{"id":9256,"date":"2025-10-17T20:01:18","date_gmt":"2025-10-17T11:01:18","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9256"},"modified":"2026-09-27T11:51:56","modified_gmt":"2026-09-27T02:51:56","slug":"ch06-natural-numbers","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch06-natural-numbers\/","title":{"rendered":"\uc790\uc5f0\uc218"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p>\uc9d1\ud569\uc758 \uae30\ubcf8 \uc131\uc9c8 \uc911 \ud558\ub098\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\uc758 \uac1c\uc218\uc774\ub2e4. \uc720\ud55c\uc9d1\ud569\uc758 \uacbd\uc6b0 \uc6d0\uc18c\uc758 \uac1c\uc218\ub97c \uc790\uc5f0\uc218\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uc9c0\ub9cc, \ubb34\ud55c\uc9d1\ud569\uc758 \ud06c\uae30\ub97c \ub2e4\ub8e8\ub824\uba74 \ub354 \uc815\uad50\ud55c \uac1c\ub150\uc774 \ud544\uc694\ud558\ub2e4. \uce78\ud1a0\uc5b4\ub294 19\uc138\uae30 \ub9d0 \ubb34\ud55c\uc758 \ud06c\uae30\ub97c \uccb4\uacc4\uc801\uc73c\ub85c \uc5f0\uad6c\ud558\uba74\uc11c \uae30\uc218\uc640 \uc11c\uc218\ub77c\ub294 \ud601\uc2e0\uc801\uc778 \uac1c\ub150\uc744 \ub3c4\uc785\ud588\ub2e4. \uc774\uac83\uc740 \uc218\ud559\uc5d0\uc11c \ubb34\ud55c\uc744 \ub2e4\ub8e8\ub294 \ubc29\uc2dd\uc744 \uc644\uc804\ud788 \ubc14\uafb8\uc5b4 \ub193\uc558\ub2e4.<\/p>\n<p>\uae30\uc218(cardinal number)\ub294 \uc9d1\ud569\uc758 \ud06c\uae30 \ub610\ub294 \uc6d0\uc18c\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uac1c\ub150\uc774\ub2e4. \ub450 \uc9d1\ud569 \uc0ac\uc774\uc5d0 \uc77c\ub300\uc77c\ub300\uc751\uc774 \uc874\uc7ac\ud558\uba74 \uac19\uc740 \uae30\uc218\ub97c \uac00\uc9c4\ub2e4\uace0 \ub9d0\ud55c\ub2e4. \uc774\uac83\uc740 \uc720\ud55c\uc9d1\ud569\ubfd0\ub9cc \uc544\ub2c8\ub77c \ubb34\ud55c\uc9d1\ud569\uc5d0\ub3c4 \uc801\uc6a9\ub418\uc5b4, \uc11c\ub85c \ub2e4\ub978 \ud06c\uae30\uc758 \ubb34\ud55c\uc774 \uc874\uc7ac\ud568\uc744 \ubcf4\uc5ec\uc900\ub2e4. \ud55c\ud3b8 \uc11c\uc218(ordinal number)\ub294 \uc9d1\ud569\uc758 \uc21c\uc11c \uad6c\uc870\ub97c \ub098\ud0c0\ub0b4\ub294 \uac1c\ub150\uc73c\ub85c, \ubb34\ud55c\uc9d1\ud569\ub3c4 \uc801\uc808\ud788 \uc21c\uc11c\ub97c \ubd80\uc5ec\ud558\uba74 \uadf8 \uc21c\uc11c \uc720\ud615\uc744 \uc11c\uc218\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\ud765\ubbf8\ub86d\uac8c\ub3c4 \ubaa8\ub4e0 \uc790\uc5f0\uc218\ub294 \uc720\ud55c\uae30\uc218\uc778 \ub3d9\uc2dc\uc5d0 \uc720\ud55c\uc11c\uc218\uc774\ub2e4. \uc608\ub97c \ub4e4\uba74, \uc790\uc5f0\uc218 \\(3\\)\uc740 \uc138 \uac1c\uc758 \uc6d0\uc18c\ub97c \uac00\uc9c4 \uc9d1\ud569\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 \uae30\uc218\uc774\uba74\uc11c, \ub3d9\uc2dc\uc5d0 \uc138 \ubc88\uc9f8 \uc704\uce58\uae4c\uc9c0\uc758 \uc21c\uc11c\ub97c \ub098\ud0c0\ub0b4\ub294 \uc11c\uc218\uc774\uae30\ub3c4 \ud558\ub2e4. \uc774 \ubd80\uc5d0\uc11c\ub294 \uba3c\uc800 \uc9d1\ud569\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc790\uc5f0\uc218\ub97c \uad6c\uc131\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf8 \ud6c4, \uc774\uac83\uc744 \ubc14\ud0d5\uc73c\ub85c \uae30\uc218\uc640 \uc11c\uc218\uc758 \uac1c\ub150\uc744 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<p><!-- \n\n<h2>6. \uc790\uc5f0\uc218<\/h2>\n\n --><\/p>\n<p>\uc55e \uc7a5\uae4c\uc9c0\ub294 \uc790\uc5f0\uc218 \uc9d1\ud569 \\(\\mathbb{N}\\)\uc744 \uc775\uc219\ud55c \uc218\uc758 \uc9d1\ud569\uc73c\ub85c \uc0ac\uc6a9\ud558\uc600\ub2e4. \uc774 \uc7a5\uc5d0\uc11c\ub294 \uc790\uc5f0\uc218\ub97c \uc9d1\ud569\uc73c\ub85c \uad6c\uc131\ud558\uace0, \uc790\uc5f0\uc218\uc758 \uc5f0\uc0b0\uacfc \uc21c\uc11c\ub97c \uc815\uc758\ud558\uba70, \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc758 \uc6d0\ub9ac\ub97c \uc0b4\ud3b4\ubcf8\ub2e4. \uc774 \uacfc\uc815\uc5d0\uc11c \uc790\uc5f0\uc218 \uc9d1\ud569\uc758 \uc874\uc7ac\uc640 \uc7ac\uadc0\uc801 \uc815\uc758\uc5d0 \ud544\uc694\ud55c \uc9d1\ud569\ub860\uc801 \uc0ac\uc2e4\ub3c4 \ud568\uaed8 \uba85\uc2dc\ud55c\ub2e4.