{"id":3310,"date":"2012-06-14T12:57:00","date_gmt":"2012-06-14T03:57:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3310"},"modified":"2021-09-01T20:28:21","modified_gmt":"2021-09-01T11:28:21","slug":"2k12springsettheory","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2012\/06\/14\/2k12springsettheory\/","title":{"rendered":"2k12SpringSetTheory"},"content":{"rendered":"
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[wiki:2k12SpringSetTheoryHW HOMEWORK]<\/h2>\n
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\uc704\uc758 \ub9c1\ud06c\ub97c \ub530\ub77c \uac00\uc138\uc694. <\/p>\n<\/div>\n<\/div>\n

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Q and A<\/h2>\n
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\uc0c8 \uc9c8\ubb38\uc740 \uc704\ucabd\uc5d0 \uc501\ub2c8\ub2e4. \uc9c8\ubb38\uacfc \ub2f5\uc744 \ud560 \ub54c\ub294 \uc9c8\ubb38 \ub05d\uc5d0 \ub0a0\uc790, \ud559\ubc88, \uc774\ub984\uc744 \uc501\ub2c8\ub2e4. \uc5ec\uae30\ub294 \uacf5\ubd80\uc911\uc5d0 \uc0dd\uae30\ub294 \uc9c8\ubb38\uc744 \ud558\uace0 \ub610 \ub2f5\uc744 \uc544\ub294 \uc0ac\ub78c\uc740 \uc774\uc5d0 \ub300\ud55c \ub2f5\uc744 \ub2f5\ub2c8\ub2e4. <\/p>\n

Q: \uc218\uc5c5 \uc678 \uc9c8\ubb38) HistorySagong \uc740 \ubb34\uc5b8\uac00\uc694? \uc218\ud559 \uc5ed\uc0ac\ub97c \uacf5\ubd80\ud558\ub294 \ubaa8\uc784\uc778\uac00\uc694? \ub9cc\uc57d \uadf8\ub7ec\uba74, \uad6c\uccb4\uc801\uc73c\ub85c \uc5b4\ub5a4 \ub0b4\uc6a9\ub4e4\uc744 \ub2e4\ub8e8\ub294 \ubaa8\uc784\uc778\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. <\/p>\n

A: \uc774\uac83\uc740 \uac1c\ubc29\ub418\uc9c0 \uc54a\uc740 \uc218\ud559 \uc5ed\uc0ac \uacf5\ubd80 \ubaa8\uc784\uc785\ub2c8\ub2e4. \ud639\uc2dc \uc218\ud559 \uc5ed\uc0ac \uacf5\ubd80\uc5d0 \uad00\uc2ec\uc774 \uc788\ub2e4\uba74 \ub2e4\uc74c \ud559\uae30\uc5d0 \uc5f4\ub9ac\ub294 \uae30\ud558\ud559 \ud2b9\uac15\uc744 \ub4e4\uc5b4\ubcf4\uc138\uc694. \uc2e4\uc81c \ub0b4\uc6a9\uc740 \ub3d9\uc591 \uc218\ud559\uc0ac\ub97c \uc911\uc2ec\uc73c\ub85c \ud55c \ub3d9 \uc11c\uc591 \uc218\ud559\uc0ac\uc758 \ube44\uad50 \uac15\uc758\uc785\ub2c8\ub2e4. (\uadf8\ub9ac\uace0 \ub098\uc11c \uacc4\uc18d \uc218\ud559\uc0ac\uc5d0 \uad00\uc2ec\uc774 \uac04\ub2e4\uba74 \uc218\ud559\uc0ac \uacf5\ubd80 \ubaa8\uc784\uc744 \ub9cc\ub4e4\uc5b4 \ubcf4\uc138\uc694.) Sagong \ubaa8\uc784\uc5d0\uc11c\ub3c4 \ub3d9 \uc11c\uc591 \uc218\ud559\uc0ac\uc758 \ube44\uad50 \ubc0f \uc5f0\uad6c\ub97c \ud569\ub2c8\ub2e4. <\/p>\n

