{"id":8488,"date":"2009-05-26T06:54:00","date_gmt":"2009-05-26T06:54:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=8488"},"modified":"2009-05-26T06:54:00","modified_gmt":"2009-05-26T06:54:00","slug":"%eb%ac%b4%ed%95%9c%ec%86%8c","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=8488","title":{"rendered":"\ubb34\ud55c\uc18c"},"content":{"rendered":"
\n
\n 0.9999… = 1\n <\/div>\n

\n \uc704 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud558\ub294\uac00\uc5d0 \ub300\ud55c \ub17c\uc758\ub294 \ub108\ubb34 \ub9ce\uc774 \uc774\ub8e8\uc5b4\uc838 \uc654\ub2e4.<\/p>\n

\uc218\ud559\uc5d0\uc11c \ub450 \uc218\uac00 \uac19\uc740\uc9c0 \ud310\ub2e8\ud558\ub824\uba74 \ube7c\uc11c 0\uc774 \ub418\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uba74 \ub41c\ub2e4. \uc591\ubcc0\uc5d0\uc11c 0.99999…\ub97c \ube7c \ubcf4\uc790.
\n
\n 0.0….1 = 0
\n
\n \ubb3c\ub860 …\uc0ac\uc774\uc5d0\ub294 0\uc774 \ubb34\ud55c\ud788 \ub9ce\uc774 \ub4e4\uc5b4\uac00 \uc788\ub2e4. \uc0ac\uc2e4 1\uc774 \uc5b8\uc820\uac00 \ub098\uc624\uae30\ub294 \ud560\uae4c? \uacb0\ucf54 \uc778\uac04\uc740 1\uc744 \uad6c\uacbd\ud560 \uc218 \uc5c6\ub2e4.<\/p>\n

\uc774\uac83\uc740 “\uadf9\ud55c”\uc758 \uac1c\ub150\uc5d0 \ub300\ud55c \uc774\ud574\uc640 \uad00\ub828\ub418\uc5b4 \uc788\ub2e4. \uc778\uac04\uc740 \ubb34\ud55c\uc744 \uc0c1\uc0c1\uc870\ucc28 \ud558\uc9c0 \ubabb\ud558\uae30 \ub54c\ubb38\uc5d0 \ub17c\ub9ac\ub77c\uace0 \ud558\ub294 \uac11\uc637 \uc18d\uc5d0\uc11c\ub9cc \uadf8\uac83\uc744 \ub2e4\ub904\ubcfc \uc218 \uc788\ub2e4. \ub9c8\uce58, \uc6b0\uc8fc\uc5d0 \ub9e8\ubab8\uc73c\ub85c \ub098\uac08 \uc218 \uc5c6\uae30 \ub54c\ubb38\uc5d0 \uc6b0\uc8fc\ubcf5\uc744 \uc785\uc5b4\uc57c \ud558\ub294 \uac83\uacfc \ube44\uc2b7\ud558\ub2e4.<\/p>\n

