800\uc758 \uae30\uc218(cardinal number)\ub85c\uc11c \uc798 \uc815\uc758\ub428\uc744 \uc0b4\ud3b4\ubcf4\ub294 \uae00\uc774\ub2e4. \uc720\ud55c\uc9d1\ud569\uc73c\ub85c \uc0dd\uc131\ub418\ub294 \ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774 \uc798 \uc815\uc758\ub41c\ub2e4\ub294 \uac83\uc740 \ubcf4\ud1b5\uc758 \uc120\ud615\ub300\uc218\ud559 \uad50\uc7ac\uc5d0 \uc544\uc8fc \uc798 \uc18c\uac1c\ub418\uc5b4 \uc788\uc73c\ubbc0\ub85c \uc5ec\uae30\uc11c\ub294 \uc0dd\ub7b5\ud558\uace0, \uc774 \uae00\uc5d0\uc11c\ub294 \uc720\ud55c\uc9d1\ud569\uc73c\ub85c \uc0dd\uc131\ub418\uc9c0 \uc54a\ub294 \ubca1\ud130\uacf5\uac04, \uc989 \ubb34\ud55c\ucc28\uc6d0\ubca1\ud130\uacf5\uac04\uc758 \ucc28\uc6d0\uc774 \uc798 \uc815\uc758\ub418\ub294 \uac83\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \uc774 \uae00\uc740 \ucc38\uace0\ubb38\ud5cc [1]\uc758 \uc81c9\uc7a5 2\uc808\uc758 \ub0b4\uc6a9\uc744 \ubc14\ud0d5\uc73c\ub85c \uc791\uc131\ud558\uc600\ub2e4. Invariance of Dimensionality \uccb4 \\(\\mathbb{F}\\) \uc704\uc758 \ubca1\ud130\uacf5\uac04 \\(V\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, (\uc120\ud0dd\uacf5\ub9ac\ub97c \uac00\uc815\ud588\uc744 \ub54c)…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[57],"tags":[568,569,413,400,505,570,571,426,572],"class_list":["post-8512","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","tag-axiom-of-choice","tag-basis","tag-dimension","tag-linear-algebra","tag-505","tag-570","tag-571","tag-426","tag-572"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8512","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=8512"}],"version-history":[{"count":2,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8512\/revisions"}],"predecessor-version":[{"id":8514,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8512\/revisions\/8514"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=8512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=8512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=8512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n \\(\\mathcal{B}’\\) \uc0ac\uc774\uc5d0 \uc77c\ub300\uc77c \ub300\uc751\uc774 \uc788\uc73c\ubbc0\ub85c \uc774\ub4e4\uc758 \uae30\uc218\ub294 \uac19\ub2e4. \ud55c\ud3b8,
\n \uc9d1\ud569\uc871 \\(\\mathcal{F}\\)\ub294, \uadf8 \uc815\uc758\uc0c1, \\(\\mathcal{C}\\)\ub97c \ubd80\ubd84\uc9d1\ud569\ub4e4\uc758 \ubaa8\uc784\uc778\ub370, \ud2b9\ud788 \uc774\ub4e4\uc740
\n \uc30d\ub9c8\ub2e4 \uc11c\ub85c\uc18c\uc778 \\(\\mathcal{C}\\)\uc758 \uc720\ud55c\ubd80\ubd84\uc9d1\ud569\ub4e4\uc758 \ubaa8\uc784\uc774\uba70, \uc804\uccb4\ub97c \ud569\uc9d1\ud569 \ud558\uba74 \\(\\mathcal{C}\\)\uac00 \ub41c\ub2e4. \uc989 \\(\\mathcal{F}\\)\ub294
\n \\(\\mathcal{C}\\)\ub97c \uc11c\ub85c \uacb9\uce58\uc9c0 \uc54a\ub294 \uc720\ud55c\uc9d1\ud569\ub4e4\ub85c \ubd84\ud560\ud55c \uac83\uc73c\ub85c \ubcfc \uc218 \uc788\ub2e4.
\n \ub354\uc6b1\uc774 \\(\\mathcal{C}\\)\uac00 \ubb34\ud55c\uc9d1\ud569\uc774\ubbc0\ub85c \\(\\mathcal{F}\\)\ub3c4 \ubb34\ud55c\uc9d1\ud569\uc774\ub2e4. \ub610\ud55c \ud45c\uc900\uc801\uc778 \uc9d1\ud569\ub860\uc758 \uae30\uc218\uc5d0 \uad00\ud55c \uba87 \uac00\uc9c0 \uc815\ub9ac\ub85c\ubd80\ud130
\n \\(\\mathcal{C}\\)\uc640 \\(\\mathcal{F}\\)\ub294 \ub3d9\uc77c\ud55c \uae30\uc218\ub97c \uac00\uc9d0\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/span>1<\/sup><\/a><\/span>\n<\/p>\n
\n \ud06c\uac70\ub098 \uac19\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc774\uc81c \\(\\mathcal{B}\\)\uc640 \\(\\mathcal{C}\\)\uc758 \uc5ed\ud560\uc744 \ubc14\uafb8\uc5b4 \ub3d9\uc77c\ud55c \ub17c\ub9ac\ub97c \uc804\uac1c\ud558\uba74
\n \\(\\mathcal{C}\\)\uc758 \uae30\uc218\uac00 \\(\\mathcal{B}\\)\uc758 \uae30\uc218\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uc74c\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c (Cantor-Bernstein\uc758 \uc815\ub9ac\uc5d0 \uc758\ud574)
\n \\(\\mathcal{B}\\)\uc640 \\(\\mathcal{C}\\)\uc758 \uae30\uc218\uac00 \uac19\uc74c\uc744 \uc5bb\ub294\ub2e4.\n<\/p>\n\ucc38\uace0\ubb38\ud5cc <\/h3>\n
\n