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Q: \ub450\ubc88\uc9f8\uad50\uc7ac Thm 3.2 \uc758 b \uc99d\uba85\uacfc\uc815\uc911\uc5d0\uc11c a\ub97c inf(a1,a2,a3,…,an) \uc774\ub7f0\uc2dd\uc73c\ub85c \uc7a1\uc558\ub294\ub370 Rudin\uc758 \ud574\uc11d\ud559\uc5d0\uc11c\ub294 \uac19\uc740 \uc99d\uba85\uacfc\uc815\uc5d0\uc11c inf \ub300\uc2e0 min\uc744 \uc0ac\uc6a9\ud588\ub358\ub370 \uc774 \ub450\uac1c\uc758 \uc5c4\ubc00\ud55c \ucc28\uc774\uac00\uc788\ub294\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4.. \uc774 \uc99d\uba85\uacfc\uc815\uc5d0\uc11c\ub294 \ub458\ub2e4\uc368\ub3c4 \ud06c\uac8c \ubb38\uc81c\uac00 \ub418\uc9c4 \uc54a\uaca0\uc8e0? (2011,06,14 2011160112 \ud669\uc6d0\uaddc) <\/p>\n

A: \uc720\ud55c\uac1c\uc758 \ub300\uc0c1\uc5d0 \ub300\ud574\uc11c\ub294 inf=min \uc785\ub2c8\ub2e4. \ucc28\uc774\ub294 \ubb34\ud55c\uac1c\uc5d0\uc11c\ub9cc \ub098\ub2c8\uae4c\uc694. \uadf8\ub7ec\ub2c8\uae4c \uc5b4\ub5a4 \uc0ac\ub78c\ub4e4\uc740 \uad73\uc774 \ub450 \uac00\uc9c0 \uae30\ud638\ub97c \uc0ac\uc6a9\ud560 \ud544\uc694\uac00 \uc788\ub294\uac00\ub77c\uace0 \uc0dd\uac01\ud560 \uc218\ub3c4 \uc788\uc9c0\uc694. \uadf8\ub7f0 \uacbd\uc6b0\uc5d0\ub294 inf \ub9cc \uc0ac\uc6a9\ud558\uac8c \ub418\uaca0\uc9c0\uc694. (\uc5b4\ub5a4 \uacbd\uc6b0\uc5d0\ub3c4 min\uc774 \uc788\uc73c\uba74 \uc774\uac83\uc774 inf\uc774\uae30\ub3c4 \ud558\ub2c8\uae4c\uc694.) <\/p>\n

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Q:\uac15\uc758\ub85d 53\ucabd\uc744 \ubcf4\uba74 \uac70\ub9ac\uc758 \uc870\uac74 4\uac00\uc9c0\uac00 \ub098\uc624\ub294\ub370\uc694. a\uc870\uac74(d(x\u2081,x\u2082)\u22650) \uc5c6\uc774 d\uc870\uac74\uc5d0\uc11c x\u2081=x\u2082\uc774\uba74 b,c\uc870\uac74\uc744 \uc774\uc6a9\ud574\uc11c a\uc870\uac74\uc744 \uc5bb\uc744 \uc218 \uc788\ub294\ub370 \uadf8\ub7fc a\uc758 \uc870\uac74\uc740 \ud544\uc694 \uc5c6\uc9c0 \uc54a\uc744\uae4c\uc694? 2012.06.11, 2011160002, \uc774\ub3d9\uadfc <\/p>\n

A: \uc5b4, \uc815\ub9d0 \uadf8\ub7f0 \uac70 \uac19\ub124\uc694. \uac11\uc790\uae30 \uace0\ubbfc\uac70\ub9ac\uac00 \uc0dd\uacbc\ub124\uc694^^, \ud559\uc0dd\/ [http:\/\/en.wikipedia.org\/wiki\/Metric_space#Definition<\/a>] \uc5ec\uae30\uc11c\ub3c4 \ub2d8\uc758 \ub9d0\uc774 \ub9de\ub2e4\uace0 \ud558\ub124\uc694. \uc74c.. \uc544\ubb34\ub798\ub3c4 \uccab\ubc88\uc9f8 \uba85\uc81c\uac00 \uac70\ub9ac\ud568\uc218\uc758 \uc81c 1\uc131\uc9c8\uc774\ub77c \uc5ec\uaca8\uc9c8 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 \ube44\ub85d \ucd94\ub860\ub420 \uc218 \uc788\ub294 \uac83\uc5d0 \uc18d\ud558\uc9c0\ub9cc \ud2b9\ubcc4\ud788 \uc5b8\uae09\ud55c\uac8c \uc544\ub2d0\uae4c\uc694? \uc78a\uc9c0\ub9d0\ub77c\ub294 \ub2f9\ubd80\uc758 \uc758\ubbf8\uc5d0\uc11c\uc694. <\/p>\n