<\/p>\n<h3>1. \uc9d1\ud569\uc744 \uc0ac\uc6a9\ud55c \uc790\uc5f0\uc218\uc758 \uc815\uc758<\/h3>\n<p><span class=\"defined\">\ud3f0 \ub178\uc774\ub9cc<\/span>(von Neumann)\uc758 \ubc29\ubc95\uc744 \ub530\ub77c \uc790\uc5f0\uc218\ub97c \uad6c\uc131\ud574 \ubcf4\uc790. \uba3c\uc800 \\(0\\)\uc744 \uacf5\uc9d1\ud569\uc73c\ub85c \uc815\uc758\ud558\uace0, \uc774\ubbf8 \ub9cc\ub4e0 \uc790\uc5f0\uc218 \\(n\\)\uc5d0\uc11c \ub530\ub984\uc218 \\(S(n)\\)\uc744 \ubc18\ubcf5\ud558\uc5ec \ub2e4\uc74c \uc790\uc5f0\uc218\ub97c \ub9cc\ub4e0\ub2e4. \ucc98\uc74c \uba87 \ub2e8\uacc4\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\n0 &#038;= \\varnothing = \\{\\},\\\\[3pt]<br \/>\n1 &#038;= \\{0\\} = \\{\\varnothing\\},\\\\[3pt]<br \/>\n2 &#038;= \\{0,\\,1\\} = \\{\\varnothing,\\,\\{\\varnothing\\}\\},\\\\[3pt]<br \/>\n3 &#038;= \\{0,\\,1,\\,2\\} = \\{\\varnothing,\\,\\{\\varnothing\\},\\,\\{\\varnothing,\\,\\{\\varnothing\\}\\}\\},\\\\[3pt]<br \/>\n&#038;\\vdots<br \/>\n\\end{aligned}\\]<\/p>\n<p>\uc77c\ubc18\uc801\uc73c\ub85c, \uc790\uc5f0\uc218 \\(n\\)\uc758 <span class=\"defined\">\ub530\ub984\uc218<\/span>(successor) \\(S(n)\\)\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[S(n)=n\\cup\\{n\\}.\\]<br \/>\n\uc9c1\uad00\uc801\uc73c\ub85c \\(S(n)\\)\uc740 \\(n\\)\uc758 \ub2e4\uc74c \uc218, \uc989 \\(n+1\\)\uc744 \ub098\ud0c0\ub0b4\ub294 \uac83\uc73c\ub85c \uc0dd\uac01\ud574\ub3c4 \ubb34\ubc29\ud558\ub2e4. \uc608\ub97c \ub4e4\uc5b4,<\/p>\n<ul>\n<li>\\(S(0)=\\varnothing\\cup\\{\\varnothing\\}=\\{\\varnothing\\}=1\\),<\/li>\n<li>\\(S(1)=\\{0\\}\\cup\\{\\{0\\}\\}=\\{0,\\,1\\}=2\\),<\/li>\n<li>\\(S(2)=\\{0,\\,1\\}\\cup\\{\\{0,\\,1\\}\\}=\\{0,\\,1,\\,2\\}=3\\).<\/li>\n<\/ul>\n<p>\uac01 \ub2e8\uacc4\uc5d0\uc11c \ub9cc\ub4e4\uc5b4\uc9c0\ub294 \uc790\uc5f0\uc218\ub294 \uc790\uc2e0\ubcf4\ub2e4 \uc55e\uc5d0\uc11c \ub9cc\ub4e4\uc5b4\uc9c4 \uc790\uc5f0\uc218\ub4e4\uc744 \uc6d0\uc18c\ub85c \uac16\ub294\ub2e4. \ub4a4\uc758 \uc21c\uc11c \uad00\uacc4 \uc808\uc5d0\uc11c\ub294 \uc774\ub97c \uc774\uc6a9\ud558\uc5ec \\(m&lt;n\\)\uc744 \\(m\\in n\\)\uc73c\ub85c \uc815\uc758\ud558\uace0, \\(m\\le n\\)\uacfc \ubd80\ubd84\uc9d1\ud569 \uad00\uacc4\uc758 \uad00\uacc4\ub97c \uc99d\uba85\ud55c\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.1.<\/span><br \/>\n\ud3f0 \ub178\uc774\ub9cc\uc758 \uc790\uc5f0\uc218 \uad6c\uc131\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(4=S(3)\\)\uacfc \\(5=S(4)\\)\ub97c \\(0,\\,1,\\,2,\\,3,\\,4\\)\ub97c \uc6d0\uc18c\ub85c \uc0ac\uc6a9\ud558\uc5ec \ub098\ud0c0\ub0b4\uc2dc\uc624.<\/li>\n<li>\ub2e4\uc74c \uac01 \uba85\uc81c\uc758 \ucc38\uacfc \uac70\uc9d3\uc744 \ud310\uc815\ud558\uc2dc\uc624.<br \/>\n\\[<br \/>\n0\\in3,\\quad 2\\in3,\\quad 3\\in3,\\quad 2\\subseteq3,\\quad 3\\subseteq2.<br \/>\n\\]\n<\/li>\n<li>\\(S(S(2))\\)\ub97c \uacc4\uc0b0\ud558\uace0 \\(4\\)\uc640 \ube44\uad50\ud558\uc2dc\uc624.<\/li>\n<li>\\(m,n\\in\\{0,\\,1,\\,2,\\,3\\}\\)\uc5d0 \ub300\ud558\uc5ec \\(m\\in n\\)\uc778 \uc21c\uc11c\uc30d \\((m,\\,n)\\)\uc744 \ubaa8\ub450 \uad6c\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<p>\uc9d1\ud569 \\(N\\)\uc774 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0ac \ub54c \\(N\\)\uc744 <span class=\"defined\">\uadc0\ub0a9\uc801 \uc9d1\ud569<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<ul>\n<li>\\(0\\in N\\)\uc774\ub2e4.<\/li>\n<li>\\(n\\in N\\)\uc77c \ub54c\ub9c8\ub2e4 \\(S(n)\\in N\\)\uc774\ub2e4.<\/li>\n<\/ul>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.2.<\/span><br \/>\n\ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\{0,\\,1,\\,2\\}\\)\ub294 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc778\uac00? \uadf8 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<li>\\(\\mathbb N\\setminus\\{2\\}\\)\ub294 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc778\uac00? \uadf8 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<li>\\(N\\)\uc774 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774\uba74 \\(0,\\,1,\\,2,\\,3,\\,4\\in N\\)\uc784\uc744 \ub530\ub984\uc218\uc758 \uc815\uc758\ub97c \uc0ac\uc6a9\ud558\uc5ec \ubcf4\uc774\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<p>\uc774\uc81c \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774 \uc801\uc5b4\ub3c4 \ud558\ub098 \uc874\uc7ac\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uc790. \uc774 \uac00\uc815\uc740 \uc55e \uc7a5\uc758 \uc9d1\ud569 \uc5f0\uc0b0\ub9cc\uc73c\ub85c\ub294 \uc99d\uba85\ud560 \uc218 \uc5c6\uc73c\uba70, \uacf5\ub9ac\uc801 \uc9d1\ud569\ub860\uc5d0\uc11c\ub294 <a href=\"\/blog\/invitation-to-mathematical-logic\/ch09-axiomatic-set-theory\/\">\ubb34\ud55c \uacf5\ub9ac<\/a>\ub85c \ubcf4\uc7a5\ub41c\ub2e4. \uadc0\ub0a9\uc801 \uc9d1\ud569 \ud558\ub098\ub97c \\(I\\)\ub77c \ud558\uace0<br \/>\n\\[\\mathcal I=\\{J\\subseteq I\\mid J\\text{\ub294 \uadc0\ub0a9\uc801 \uc9d1\ud569}\\}\\]<br \/>\n\ub85c \ub450\uc790. \\(I\\in\\mathcal I\\)\uc774\ubbc0\ub85c \\(\\mathcal I\\)\ub294 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\ub2e4. \uc774\ub54c<br \/>\n\\[\\mathbb N=\\bigcap_{J\\in\\mathcal I}J\\]<br \/>\n\ub85c \uc815\uc758\ud558\uace0 \uc774\ub97c <span class=\"defined\">\uc790\uc5f0\uc218 \uc9d1\ud569<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ub610\ud55c \\(\\omega\\)\ub85c\ub3c4 \ub098\ud0c0\ub0b8\ub2e4. [\ucd08\uc911\ub4f1 \uad50\uc721\uacfc\uc815\uc5d0\uc11c\ub294 \\(1\\) \uc774\uc0c1\uc778 \uc815\uc218\ub97c \uc790\uc5f0\uc218\ub77c\uace0 \ubd80\ub974\uc9c0\ub9cc \uc9d1\ud569\ub860\uc5d0\uc11c\ub294 \\(0\\) \uc774\uc0c1\uc778 \uc815\uc218\ub97c \uc790\uc5f0\uc218\ub77c\uace0 \ubd80\ub978\ub2e4. \uacf5\ub9ac\uc801 \uc9d1\ud569\ub860\uc5d0\uc11c \uc704 \uc9d1\ud569\uc871\uc744 \uc2e4\uc81c \uc9d1\ud569\uc73c\ub85c \ub9cc\ub4dc\ub294 \uacfc\uc815\uc5d0\ub294 \uba71\uc9d1\ud569 \uacf5\ub9ac\uc640 \ubd84\ub9ac \uacf5\ub9ac\uaf34\uc774 \uc0ac\uc6a9\ub41c\ub2e4.] \uc774 \uc815\uc758\ub294 \ucc98\uc74c \ud0dd\ud55c \uadc0\ub0a9\uc801 \uc9d1\ud569 \\(I\\)\uc5d0 \uc758\uc874\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc989 \\(\\mathbb N\\)\uc740 \ubaa8\ub4e0 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub418\ub294 \uac00\uc7a5 \uc791\uc740 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774\ub2e4. \uc6d0\uc18c\ub098\uc5f4\ubc95\uc73c\ub85c \uc4f0\uba74<br \/>\n\\[\\mathbb N=\\{0,\\,1,\\,2,\\,3,\\,4,\\,\\ldots\\}.\\]<\/p>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 6.3.<\/span><br \/>\n\uacf5\uc9d1\ud569\uc774 \uc544\ub2cc \uadc0\ub0a9\uc801 \uc9d1\ud569\uc871\uc758 \uad50\uc9d1\ud569\uc774 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc774\ub97c \uc774\uc6a9\ud558\uc5ec \uc704\uc5d0\uc11c \uc815\uc758\ud55c \\(\\mathbb N\\)\uc774 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774\uace0 \ubaa8\ub4e0 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub428\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n<h3>2. \uc218\ud559\uc801 \uadc0\ub0a9\ubc95<\/h3>\n<p>\ub2e4\uc74c \uc6d0\ub9ac\ub97c <span class=\"defined\">\uc218\ud559\uc801 \uadc0\ub0a9\ubc95<\/span>(mathematical induction)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 6.1. (\uc218\ud559\uc801 \uadc0\ub0a9\ubc95)<\/span><\/p>\n<p>\uc790\uc5f0\uc218\uc5d0 \ub300\ud55c \uba85\uc81c \\(P(n)\\)\uc774 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\uba74 \ubaa8\ub4e0 \uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(P(n)\\)\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uae30\ucd08 \ub2e8\uacc4<\/span>: \\(P(0)\\)\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\uadc0\ub0a9 \ub2e8\uacc4<\/span>: \uc784\uc758\uc758 \uc790\uc5f0\uc218 \\(k\\)\uc5d0 \ub300\ud558\uc5ec \\(P(k)\\)\uac00 \uc131\ub9bd\ud558\uba74 \\(P(S(k))\\)\ub3c4 \uc131\ub9bd\ud55c\ub2e4.<\/li>\n<\/ul>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 6.4.<\/span><br \/>\n\uc790\uc5f0\uc218 \uc9d1\ud569\uc774 \uac00\uc7a5 \uc791\uc740 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774\ub77c\ub294 \uc0ac\uc2e4\uc744 \uc774\uc6a9\ud558\uc5ec \uc815\ub9ac 6.1\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<p>\uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uacfc \uc9dd\uc744 \uc774\ub8e8\ub294 \uc815\uc758 \uc6d0\ub9ac\ub97c <span class=\"defined\">\uc7ac\uadc0\uc801 \uc815\uc758<\/span>(recursive definition)\ub77c\uace0 \ubd80\ub978\ub2e4. \uc7ac\uadc0\uc801\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uaddc\uce59\uc774 \uc2e4\uc81c\ub85c \ud558\ub098\uc758 \ud568\uc218\ub97c \uc815\uc758\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc740 \ubcc4\ub3c4\uc758 \uc815\ub9ac\ub97c \ud544\uc694\ub85c \ud55c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 6.2. (\uc790\uc5f0\uc218 \uc704\uc758 \uc7ac\uadc0 \uc815\ub9ac)<\/span><\/p>\n<p>\uc9d1\ud569 \\(A\\), \uc6d0\uc18c \\(a\\in A\\), \ud568\uc218 \\(F\\colon A\\to A\\)\uac00 \uc8fc\uc5b4\uc9c0\uba74<br \/>\n\\[f(0)=a,\\quad f(S(n))=F(f(n))\\]<br \/>\n\uc744 \ubaa8\ub4e0 \\(n\\in\\mathbb N\\)\uc5d0 \ub300\ud558\uc5ec \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud568\uc218 \\(f\\colon\\mathbb N\\to A\\)\uac00 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<\/div>\n<p>\uc774 \uc815\ub9ac\uc758 \uc5c4\ubc00\ud55c \uc9d1\ud569\ub860\uc801 \uc99d\uba85\uc740 \uc5ec\ub7ec \uc9d1\ud569 \uc874\uc7ac \uacf5\ub9ac\ub97c \uc0ac\uc6a9\ud558\ubbc0\ub85c \uc5ec\uae30\uc11c\ub294 \uc99d\uba85 \uc5c6\uc774 \uc0ac\uc6a9\ud55c\ub2e4. \uc544\ub798\uc758 \ub367\uc148, \uacf1\uc148, \uac70\ub4ed\uc81c\uacf1\uc740 \ubaa8\ub450 \uc774 \uc7ac\uadc0 \uc815\ub9ac\uc5d0 \uc758\ud574 \uc874\uc7ac\uc131\uacfc \uc720\uc77c\uc131\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.5.<\/span><br \/>\n\uc790\uc5f0\uc218 \uc704\uc758 \uc7ac\uadc0 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc815\uc758\ub418\ub294 \ud568\uc218 \\(f\\colon\\mathbb N\\to\\mathbb N\\)\uc774<br \/>\n\\[<br \/>\nf(0)=1,\\quad f(S(n))=S(S(f(n)))<br \/>\n\\]<br \/>\n\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ud558\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(f(0),\\,f(1),\\,f(2),\\,f(3),\\,f(4)\\)\ub97c \ucc28\ub840\ub85c \uad6c\ud558\uc2dc\uc624.<\/li>\n<li>\uc774 \uc7ac\uadc0\uc2dd\uc774 \ud568\uc218 \\(f\\)\ub97c \uc720\uc77c\ud558\uac8c \uc815\ud55c\ub2e4\ub294 \uac83\uc744 \uc815\ub9ac 6.2\uc5d0 \ub9de\ucd94\uc5b4 \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<p>\uc790\uc5f0\uc218\uc758 \ud3f0 \ub178\uc774\ub9cc \uad6c\uc131\uc5d0 \uad00\ud558\uc5ec \ub2e4\uc74c \uc131\uc9c8\ub3c4 \uc790\uc8fc \uc0ac\uc6a9\ud55c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\ubcf4\uc870\uc815\ub9ac 6.3. (\uc790\uc5f0\uc218\uc758 \ucd94\uc774\uc131\uacfc \uc790\uae30 \ube44\uc18c\uc18d)<\/span><\/p>\n<p>\ubaa8\ub4e0 \\(n\\in\\mathbb N\\)\uc5d0 \ub300\ud558\uc5ec \\(n\\)\uc740 \ucd94\uc774\uc801 \uc9d1\ud569\uc774\ub2e4. \uc989 \\(x\\in y\\in n\\)\uc774\uba74 \\(x\\in n\\)\uc774\ub2e4. \ub610\ud55c \\(n\\notin n\\)\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofbegin\"><span class=\"proof\">\uc99d\uba85<\/span><br \/>\n\\(n\\)\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \\(n=0\\)\uc77c \ub54c \ub450 \uc8fc\uc7a5\uc740 \uc790\uba85\ud558\ub2e4. \\(n\\)\uc774 \ucd94\uc774\uc801\uc774\uace0 \\(n\\notin n\\)\uc774\ub77c\uace0 \uac00\uc815\ud558\uc790. \\(x\\in y\\in S(n)=n\\cup\\{n\\}\\)\uc774\uba74 \\(y\\in n\\)\uc774\uac70\ub098 \\(y=n\\)\uc774\ub2e4. \uc5b4\ub290 \uacbd\uc6b0\uc5d0\ub3c4 \\(x\\in n\\subseteq S(n)\\)\uc774\ubbc0\ub85c \\(S(n)\\)\uc740 \ucd94\uc774\uc801\uc774\ub2e4.<\/p>\n<p>\uc774\uc81c \\(S(n)\\in S(n)\\)\uc774\ub77c\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub7ec\uba74 \\(S(n)\\in n\\)\uc774\uac70\ub098 \\(S(n)=n\\)\uc774\ub2e4. \ud6c4\uc790\uc774\uba74 \\(n\\in S(n)=n\\)\uc774 \ub418\uc5b4 \ubaa8\uc21c\uc774\ub2e4. \uc804\uc790\uc774\uba74 \\(n\\in S(n)\\in n\\)\uc774\uace0 \\(n\\)\uc758 \ucd94\uc774\uc131\uc5d0 \uc758\ud574 \\(n\\in n\\)\uc774 \ub418\uc5b4 \uc5ed\uc2dc \ubaa8\uc21c\uc774\ub2e4. \ub530\ub77c\uc11c \\(S(n)\\notin S(n)\\)\uc774\ub2e4.<span class=\"qed\"><\/span><\/p>\n<\/div>\n<h3>3. \uc790\uc5f0\uc218\uc758 \ub367\uc148<\/h3>\n<p>\uc790\uc5f0\uc218\uc758 \ub367\uc148\uc744 \uc7ac\uadc0\uc801\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \uc790\uc5f0\uc218 \\(m\\)\uc744 \uace0\uc815\uc2dc\ud0a4\uba74 \uc815\ub9ac 6.2\ub97c \\(a=m\\), \\(F=S\\)\uc5d0 \uc801\uc6a9\ud560 \uc218 \uc788\uc73c\ubbc0\ub85c, \uc784\uc758\uc758 \uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \ub450 \uc2dd\uc5d0 \uc758\ud558\uc5ec \\(m+n\\)\uc774 \uc720\uc77c\ud558\uac8c \uc815\ud574\uc9c4\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\nm+0&#038;=m,\\\\[3pt]<br \/>\nm+S(n)&#038;=S(m+n).