\ub2e4\uc74c\uacfc \uac19\uc740 \uc218\uc5f4\uc744 \uc0dd\uac01\ud574 \ubcf4\uc790.
\n
\n 0.1
\n
\n 0.01
\n
\n 0.001
\n
\n 0.0001
\n
\n …
\n
\n \uc774 \uc218\uc5f4\uc758 \uaddc\uce59\uc740 (\ub0b4\uac00 \uadf8\ub807\uac8c \ud558\uae30\ub85c \uacb0\uc815\ud558\uc600\uc73c\ubbc0\ub85c) n\ubc88\uc9f8 \ud56d\uc740 1\uc744 10\uc73c\ub85c n\ubc88 \ub098\ub208 \uac12\uc774\ub77c\uace0 \ud55c\ub2e4.
\n
\n \uc774 \uc218\uc5f4\uc740 0\uc774 \ub418\ub294\uac00? \uc54c\ub2e4\uc2dc\ud53c, \uc774 \uc218\uc5f4\uc740 \uc5b4\ub5a0\ud55c \uc815\uc218 n\uc5d0 \ub300\ud574\uc11c\ub3c4 0\uc774 \ub418\uc9c0 \uc54a\ub294\ub2e4. n\uc744 \uc544\ubb34\ub9ac \ud070 \uac12\uc744 \uac00\uc9c0\uace0 \uc624\ub354\ub77c\ub3c4 \uacb0\ucf54 0\uc774 \ub418\uc9c0 \uc54a\ub294\ub2e4. \ud558\uc9c0\ub9cc, \uc6b0\ub9ac\ub294 \uc774 \uc218\uc5f4\uc774 n\uc774 \ucee4\uc9d0\uc5d0 \ub530\ub77c 0\uc5d0 \uc810\uc810 \uac00\uae4c\uc6cc \uc9c0\uace0 \uc788\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc54c \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc \uadf8\uac83\uc774 \uacfc\uc5f0 \ubaa8\ub4e0 \uc815\uc218 n\uc5d0 \ub300\ud574\uc11c \uc815\ub9d0 \uadf8\ub807\uac8c \ub418\ub294\uc9c0 \uc804\ubd80 \uc870\uc0ac\ud574 \ubcfc \uc218\ub3c4 \uc5c6\ub2e4. 10\uc5b5\ubcf4\ub2e4 \uc791\uc740 n\uc5d0 \ub300\ud574\uc11c\ub294 \uadf8\ub807\ub2e4\uace0 \ub9d0\ud560 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc 100\uc5b5\ubcf4\ub2e4 \uc791\uc740 n\uc5d0 \ub300\ud574\uc11c\ub294? 100\uc5b5\ubcf4\ub2e4 \uc791\uc740 n\uc5d0 \ub300\ud574\uc11c\ub3c4 \ubb3c\ub860 \uc131\ub9bd\ud55c\ub2e4. \ud558\uc9c0\ub9cc \uadf8\ub807\ub2e4\uace0 \uadf8\uac83\uc774 1000\uc5b5\ubcf4\ub2e4 \uc791\uc740 n\uc5d0 \ub300\ud574\uc11c \uc774 \uc218\uc5f4\uc774 \uc810\uc810 0\uc5d0 \uac00\uae4c\uc6cc \uc9c0\uace0 \uc788\ub2e4\ub294 \uac83\uc744 \ubcf4\uc99d\ud574 \uc8fc\uc9c0\ub294 \ubabb\ud55c\ub2e4. \uc870\uc0ac\ud574 \ubcf4\uae30 \uc804\uc5d0\ub294 \uc54c \uc218 \uc5c6\ub294 \uac83\uc774\ub2e4.<\/p>\n

\uc774\ub7ec\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c \uc218\ud559\uc790\ub4e4\uc740 “\uadf9\ud55c”\uc774\ub77c\ub294 \uac1c\ub150\uc744 \ub9cc\ub4e4\uace0, “\uc218\ub834\uc131”\uc5d0 \ub300\ud574\uc11c \uc77c\ubc18\uc801\uc73c\ub85c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \ubc29\uc2dd\uc73c\ub85c \uc815\uc758\ud558\uc600\ub2e4.
\n <\/p>\n

\n \uc784\uc758\uc758 \uc591\uc758 \uc2e4\uc218 d\uc5d0 \ub300\ud574\uc11c, \uc5b4\ub5a4 \uc22b\uc790 N\uc774 \uc874\uc7ac\ud558\uc5ec n>N\uc774\uae30\ub9cc \ud558\uba74 |a(n)-a|\n