A: <\/p>\n

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Q: 3\ub2e8\uc6d0 Open sets and Closed sets \uc218\uc5c5\uc2dc\uac04 \uc911 \uad50\uc218\ub2d8\uaed8\uc11c \ub2e4\ub8e8\uc2e0 \ub0b4\uc6a9 \uc911 \uacf5\uc9d1\ud569\uc740 Open in X \ub77c\ub294 \uac83\uc5d0 \uad00\ud558\uc5ec \uc9c8\ubb38\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uacf5\uc9d1\ud569\uc740 \ub9ac\ubbf8\ud2b8 \ud3ec\uc778\ud2b8\ub97c \uac00\uc9c0\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc5d0 Closed \ub77c\uace0 \ud560 \uc218 \uc788\uc744\uae4c\uc694? \uc608\ub97c\ub4e4\uc5b4 \uc218\uc5c5 \uc911 \ud55c \uc810 \uc9d1\ud569\uc740 \ub9ac\ubbf8\ud2b8 \ud3ec\uc778\ud2b8\uac00 \uc5c6\uae30 \ub54c\ubb38\uc5d0(\uac00\uc815\uc774 \ube44\uc5b4\uc788\uc73c\ubbc0\ub85c) Closed\ub77c\uace0 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4. (5\/15 \uad50\uc218\ub2d8 \uc218\uc5c5 \ub0b4\uc6a9 \uc911 Vacously true\uc5d0 \uad00\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4.) 2012.05.29, 2011160165, \uc7a5\ud61c\ucca0 <\/p>\n

A: (\uc5b4\ub290 \ud559\uc0dd \ub2f5) \ub2d8\uc758 \ub9d0\uc774 \ub9de\ub294 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \uadf8\ub798\uc11c \uacf5\uc9d1\ud569\uacfc \uc804\uccb4\uc9d1\ud569\uc740 \uc5f4\ub824\uc788\uc73c\uba74\uc11c \ub2eb\ud600\uc788\ub294 \uc2e0\uae30\ud55c \uc9d1\ud569\uc774 \ub41c \uac70 \uac19\uc544\uc694. <\/p>\n

A: <\/p>\n

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Q: 1. $ [0,1) $ \uacfc $ [0,∞) $ \uc758 1\ub3001 \ub300\uc751\uc774 \uc27d\uac8c \ub5a0\uc624\ub974\uc9c0\uac00 \uc54a\uc2b5\ub2c8\ub2e4. \uc5ed\uc218\ud568\uc218\ub97c \uc0dd\uac01\ud588\uc5c8\ub294\ub370 $ 0 $ \uc774 \ubb38\uc81c\uac00 \ub418\uc9c0 \uc54a\ub098\uc694? <\/p>\n

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  1. \uc2e4\uc218\uc9d1\ud569\uc758 completeness\ub97c \uae68\ub294 metric\uc774 \ubb50\uac00 \uc788\uc744 \uae4c\uc694? \ub9cc\ub4e4\uae30\uac00 \uc27d\uc9c0 \uc54a\uc744 \uac83 \uac19\ub2e4\ub294 \uc0dd\uac01\uc774..<\/li>\n<\/ol>\n

    A: 2\ubc88\uc5d0 \ub300\ud55c \uc790\ub2f5) \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4\ub294 \uc0dd\uac01\uc774 \ub4ed\ub2c8\ub2e4. \ub9cc\uc57d \uadf8\ub807\ub2e4\uba74, \uc774\ubbf8 compete\ub77c\uace0 \uc548 \uac70\ub9ac\uacf5\uac04\uc740 metric\uc5d0 \uc0c1\uad00\uc5c6\uc774 \ud56d\uc0c1 complete\uc778\uac00\uc694? \ud639\uc2dc, \uc774\uac83\uc744 \uc99d\uba85\ud558\ub294\ub370 metric-equivalence\ub780 \ub140\uc11d\uc774 \uc0ac\uc6a9\ub418\ub098\uc694? 1\ubc88 \uc790\ub2f5) 0\uc744 0\uc5d0 \ub300\uc751\uc2dc\ud0a4\uba74 \ub418\ub124\uc694. \ub530\ub77c\uc11c 1\ub3001 \ub300\uc751 \uc874\uc7ac! \uc774 \uc0ac\uc2e4\uacfc \uc544\ub798 \uc9c8\ubb38\uc5d0 \ub300\ud55c \uad50\uc218\ub2d8\uc758 \ub2f5\uc5d0 \uadfc\uac70\ud574 2\ubc88\uc790\ub2f5\uc758 \ucd94\uac00\uc9c8\ubb38\uc774 \ud574\uacb0\ub41c \uac70 \uac19\uc544\uc694. \uc9c8\ubb38\uc790\uccb4\uac00 \uc798\ubabb\ub41c \uc9c8\ubb38! \uc544\ub798\uc758 \uad50\uc218\ub2d8\uc758 \ub2f5\ucc98\ub7fc metric\uc5d0 \ub530\ub77c completion\uc774 \ub2ec\ub77c\uc9c0\ub124\uc694. <\/p>\n