<br \/>\n\\end{aligned}\\]<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4, \\(2+2\\)\ub97c \uacc4\uc0b0\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\n2+2&#038;=2+S(1)<br \/>\n=S(2+1)<br \/>\n=S(2+S(0))\\\\[3pt]<br \/>\n&#038;=S(S(2+0))<br \/>\n=S(S(2))<br \/>\n=S(3)<br \/>\n=4.<br \/>\n\\end{aligned}\\]<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.6.<\/span><br \/>\n\ub367\uc148\uc758 \uc815\uc758\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c\uc744 \uacc4\uc0b0\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(3+2\\)<\/li>\n<li>\\(2+3\\)<\/li>\n<li>\\(4+1\\)<\/li>\n<li>\\(1+4\\)<\/li>\n<\/ol>\n<\/div>\n<p>\uc790\uc8fc \uc0ac\uc6a9\ud558\ub294 \ub367\uc148\uc758 \uae30\ubcf8 \uc131\uc9c8\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 6.4. (\uc790\uc5f0\uc218 \ub367\uc148\uc758 \uae30\ubcf8 \ubc95\uce59)<\/span><\/p>\n<p>\uc790\uc5f0\uc218 \\(m,\\,n,\\,p\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li><span class=\"defined\">\uacb0\ud569\ubc95\uce59<\/span>: \\((m+n)+p=m+(n+p)\\)<\/li>\n<li><span class=\"defined\">\uad50\ud658\ubc95\uce59<\/span>: \\(m+n=n+m\\)<\/li>\n<li><span class=\"defined\">\uc18c\uac70\ubc95\uce59<\/span>: \\(m+p=n+p\\)\uc774\uba74 \\(m=n\\)\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.7.<\/span><br \/>\n\uc790\uc5f0\uc218 \\(n,m,p\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624. (7\uc808\uc758 \ub0b4\uc6a9\uc744 \ucc38\uc870\ud558\uc2dc\uc624.)<\/p>\n<ol class=\"parenthesis\">\n<li>\\((n+m)+p=n+(m+p)\\)<\/li>\n<li>\\(n+S(p)=S(n)+p\\)<\/li>\n<li>\\(p+0=0+p\\)<\/li>\n<li>\\(n+1=S(n)\\)<\/li>\n<li>\\(n+p=p+n\\)<\/li>\n<li>\\(n+p=m+p\\)\uc774\uba74 \\(n=m\\)\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<h3>4. \uc790\uc5f0\uc218\uc758 \uacf1\uc148<\/h3>\n<p>\uc790\uc5f0\uc218\uc758 \uacf1\uc148\ub3c4 \uc7ac\uadc0\uc801\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \uc790\uc5f0\uc218 \\(m\\)\uc744 \uace0\uc815\uc2dc\ud0a4\uace0 \uc774\ubbf8 \uc815\uc758\ud55c \ub367\uc148\uc744 \uc0ac\uc6a9\ud558\uba74, \uc815\ub9ac 6.2\uc640 \ub2e4\uc74c \ub450 \uc2dd\uc5d0 \uc758\ud558\uc5ec \\(m\\cdot n\\)\uc774 \uc720\uc77c\ud558\uac8c \uc815\ud574\uc9c4\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\nm\\cdot0&#038;=0,\\\\[3pt]<br \/>\nm\\cdot S(n)&#038;=m\\cdot n+m.<br \/>\n\\end{aligned}\\]<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4, \\(2\\cdot3\\)\uc744 \uacc4\uc0b0\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\n2\\cdot3&#038;=2\\cdot S(2)<br \/>\n=2\\cdot2+2\\\\[3pt]<br \/>\n&#038;=2\\cdot S(1)+2<br \/>\n=(2\\cdot1+2)+2\\\\[3pt]<br \/>\n&#038;=(2\\cdot S(0)+2)+2<br \/>\n=((2\\cdot0+2)+2)+2\\\\[3pt]<br \/>\n&#038;=(0+2)+2+2<br \/>\n=6.<br \/>\n\\end{aligned}\\]<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.8.<\/span><br \/>\n\uacf1\uc758 \uc815\uc758\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c\uc744 \uacc4\uc0b0\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(3\\cdot2\\)<\/li>\n<li>\\(4\\cdot1\\)<\/li>\n<li>\\(1\\cdot3\\)<\/li>\n<li>\\(3\\cdot3\\)<\/li>\n<\/ol>\n<\/div>\n<p>\uc790\uc8fc \uc0ac\uc6a9\ud558\ub294 \uacf1\uc148\uc758 \uae30\ubcf8 \uc131\uc9c8\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 6.5. (\uc790\uc5f0\uc218 \uacf1\uc148\uc758 \uae30\ubcf8 \ubc95\uce59)<\/span><\/p>\n<p>\uc790\uc5f0\uc218 \\(m,n,p\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li><span class=\"defined\">\uacb0\ud569\ubc95\uce59<\/span>: \\((m\\cdot n)\\cdot p=m\\cdot(n\\cdot p)\\)<\/li>\n<li><span class=\"defined\">\uad50\ud658\ubc95\uce59<\/span>: \\(m\\cdot n=n\\cdot m\\)<\/li>\n<li><span class=\"defined\">\ubd84\ubc30\ubc95\uce59<\/span>: \\(m\\cdot(n+p)=m\\cdot n+m\\cdot p\\)\uc774\uace0 \\((m+n)\\cdot p=m\\cdot p+n\\cdot p\\)\uc774\ub2e4.<\/li>\n<li>\ud56d\ub4f1\uc6d0\uc758 \uc131\uc9c8: \\(m\\cdot1=1\\cdot m=m\\)<\/li>\n<li>\\(0\\)\uc758 \uc131\uc9c8: \\(m\\cdot0=0\\cdot m=0\\)<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.9.