\uc800\uae30\uc11c \ub098\uc628 \uc791\ub300\uae30 \ub450\uac1c\ub294 \uc808\ub300\uac12 \uae30\ud638\ub2e4. \uc989, \uc544\ubb34 \uc22b\uc790\ub77c\ub3c4 \uc88b\uc73c\ub2c8, \uc544\ubb34\uac70\ub098 \uac16\uace0 \uc624\ub77c\ub294 \uac70\ub2e4. d\ub85c\uc11c \uc5b4\ub5a4 \uc22b\uc790\ub97c \uc81c\uc2dc\ud558\ub354\ub77c\ub3c4 \uc815\uc218 N\uc744 \uc81c\uc2dc\ud560 \uc218 \uc788\uc5b4\uc11c, N\ubc88\uc9f8 \ud56d \uc774\ud6c4\uc758 \ubaa8\ub4e0 \ud56d\uc774 \ud2b9\uc815\ud55c \uac12\uc778 a\uc5d0 d\ub9cc\ud07c\uc758 \uac70\ub9ac\ubcf4\ub2e4\ub294 \uac00\uae5d\uac8c \uc788\ub3c4\ub85d \ud560 \uc218 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4. \uc5ec\uae30\uc11c d\ub294 \uc591\uc758 \uc2e4\uc218\uc774\ub2e4. 0\uc774 \uc544\ub2c8\ub2e4. \uc544\ubb34\ub9ac \uc791\uc544\ub3c4 \uc88b\uace0 \uc544\ubb34\ub9ac \ucee4\ub3c4 \uc88b\ub2e4. d\ub97c 0.000000000000000000000000000000001421\ub85c \uc7a1\uc544\ubcf4\uc790. \ub09c N\uc744 40\uc744 \uc81c\uc2dc\ud560 \uc218 \uc788\ub2e4. \ub354 \uc791\uc740 \uac12\uc744 \uac16\uace0 \uc640\ub3c4 \uc88b\ub2e4.<\/p>\n

\uc989, \uc774 \uc218\uc5f4\uc740 0\uc73c\ub85c \uc218\ub834\ud55c\ub2e4.<\/p>\n

\uc218\uc2dd\uc5d0 \ubb34\ud55c\ub300 \uae30\ud638\uac00 \ub4f1\uc7a5\ud55c\ub2e4\uba74, \uadf8 \uae30\ud638\ub294 \ubb34\ud55c\ub300 \uadf8 \uc790\uccb4\ub97c \uc758\ubbf8\ud558\ub294 \uacbd\uc6b0\ub294 \uac70\uc758 \uc5c6\ub2e4. \ubb34\ud55c\ub300 \uae30\ud638\ub294 \ub300\ubd80\ubd84\uc758 \uacbd\uc6b0 “\uc77c\ub2e8 \uacc4\uc0b0\ubd80\ud130 \ud558\uace0, \ub098\uc911\uc5d0 \ubb34\ud55c\ub300\uc5d0 \ud574\ub2f9\ud558\ub294 n\uc744 \ubb34\ud55c\ud788 \ucee4\uc9c0\ub294 \uadf9\ud55c\uc73c\ub85c \ubcf4\ub0b4\uc11c \uacc4\uc0b0\uc744 \uc644\ub8cc\ud55c\ub2e4”\ub294 \ub73b\uc774\ub2e4.<\/p>\n

\ub2e4\uc2dc, \uc6d0\ub798\uc758 \ubb38\uc81c\ub85c \ub3cc\uc544\uc640 \ubcf4\uc790.<\/p>\n

\n 0.9999… = 1\n <\/div>\n

\n \uc704\uc758 \ub4f1\uc2dd\uc774 \ud2c0\ub838\ub2e4\uace0 \uc8fc\uc7a5\ud558\ub294 \uc0ac\ub78c\ub4e4\uc740 \uc88c\ubcc0\uacfc \uc6b0\ubcc0 \uc0ac\uc774\uc5d0 0\uc774 \uc544\ub2cc \ucc28\uc774\uac00 \uc788\uc5b4\uc57c \ud568\uc744 \uc99d\uba85\ud574\uc57c \ud55c\ub2e4. \uadf8\ub7f0\ub370, \uc591 \ubcc0\uc758 \ucc28\uc774\uac00 0\uc778\uc9c0 \uc5b4\ub5a4\uc9c0\ub294 \ubaa8\ub974\uaca0\uc9c0\ub9cc, 0\uc774 \uc544\ub2cc \uadf8 \uc5b4\ub5a0\ud55c \uc22b\uc790\ub97c \uac16\uace0 \uc640\uc11c \uadf8 \ucc28\uc774\uc640 \ube44\uad50\ud558\ub354\ub77c\ub3c4 \uadf8 \uc22b\uc790\ubcf4\ub2e4 \ub354 \uc791\ub2e4.<\/p>\n