    A: \uc704\uc758 \ub2f5\uc740 \ub300\ubd80\ubd84 \ub9de\uc544\uc694. \ub2e8\uc9c0 2\ubc88\uc740 \uadf8\ub0e5 \ubaa8\ub4e0 \ub450 \uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\uac00 1\uc778 metric\uc744 \uc0dd\uac01\ud558\ub294\ub370 \ub2e8\uc9c0 \uc774 \uc911\uc5d0\uc11c $ \\{ 1\/n \\} $ \ub9cc \ub530\ub85c \uc6d0\ub798\ub300\ub85c\uc758 \uac70\ub9ac\ub97c \uc8fc\uace0 \uc774 \uc218\uc5f4\uc5d0\uc11c \ub2e4\ub978 \uc810\ub4e4\uae4c\uc9c0\uc758 \uac70\ub9ac\ub294 \uadf8\ub0e5 1\uc744 \uc8fc\uae30\ub85c \ud558\uba74 \uc774\uac83\uc740 complete\ud558\uc9c0 \uc54a\uc744 \uac83 \uac19\uc740\ub370. – \uae40\uc601\uc6b1. <\/p>\n

    Q: \uc2e4\uc218 \uc9d1\ud569\uc5d0\uc11c \ubaa8\ub4e0 \ucf54\uc2dc \uc218\uc5f4\uc774 \uc218\ub834\ud55c\ub2e4\ub294 \uac83\uc744 \uc99d\uba85\ud560 \ub54c metric\uc744 Spanier\uc758 \uac15\uc758\ub85d 60\ucabd\uc5d0 \ub098\uc628 \uac83\ucc98\ub7fc \uad6c\uccb4\uc801\uc73c\ub85c \uc7a1\uc544\uc11c \uc99d\uba85\uc744 \ud574\uc57c\ud558\ub098\uc694? completenesss\ub294 metric\uc744 \uc5b4\ub5bb\uac8c \uc8fc\ub0d0\uc5d0 \ub530\ub77c\uc11c \ubcc0\ud560 \uc218 \uc788\ub294\uac74\uac00\uc694? 2012.5.24 2011160168 \uae40\uc9c0\uc218 <\/p>\n

    A: completeness\ub294 metric\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9d1\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uad6c\uac04 $ [0,1) $ \uc740 $ [0,∞) $ \uc640 \ub611\uac19\uc740 \uc9d1\ud569\uc5d0 \uac70\ub9ac\ub9cc \ubc14\uafb8\uc5c8\ub2e4\uace0 \uc0dd\uac01\ud574\ub3c4 \ub429\ub2c8\ub2e4. 1\ub3001\ub300\uc751\uc744 \ub9cc\ub4e4 \uc218 \uc788\uc9c0\uc694? \uadf8\ub7f0\ub370 \uc55e\uc758 \uc720\ud55c\uad6c\uac04\uc740 complete\uac00 \uc544\ub2c8\uace0 \ub4a4\uc758 \ubb34\ud55c\uad6c\uac04\uc740 complete\uc785\ub2c8\ub2e4. – \uae40\uc601\uc6b1. <\/p>\n

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    Q: \uc5b8\uce74\uc6b4\ud130\ube14 \uc9d1\ud569\ub3c4 well-ordering\ud55c \uc2ec\ud50c\uc624\ub354\ub97c \uac00\uc9c8 \uc218 \uc788\ub2e4\uba74, \uc774 \uc9d1\ud569 \uc140 \uc218 \uc788\uc9c0 \uc54a\uc744 \uae4c\uc694? \uc774\ub807\uac8c\uc694: \uc138\ub294 \ubc29\ubc95 : n |——–—> the n-th smallest element <\/p>\n