<\/span><br \/>\n\uc790\uc5f0\uc218 \\(n\\), \\(m\\), \\(p\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(n\\cdot1=n\\)<\/li>\n<li>\\(n\\cdot(m+p)=n\\cdot m+n\\cdot p\\)<\/li>\n<li>\\((n\\cdot m)\\cdot p=n\\cdot(m\\cdot p)\\)<\/li>\n<li>\\(0\\cdot p=0\\)<\/li>\n<li>\\(1\\cdot p=p\\)<\/li>\n<li>\\((1+n)\\cdot p=1\\cdot p+n\\cdot p\\)<\/li>\n<li>\\(n\\cdot p=p\\cdot n\\)<\/li>\n<li>\\((m+p)\\cdot n=m\\cdot n+p\\cdot n\\)<\/li>\n<\/ol>\n<\/div>\n<h3>5. \uc790\uc5f0\uc218\uc758 \uac70\ub4ed\uc81c\uacf1<\/h3>\n<p>\uc790\uc5f0\uc218\uc758 \uac70\ub4ed\uc81c\uacf1\ub3c4 \uc7ac\uadc0\uc801\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \uc790\uc5f0\uc218 \\(m\\)\uc744 \uace0\uc815\uc2dc\ud0a4\uace0 \uc815\ub9ac 6.2\ub97c \uc801\uc6a9\ud558\uba74 \ub2e4\uc74c \ub450 \uc2dd\uc5d0 \uc758\ud558\uc5ec \\(m^n\\)\uc774 \uc720\uc77c\ud558\uac8c \uc815\ud574\uc9c4\ub2e4.<br \/>\n\\[\\begin{aligned}<br \/>\nm^0&#038;=1,\\\\[3pt]<br \/>\nm^{S(n)}&#038;=m^n\\cdot m.<br \/>\n\\end{aligned}\\]<\/p>\n<p>\ud2b9\ubcc4\ud788 \\(0^0=1\\)\ub85c \uc815\uc758\ud55c\ub2e4\ub294 \uc810\uc5d0 \uc8fc\ubaa9\ud558\uc790. \uc774\uac83\uc740 \uc870\ud569\ub860\uacfc \uc9d1\ud569\ub860\uc5d0\uc11c \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uc815\uc758\uc774\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.10.<\/span><br \/>\n\uac70\ub4ed\uc81c\uacf1\uc758 \uc7ac\uadc0\uc801 \uc815\uc758\ub9cc\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c\uc744 \uacc4\uc0b0\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(2^3\\)<\/li>\n<li>\\(3^2\\)<\/li>\n<li>\\(0^0\\)<\/li>\n<li>\\(0^3\\)<\/li>\n<li>\\(1^4\\)<\/li>\n<\/ol>\n<\/div>\n<p>\uc790\uc8fc \uc0ac\uc6a9\ud558\ub294 \uac70\ub4ed\uc81c\uacf1\uc758 \uae30\ubcf8 \uc131\uc9c8\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 6.6. (\uc790\uc5f0\uc218 \uac70\ub4ed\uc81c\uacf1\uc758 \uae30\ubcf8 \ubc95\uce59)<\/span><\/p>\n<p>\uc790\uc5f0\uc218 \\(m,n,a,b\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(m^{a+b}=m^a\\cdot m^b\\)<\/li>\n<li>\\((m^a)^b=m^{a\\cdot b}\\)<\/li>\n<li>\\((m\\cdot n)^a=m^a\\cdot n^a\\)<\/li>\n<li>\\(1^n=1\\)<\/li>\n<li>\\(m^1=m\\)<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 6.11.<\/span><br \/>\n\uc815\ub9ac 6.6\uc758 \ub2e4\uc12f \uc2dd\uc744 \uc790\uc5f0\uc218\uc5d0 \ub300\ud55c \uadc0\ub0a9\ubc95\uc73c\ub85c \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<p>3\uc7a5\uc5d0\uc11c \\(A^B\\)\ub294 \\(B\\)\uc5d0\uc11c \\(A\\)\ub85c \uac00\ub294 \ud568\uc218\ub4e4\uc758 \uc9d1\ud569\uc744 \ub73b\ud558\uc600\ub2e4. \uc790\uc5f0\uc218 \\(m,n\\)\ub3c4 \uc9d1\ud569\uc774\ubbc0\ub85c \uc774 \ud45c\uae30\uc640 \uc0b0\uc220\uc801 \uac70\ub4ed\uc81c\uacf1 \\(m^n\\)\uc774 \uac19\uc740 \ubaa8\uc591\uc73c\ub85c \ub098\ud0c0\ub098\uc9c0\ub9cc, \ub450 \ub300\uc0c1\uc774 \uc9d1\ud569\uc73c\ub85c\uc11c \uac19\ub2e4\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4. \ud63c\ub3d9\uc744 \ud53c\ud558\uae30 \uc704\ud558\uc5ec<br \/>\n\\[\\operatorname{Fun}(n,m)=\\{f\\mid f\\colon n\\to m\\}\\]<br \/>\n\ub85c \uc4f0\uc790.<\/p>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 6.12.<\/span><br \/>\n\uc790\uc5f0\uc218 \\(m,n\\)\uc5d0 \ub300\ud558\uc5ec \\(\\operatorname{Fun}(n,m)\\)\uc740 \uc720\ud55c\uc9d1\ud569\uc774\uace0<br \/>\n\\[|\\operatorname{Fun}(n,m)|=m^n\\]<br \/>\n\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc624\ub978\ucabd\uc758 \\(m^n\\)\uc740 \uc774 \uc808\uc5d0\uc11c \uc7ac\uadc0\uc801\uc73c\ub85c \uc815\uc758\ud55c \uc790\uc5f0\uc218\uc758 \uac70\ub4ed\uc81c\uacf1\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.13.<\/span><br \/>\n\\(2=\\{0,1\\}\\), \\(3=\\{0,1,2\\}\\)\ub85c \ub450\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\ud568\uc218 \\(f\\colon2\\to3\\)\ub97c \uc21c\uc11c\uc30d \\((f(0),f(1))\\)\ub85c \ub098\ud0c0\ub0b4\uc5b4 \ubaa8\ub450 \ub098\uc5f4\ud558\uc2dc\uc624.<\/li>\n<li>\\(|\\operatorname{Fun}(2,3)|=3^2\\)\uc784\uc744 \uc9c1\uc811 \ud655\uc778\ud558\uc2dc\uc624.