\uc989, \uc88c\ubcc0\uc5d0\uc11c \uc6b0\ubcc0\uc744 \ube80 \uac12\uc758 \ud06c\uae30\ub294, 0\uc774 \uc544\ub2cc \uc591\uc758 \uc2e4\uc218 \uc911 \uc544\ubb34\uac70\ub098 (\uc791\uac70\ub098, \ud06c\uac70\ub098, \uc5b4\ub5bb\ub4e0) \uac16\uace0 \uc640\uc11c \ube44\uad50\ud558\ub3c4\ub77c\ub3c4 \ud56d\uc0c1 \uadf8 \uc2e4\uc218\ubcf4\ub2e4\ub294 \uc791\ub2e4. “\uc544\ubb34\uac70\ub098” \uc801\uc6a9\ud574\ub3c4 \uc131\ub9bd\ud55c\ub2e4\ub294 \uac83\uc740, “\ubaa8\ub4e0” \uc218\uc5d0 \ub300\ud574\uc11c \uc131\ub9bd\ud55c\ub2e4\ub294 \ub73b\uacfc \uac19\uace0 (\uc544\ub2c8\ub77c\uace0 \uc0dd\uac01\ud558\ub294\uac00?) \uadf8 \ud06c\uae30(\uc808\ub300\uac12)\ub97c \ube44\uad50\ud588\uc744 \ub54c, 0\uc774 \uac00\uc7a5 \uc791\uc740 \uc218\uac00 \ub41c\ub2e4. \ub9cc\uc57d 0\uc774 \uc544\ub2cc \ub2e4\ub978 \uc218\uac00 \uc628\ub2e4\uba74, \uadf8 \uc218\uc640 0\uc758 \uc0ac\uc774\uc5d0\ub294 \ud56d\uc0c1 \ub2e4\ub978 \uc218\uac00 \uc788\uc5b4\uc11c \uadf8\ubcf4\ub2e4 \ub354 \uc791\uc740 \uc218\ub97c \ub9cc\ub4e4\uc5b4 \ub0bc \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 \uac00\uc7a5 \uc791\uc740 \uc218\uac00 \ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n

\uc88c\ubcc0\uacfc \uc6b0\ubcc0\uc758 \ucc28\uc774\ub294 0\uc774\uc5b4\uc57c\ub9cc \ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n

\uc88c\ubcc0\uc5d0\uc11c \uc6b0\ubcc0\uc758 \ucc28\uc774\ub97c \uacc4\uc0b0\ud588\ub294\ub370 0\uc774 \ub098\uc654\ub2e4\uba74, \uc6b0\ub9ac\ub294 \uadf8 \ub450 \uc218\ub97c “\uac19\ub2e4”\ub77c\uace0 \uc0dd\uac01\ud55c\ub2e4. \ub2e4\ub978 \uac83\uc740 \ud45c\ud604 \ubc29\uc2dd\uc77c \ubfd0\uc774\ub2e4.<\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

0.9999… = 1 \uc704 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud558\ub294\uac00\uc5d0 \ub300\ud55c \ub17c\uc758\ub294 \ub108\ubb34 \ub9ce\uc774 \uc774\ub8e8\uc5b4\uc838 \uc654\ub2e4. \uc218\ud559\uc5d0\uc11c \ub450 \uc218\uac00 \uac19\uc740\uc9c0 \ud310\ub2e8\ud558\ub824\uba74 \ube7c\uc11c 0\uc774 \ub418\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uba74 \ub41c\ub2e4. \uc591\ubcc0\uc5d0\uc11c 0.99999…\ub97c \ube7c \ubcf4\uc790. 0.0….1 = 0 \ubb3c\ub860 …\uc0ac\uc774\uc5d0\ub294 0\uc774 \ubb34\ud55c\ud788 \ub9ce\uc774 \ub4e4\uc5b4\uac00 \uc788\ub2e4. \uc0ac\uc2e4 1\uc774 \uc5b8\uc820\uac00 \ub098\uc624\uae30\ub294 \ud560\uae4c? \uacb0\ucf54 \uc778\uac04\uc740 1\uc744 \uad6c\uacbd\ud560 \uc218 \uc5c6\ub2e4. \uc774\uac83\uc740 “\uadf9\ud55c”\uc758 \uac1c\ub150\uc5d0 \ub300\ud55c \uc774\ud574\uc640 \uad00\ub828\ub418\uc5b4 \uc788\ub2e4. \uc778\uac04\uc740 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-8488","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2cU","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8488","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8488"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8488\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8488"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8488"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}