    \uc544\uc2dc\ub294 \ubd84\ub4e4 \ub2f5\uc744 \uc880 \uc8fc\uc2dc\uaca0\uc5b4\uc694. <\/p>\n

    A: \uadf8\ub807\uac8c \uac04\ub2e8\ud558\uac8c \uc140 \uc218\ub294 \uc5c6\ub2f5\ub2c8\ub2e4. countable \uc9d1\ud569\uc778\ub370 \uc21c\uc11c\ub294 \uc790\uc5f0\uc218\uc9d1\ud569\uc744 \ub450 \uac1c \uc5f0\uc18d\ud574\uc11c \ub298\uc5b4\ub193\uc740 \uac83\uc744 \uc0dd\uac01\ud574\ubcf4\uc9c0\uc694. \uc989 1, 2, 3, …, 1, 2, 3, … \uac19\uc774 \ubb34\ud55c\uc774 \ub9ce\uc774 \ub298\uc5b4\ub193\ub294 \uac83\uc744 \ub450 \ubc88 \ud55c \uac83\uc785\ub2c8\ub2e4. \uc774\uac83\ub3c4 Well-ordered\uc785\ub2c8\ub2e4. \uadf8\ub7f0\ub370 \uc774\uac83\uc744 \uadf8\ub0e5 \ub298\uc5b4\ub193\uc740\ucc44\ub85c \uc140 \uc218 \uc788\ub098\uc694? \uc774\ub300\ub85c\ub294 \uc140 \uc218 \uc5c6\uc9c0\uc694? \uc21c\uc11c\ub97c \uc798 \ubc14\uafb8\uc5b4 \ub193\uc544\uc57c\ub9cc \uc790\uc5f0\uc218\ud558\uace0 \uc21c\uc11c\ub300\ub85c 1\ub3001\ub300\uc751\uc774 \ub9cc\ub4e4\uc5b4\uc9c0\uc9c0\uc694? uncountable\uc774\uba74 well-ordering\uc744 \uc2dc\ucf1c \ub193\uc544\ub3c4 \ud6e8\uc52c \ubcf5\uc7a1\ud560 \uac83\uc774\uace0 \uc774 \uacbd\uc6b0\ub294 \uc5b4\ub5bb\uac8c \uc21c\uc11c\ub97c \ubc14\uafb8\uc5b4 \ubcf4\uc544\ub3c4 \uc140 \uc218 \uc5c6\ub2f5\ub2c8\ub2e4. – \uae40\uc601\uc6b1. <\/p>\n

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    Q: 54\ucabd \uc608\uc81c 2.1\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4. \uacf5\ub9ac $ x = y ⇒ d(x – y) = 0 $ \uc744 \ubcf4\uc774\ub294 \ub370 \uc788\uc5b4\uc11c \uc5b4\ub824\uc6c0\uc744 \uacaa\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc544\ub9c8\ub3c4, \ub450 \uc218\uc5f4\uc758 \uac19\uc74c\uc774 \ud655\uc2e4\ud788 \uc815\uc758\uac00 \ub418\uc9c0 \uc54a\uc544\uc11c \uc778 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \ucf54\uc2dc\uc218\uc5f4\ub4e4\uc758 \uc0c1\ub4f1\uc870\uac74\uc744 \ub530\ub974\uace0 \uc2f6\uc9c0\ub9cc, \ub9cc\uc57d \uadf8\ub807\uac8c \ud55c\ub2e4\uba74 \ub2e4\uc74c\uc774 \ubb38\uc81c\uc77c \uac83 \uac19\uc2b5\ub2c8\ub2e4. <\/p>\n

    { $ x_n $ } = { $ y_n $ } does not imply $ \\mbox{sup}|x_n – y_n| = 0 $ because if $ x_1 – y_1 = 1 $ and $ \\mbox{lim}(x_n – y_n) = 0 $ , $ \\mbox{sup} >= 1. $ <\/p>\n

    \uc5b4\ub5bb\uac8c \ud574\uacb0\ud574\uc57c \ud560\uae4c\uc694? \uc81c\uac00 \uc2e4\uc218\ud558\uac70\ub098 \ub193\uce5c \ubd80\ubd84\uc774 \ubb34\uc5bc\uae4c\uc694? <\/p>\n