<\/li>\n<li>\uc77c\ubc18\uc801\uc73c\ub85c \\(n\\)\uc5d0\uc11c \\(m\\)\uc73c\ub85c \uac00\ub294 \ud568\uc218\ub97c \uc815\ud560 \ub54c \uac01 \uc785\ub825\uac12\ub9c8\ub2e4 \uba87 \uac00\uc9c0 \uc120\ud0dd\uc774 \uc788\ub294\uc9c0 \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<h3>6. \ud398\uc544\ub178 \uacf5\ub9ac<\/h3>\n<p><span class=\"defined\">\ud398\uc544\ub178 \uacf5\ub9ac<\/span>(Peano axioms)\ub294 \uc790\uc5f0\uc218\uc758 \ubcf8\uc9c8\uc801 \uc131\uc9c8\uc744 \uc124\uba85\ud558\ub294 \uacf5\ub9ac \uccb4\uacc4\uc774\ub2e4. \uc9d1\ud569 \\(N\\), \uc6d0\uc18c \\(0\\in N\\), \ud568\uc218 \\(S\\colon N\\to N\\)\uc774 \ub2e4\uc74c\uc744 \ub9cc\uc871\uc2dc\ud0ac \ub54c \ud398\uc544\ub178 \uacf5\ub9ac\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ub9d0\ud55c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uacf5\ub9ac 6.7. (\ud398\uc544\ub178 \uacf5\ub9ac)<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\\(0\\in N\\)\uc774\ub2e4.<\/li>\n<li>\\(n\\in N\\)\uc774\uba74 \\(S(n)\\in N\\)\uc774\ub2e4.<\/li>\n<li>\ubaa8\ub4e0 \\(n\\in N\\)\uc5d0 \ub300\ud558\uc5ec \\(S(n)\\ne0\\)\uc774\ub2e4.<\/li>\n<li>\\(S(m)=S(n)\\)\uc774\uba74 \\(m=n\\)\uc774\ub2e4.<\/li>\n<li><span class=\"defined\">\uadc0\ub0a9 \uacf5\ub9ac<\/span>: \\(A\\subseteq N\\)\uc774 \\(0\\in A\\)\uc774\uace0 \\(n\\in A\\)\uc77c \ub54c\ub9c8\ub2e4 \\(S(n)\\in A\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\uba74 \\(A=N\\)\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.14.<\/span><br \/>\n\uc9d1\ud569 \\(N=\\{0,1,2\\}\\)\uc640 \uc6d0\uc18c \\(0\\)\uc744 \uc0dd\uac01\ud558\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\ud568\uc218 \\(S\\colon N\\to N\\)\uc744<br \/>\n\\[<br \/>\nS(0)=1,\\quad S(1)=2,\\quad S(2)=2<br \/>\n\\]<br \/>\n\ub85c \uc815\uc758\ud560 \ub54c, \ud398\uc544\ub178 \uacf5\ub9ac\uc758 \ub2e4\uc12f \uc870\uac74 \uc911 \uc5b4\ub290 \uac83\uc774 \uc131\ub9bd\ud558\uace0 \uc5b4\ub290 \uac83\uc774 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\uc9c0 \ud310\uc815\ud558\uc2dc\uc624.<\/li>\n<li>\ud568\uc218 \\(T\\colon N\\to N\\)\uc744<br \/>\n\\[<br \/>\nT(0)=1,\\quad T(1)=2,\\quad T(2)=0<br \/>\n\\]<br \/>\n\ub85c \uc815\uc758\ud560 \ub54c\ub3c4 \uac19\uc740 \uc9c8\ubb38\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/li>\n<li>\uc704 \ub450 \uc608\uac00 \ud398\uc544\ub178 \uacf5\ub9ac \uc804\uccb4\ub97c \ub9cc\uc871\uc2dc\ud0a4\uc9c0 \ubabb\ud558\ub294 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<p>\ud3f0 \ub178\uc774\ub9cc\uc758 \ubc29\ubc95\uc73c\ub85c \uad6c\uc131\ud55c \\((\\mathbb N,0,S)\\)\ub294 \ud398\uc544\ub178 \uacf5\ub9ac\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4. \uccab\uc9f8\uc640 \ub458\uc9f8 \uacf5\ub9ac\ub294 \\(\\mathbb N\\)\uc774 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc774\ub77c\ub294 \uc0ac\uc2e4\uc5d0\uc11c \ub530\ub978\ub2e4. \uc14b\uc9f8\ub294 \\(S(n)=n\\cup\\{n\\}\\)\uac00 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\ubbc0\ub85c \uc131\ub9bd\ud55c\ub2e4. \ub137\uc9f8\ub97c \ubcf4\uc774\uae30 \uc704\ud558\uc5ec \\(S(m)=S(n)\\)\uc774\ub77c\uace0 \ud558\uc790. \\(m\\in S(m)=S(n)\\)\uc774\uace0 \\(n\\in S(n)=S(m)\\)\uc774\ub2e4. \\(m\\ne n\\)\uc774\uba74 \\(m\\in n\\)\uc774\uace0 \\(n\\in m\\)\uc774\ubbc0\ub85c, \ubcf4\uc870\uc815\ub9ac 6.3\uc5d0 \uc758\ud574 \\(n\\in m\\in n\\)\uc5d0\uc11c \\(n\\in n\\)\uc774 \ub418\uc5b4 \ubaa8\uc21c\uc774\ub2e4. \ub530\ub77c\uc11c \\(m=n\\)\uc774\ub2e4. \ub9c8\uc9c0\ub9c9\uc73c\ub85c \\(A\\subseteq\\mathbb N\\)\uc774 \uadc0\ub0a9\uc801\uc774\uba74 \\(\\mathbb N\\)\uc758 \ucd5c\uc18c\uc131\uc5d0 \uc758\ud574 \\(\\mathbb N\\subseteq A\\)\uc774\uace0, \uc774\ubbf8 \\(A\\subseteq\\mathbb N\\)\uc774\ubbc0\ub85c \\(A=\\mathbb N\\)\uc774\ub2e4.<\/p>\n<h3>7. \uc5f0\uc0b0 \ubc95\uce59\uc758 \uc99d\uba85<\/h3>\n<p>\uc790\uc5f0\uc218\uc758 \uc5f0\uc0b0 \ubc95\uce59\ub4e4\uc740 \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc99d\uba85\ud560 \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \ub367\uc148\uc758 \uacb0\ud569\ubc95\uce59<br \/>\n\\[(m+n)+p=m+(n+p)\\]<br \/>\n\ub294 \\(p\\)\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.<\/p>\n<ul>\n<li><strong>\uae30\ucd08 \ub2e8\uacc4<\/strong>: \\(p=0\\)\uc77c \ub54c, \\((m+n)+0=m+n=m+(n+0)\\).