    A: \uc608 2.1\uc758 \uc218\uc5f4\uc740 \ucf54\uc2dc \uc218\uc5f4 \uc544\ub2d9\ub2c8\ub2e4. \uc774 \uc608\uc5d0\uc11c \ub450 \uc218\uc5f4\uc758 \uac19\uc74c(\uc0c1\ub4f1)\uc740 \ub450 \uc218\uc5f4\uc758 \ubaa8\ub4e0 $ n $ \ubc88\uc9f8 \ud56d\uc774 \uc11c\ub85c \uac19\ub2e4\ub294 \uac83\uc785\ub2c8\ub2e4. <\/p>\n

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    Q.topology\ucc45\uc744 \uacf5\ubd80\ud558\ub2e4 \uc758\ubb38\uc774 \ub4e4\uc5b4 \uc9c8\ubb38\uc744 \uc62c\ub9bd\ub2c8\ub2e4. P.19\uc544\ub798 \ubd80\ubd84\uc5d0 A0\uac00 f-(f(A0))\uc5d0 \ud3ec\ud568 and f-(f(B0))\uac00 b0\uc5d0 \ud3ec\ud568 \ub41c\ub2e4. (-\ub294 \uc5ed\ud568\uc218\ub97c \ub098\ud0c0\ub0b8 \uac83\uc785\ub2c8\ub2e4) \ub77c\ub294 \ubd80\ubd84\uc774 \uc788\ub294\ub370\uc694. \uc55e\uc758 \uac83\uc774 f\uac00 injective\ub77c\ub294 \uac83\uc744 \ub4a4\uc758 \uac83\uc774 f\uac00 surjective\ub77c\ub294 \uac83\uc744 \ub9d0\ud574\uc900\ub2e4\uace0 \ud558\ub294\ub370\uc694. \ucc45\uc758 \uc758\ub3c4\ub294 \uc774\ud574\uac00 \uac11\ub2c8\ub2e4\ub9cc \uc5ed\ud568\uc218\uac00 \uc131\ub9bd\ub41c\ub2e4\ub294 \uac83\uc740 bijective\ub77c\ub294 \uac83\uc774 \uac00\uc815\ub418\uc5b4 \uc788\ub294 \uac83\uc778\ub370 \uc774\ub807\uac8c \ud45c\ud604\ud558\ub294 \uac83\uc740 \ubb38\uc81c\uac00 \ub418\uc9c0\ub294 \uc54a\ub294\uac00\uc694? 2012.4.13. 2010160047 \uc774\uacbd\ud654 <\/p>\n

    A: \uc6b0\uc120 19\ucabd\uc758 \ub9e8 \ubc11\uc758 7\uc904\uc744 \ubc88\uc5ed\ud574 \uc904\uac8c\uc694… <\/p>\n

    \uc8fc\uc758\uac00 \ud544\uc694\ud55c \ub610 \ud558\ub098\uc758 \uc0c1\ud669\uc73c\ub85c\uc11c, \ub450 \ub4f1\uc2dd $ f^{-1}(f(A_0))=A_0 $ \uc640 $ f(f^{-1}(B_0))=B_0 $ \uc740 \ud56d\uc0c1 \uc131\ub9bd\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4. (\ub2e4\uc74c \uc608\ub97c \ubcfc \uac83) \uc774 \uc0c1\ud669\uc5d0 \ub9de\ub294 \uc81c\ub300\ub85c\ub41c \uaddc\uce59\uc740 \uc544\ub798\uc640 \uac19\uace0 \uc774\uc758 \uc99d\uba85\uc740 \ub3c5\uc790\uac00 \uc9c1\uc811 \ud574 \ubcf4\uae30 \ubc14\ub780\ub2e4: $ f: A → B $ \uc774\uace0 $ A_0⊂ A $ , $B_0 ⊂ B $ \uc774\ub77c\uba74 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4. \\[ A_0 \\subset f^{-1} (f( A_0 ))\\] \uc774\uace0 \\[ f ( f^{-1} ( B_0 )) \\subset B_0 . \\] \uc774 \ub450 \ud3ec\ud568\uad00\uacc4\uc5d0\uc11c $ f $ \uac00 injective\uc774\uba74 \uccab\ubc88\uc9f8 \ud3ec\ud568\uad00\uacc4\ub97c \ub4f1\ud638\ub85c \ubc14\uafb8\uc5b4\ub3c4 \ucc38\uc774\uace0, $ f $ \uac00 surjective\uc774\uba74 \ub450 \ubc88\uc9f8 \ud3ec\ud568\uad00\uacc4\ub97c \ub3d9\ud638\ub85c \ubc14\uafb8\uc5b4\ub3c4 \ucc38\uc774\ub2e4. <\/p>\n

    \uadf8\ub7ec\ub2c8\uae4c \ud558\uace0 \uc2f6\uc740 \ub9d0\uc740 $ f^{-1} $ \uc740 \uc77c\ubc18\uc801\uc778 \uacbd\uc6b0\uc5d0 (\uc989 $ f $ \uac00 bijection\uc774 \uc544\ub2cc \uacbd\uc6b0\uc5d0) \uc9d1\ud569\uc758 \uc5ed\uc0c1\uc744 \ub098\ud0c0\ub0b8\ub2e4\uace0 \ubcf4\uc544\uc57c \ud569\ub2c8\ub2e4. \uc774 \uacbd\uc6b0\uc5d0\ub3c4 \ubb3c\ub860 \uadf8\ub807\uace0\uc694. 19\ucabd \uc815\uc758 \uc544\ub798 \uc2dc\uc791\ubd80\ubd84\uc5d0\uc11c $ f $ \uac00 bijection\uc778 \uacbd\uc6b0\uc5d0\ub294 $ f^{-1} $ \ub97c \uc5ed\ud568\uc218\ub85c \ud574\uc11d\ud558\ub098 \uc5ed\uc0c1\uc73c\ub85c \ud574\uc11d\ud558\ub098 \ub611\uac19\uc740 \uac83\uc774\ub77c\uace0 \ud588\uc9c0\uc694? \ud558\uc9c0\ub9cc bijection\uc774 \uc544\ub2cc \uacbd\uc6b0\uc5d0\ub294 \uc5ed\ud568\uc218\ub294 \uc815\uc758\ub418\uc9c0 \uc54a\uace0 \uc5ed\uc0c1\ub9cc \uc815\uc758\ub418\ub2c8\uae4c \ubaa8\ub4e0 \uacbd\uc6b0\uc5d0 \uc5ed\uc0c1\uc774\ub77c\uace0 \ud574\uc11d\ud558\uba74 \uc544\ubb34 \ubb38\uc81c\uac00 \uc5c6\uac8c \ub418\uaca0\uc9c0\uc694? <\/p>\n

    \n

    Q: \uc218\uc5c5 \uc2dc\uac04\uc5d0 “\uc88c\ud45c\uac00 \uc120(\uc9c1\uc120)\uc774\ub2e4”\ub77c\uace0 \ub9d0\uc500\ud574 \uc8fc\uc168\ub294\ub370, \uc608\ub97c\ub4e4\uba74 \uc774\ub7f0 \ub73b\uc785\uac00\uc694? given (1,2), a set A = {c(1,2) | c in R) <\/p>\n

    \uc88c\ud45c\uac00 \uc120\uc774\ub2e4\ub77c\ub294 \ub9d0\uc774 \uc798 \uc774\ud574\uac00 \ub418\uc9c0 \uc54a\uc544\uc694. \ud55c \uc88c\ud45c\ub294 \uc120\uc740 \ubb3c\ub860 \uc6d0\uc774\ub098 \ud3ec\ubb3c\uc120 \ub4f1 \uc5ec\ub7ec \uace1\uc120\uc5d0 \ud3ec\ud568\ub420 \uc218 \uc788\uc796\uc544\uc694. 2010160189 \ubc15\uc815\uaddc <\/p>\n

    A: \uc544\ub9c8\ub3c4 \uc88c\ud45c\uac00 1\ucc28\ud568\uc218\uc774\uace0 1\ucc28\ud568\uc218\ub294 \uc9c1\uc120\uc744 \ub098\ud0c0\ub0b8\ub2e4\uace0 \ub9d0\ud588\uaca0\uc9c0\uc694. $ x $ \ub77c\ub294 \uc88c\ud45c\ub97c \uc0dd\uac01\ud560 \ub54c\ub294 \uc774\ub807\uac8c \ud574\uc694. \uc810 $ P $ \uac00 \uc788\uc744 \ub54c $ P $ \uc758 $ x $ \uc88c\ud45c \uc989 $ x(P) $ \ub294 $ P $ \ub97c \ubcc0\uc218\ub85c \ubcfc \ub54c (\ub530\ub77c\uc11c \uc815\uc758\uc5ed\uc740 \ud3c9\uba74), 1\ucc28\ud568\uc218\uc774\uc9c0\uc694. $ x=1x + 0y $ \ub77c\ub294 1\ucc28\ud568\uc218\uc608\uc694. \uadf8\ub7ec\ub2c8\uae4c \uc774\ub7f0 \uc77c\ucc28\ud568\uc218\uac00 \uc788\uc73c\uba74 \ub2f9\uc5f0\ud788 \uc774\uac83\uc740 $ x=c $ \ub77c\ub294 \uc9c1\uc120\ub4e4\uc744 \uc815\uc758\ud558\uc9c0\uc694. \uadf8\ub7ec\ub2c8\uae4c \uc77c\ucc28\ud568\uc218\uac00 \uc788\ub2e4\ub294 \uac83\uc740 \uc5b4\ub5a4 \uc885\ub958\uc758 \uc9c1\uc120\ub4e4\uc744 \uc548\ub2e4\ub294 \uac83\uc774\uace0, \uadf8\ub7ec\ub2c8\uae4c \uc88c\ud45c\ud568\uc218\ub3c4 \ub2f9\uc5f0\ud788 \uc5b4\ub5a4 \uc885\ub958\uc758 \uc9c1\uc120\ub4e4\uc744 \uc0dd\uac01\ud558\ub294 \uac83\uacfc \uac19\uc544\uc694. \uc774 \uacbd\uc6b0\uc5d0 \uc9c1\uc120\uc740 \uc88c\ud45c\ucd95\uc5d0 \ud3c9\ud589\ud55c \uc9c1\uc120\ub4e4\uc774\uace0 \uc774 \uc9c1\uc120\uc744 \ub530\ub77c \uac00\ubcf4\uba74 \uc815\uc0ac\uc601\uc744 \ud558\uac8c \ub418\uc9c0\uc694. \uc544\ub9c8 \uc774\ub7f0 \uc124\uba85\uc744 \ud588\uc5c8\uc8e0? \uadf8\ub7ec\ub2c8\uae4c $ x=c $ \ub77c\ub294 \uc9c1\uc120\uc740 $ \\{ (c,y) | y∈ \\mathbb{R} \\} $ \ub4e4\uc758 \ubaa8\uc784\uc774\uc8e0. – \uae40\uc601\uc6b1. <\/p>\n

    \n

    Q: \ubb38\ud06c\ub808\uc2a4\ub294 \uad50\uc7ac 15\ucabd\uc5d0\uc11c “\ubc30\uc815\uaddc\uce59(a rule of assignment)”\ub97c \uc11c\uc220\uc2dd\uc73c\ub85c \uc815\uc758\ud588\uc2b5\ub2c8\ub2e4. \uadf8\ub7f0\ub370, \uc774 \uc815\uc758 \uc804\uae4c\uc9c0 \uc815\uc758\ud55c \uac83\ub4e4\ub9cc\uc744 \uac00\uc9c0\uace0\ub3c4 \uc774 \uaddc\uce59\uc744 \uc548\uc804(formal)\ud558\uac8c \uc815\uc758\ud560 \uc218 \uc788\uc744\uae4c\uc694? 16\ucabd \ub9e8 \uc717\uc904\uc5d0 \uac04\ub2e8\ud558\uac8c \ub2f5\uc744 \uc900 \uac83 \uac19\uc9c0\ub9cc, d = d’\ub77c\ub294 \uac83\uc740 \ub3d9\uce58\uad00\uacc4\uac00 \uba3c\uc800 \uc18c\uac1c\ub418\uc57c \ud5c8\uc6a9\ub420 \uc218 \uc788\uc744 \uac83 \uac19\ub2e4\ub294 \uc0dd\uac01\uc774 \ub4ed\ub2c8\ub2e4. \ub9cc\uc57d, \ubd88\uac00\ub2a5\ud558\ub2e4\uba74, \uc801\uc5b4\ub3c4 1\uc7a5 \ub9cc\ud07c\uc740 “\ub17c\ub9ac\uc801 \uc21c\uc11c”\ub77c\ub294 \uac1c\ub150\uc744 \uc811\uc5b4 \ub123\uc5b4\uc57c \ub420\uae4c\uc694? \uc65c \uc800\uc790\ub294 \uad00\uacc4\ubcf4\ub2e4 \ud568\uc218\ub97c \uba3c\uc800 \uace0\ub824\ud588\uc744\uae4c\uc694? <\/p>\n