<\/li>\n<li><strong>\uadc0\ub0a9 \ub2e8\uacc4<\/strong>: \\((m+n)+p=m+(n+p)\\)\ub77c\uace0 \uac00\uc815\ud558\uba74,<br \/>\n\\[\\begin{aligned}<br \/>\n(m+n)+S(p)&#038;=S((m+n)+p) &#038;&#038;\\text{(\ub367\uc148\uc758 \uc815\uc758)}\\\\[3pt]<br \/>\n&#038;=S(m+(n+p)) &#038;&#038;\\text{(\uadc0\ub0a9 \uac00\uc815)}\\\\[3pt]<br \/>\n&#038;=m+S(n+p) &#038;&#038;\\text{(\ub367\uc148\uc758 \uc815\uc758)}\\\\[3pt]<br \/>\n&#038;=m+(n+S(p)). &#038;&#038;\\text{(\ub367\uc148\uc758 \uc815\uc758)}<br \/>\n\\end{aligned}\\]\n<\/li>\n<\/ul>\n<p>\ub2e4\ub978 \ubc95\uce59\ub4e4\ub3c4 \uc720\uc0ac\ud55c \ubc29\ubc95\uc73c\ub85c \uc99d\uba85\ud560 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uc99d\uba85\uc740 \uc790\uc5f0\uc218\uc758 \uadc0\ub0a9\uc801 \uad6c\uc870\ub97c \ud65c\uc6a9\ud55c\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.15.<\/span><br \/>\n\ud568\uc218 \\(T\\colon\\mathbb N\\to\\mathbb N\\)\uc744<br \/>\n\\[<br \/>\nT(0)=0,\\quad T(S(n))=T(n)+S(n)<br \/>\n\\]<br \/>\n\uc73c\ub85c \uc7ac\uadc0\uc801\uc73c\ub85c \uc815\uc758\ud558\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(T(0),\\,T(1),\\,T(2),\\,T(3),\\,T(4)\\)\ub97c \uad6c\ud558\uc2dc\uc624.<\/li>\n<li>\ubaa8\ub4e0 \\(n\\in\\mathbb N\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n2\\cdot T(n)=n\\cdot S(n)<br \/>\n\\]<br \/>\n\uc784\uc744 \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc99d\uba85\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<h3>8. \uc21c\uc11c \uad00\uacc4<\/h3>\n<p>\uc790\uc5f0\uc218 \\(m,n\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[m&lt;n\\quad\\Longleftrightarrow\\quad m\\in n\\]<br \/>\n\uc73c\ub85c \uc815\uc758\ud558\uace0, \\(m\\le n\\)\uc740 \\(m&lt;n\\) \ub610\ub294 \\(m=n\\)\uc774\ub77c\ub294 \ub73b\uc73c\ub85c \uc0ac\uc6a9\ud55c\ub2e4. \ud3f0 \ub178\uc774\ub9cc \uc790\uc5f0\uc218\uc5d0\uc11c\ub294 \uc774 \uc21c\uc11c\uac00 \ubd80\ubd84\uc9d1\ud569 \uad00\uacc4\uc640 \uc0b0\uc220\uc801 \ucc28\uc774\uc758 \uc874\uc7ac\ub85c\ub3c4 \ud45c\ud604\ub41c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 6.8. (\uc790\uc5f0\uc218 \uc21c\uc11c\uc758 \uc131\uc9c8)<\/span><\/p>\n<p>\uc790\uc5f0\uc218 \\(m,n\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(m\\le n\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(m\\subseteq n\\)\uc778 \uac83\uc774\ub2e4.<\/li>\n<li>\\(m&lt;n\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uc5b4\ub5a4 \\(k\\in\\mathbb N\\setminus\\{0\\}\\)\uc5d0 \ub300\ud558\uc5ec \\(m+k=n\\)\uc778 \uac83\uc774\ub2e4.<\/li>\n<li>\\(m&lt;n\\), \\(m=n\\), \\(n&lt;m\\) \uc911 \uc815\ud655\ud788 \ud558\ub098\uac00 \uc131\ub9bd\ud55c\ub2e4.<\/li>\n<li>\uacf5\uc9d1\ud569\uc774 \uc544\ub2cc \\(\\mathbb N\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc740 \ucd5c\uc18c\uc6d0\uc18c\ub97c \uac00\uc9c4\ub2e4.<\/li>\n<li>\\(n&lt;S(n)\\)\uc774\ubbc0\ub85c \\(\\mathbb N\\)\uc5d0\ub294 \ucd5c\ub300\uc6d0\uc18c\uac00 \uc5c6\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<p>\uc704 \uc815\ub9ac\uc758 \ub124 \ubc88\uc9f8 \uc131\uc9c8\uc744 <span class=\"defined\">\uc815\ub82c\uc131<\/span>(well-ordering property)\uc774\ub77c\uace0 \ud55c\ub2e4. \ub9c8\uc9c0\ub9c9 \uc131\uc9c8\uc740 \ub2e8\uc21c\ud788 \uc790\uc5f0\uc218 \uc9d1\ud569\uc5d0 \ucd5c\ub300\uc6d0\uc18c\uac00 \uc5c6\ub2e4\ub294 \ub73b\uc774\uba70, \uc2e4\uc218\ub098 \uc21c\uc11c\uccb4\uc5d0\uc11c \ub9d0\ud558\ub294 \uc544\ub974\ud0a4\uba54\ub370\uc2a4 \uc131\uc9c8\uacfc\ub294 \uad6c\ubcc4\ud55c\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.16.<\/span><br \/>\n\ud3f0 \ub178\uc774\ub9cc \uc790\uc5f0\uc218\uc758 \uc21c\uc11c\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(1&lt;4\\), \\(4&lt;1\\), \\(2\\le2\\), \\(3\\le4\\)\uc758 \ucc38\uacfc \uac70\uc9d3\uc744 \uac01\uac01 \ud310\uc815\ud558\uace0, \uc9d1\ud569\uc758 \uc6d0\uc18c \uad00\uacc4 \ub610\ub294 \ubd80\ubd84\uc9d1\ud569 \uad00\uacc4\ub85c \ud655\uc778\ud558\uc2dc\uc624.<\/li>\n<li>\\(2&lt;5\\)\ub97c \\(2\\in5\\), \\(2\\subseteq5\\), \uadf8\ub9ac\uace0 \\(2+k=5\\)\uc778 \\(k\\ne0\\)\uc758 \uc874\uc7ac\ub77c\ub294 \uc138 \uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c \ud655\uc778\ud558\uc2dc\uc624.<\/li>\n<li>\\(n&lt;4\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc790\uc5f0\uc218 \\(n\\)\uc744 \ubaa8\ub450 \uad6c\ud558\uc2dc\uc624. \ub610\ud55c \\(n\\le4\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc790\uc5f0\uc218 \\(n\\)\uc744 \ubaa8\ub450 \uad6c\ud558\uc2dc\uc624.<\/li>\n<li>\uc9d1\ud569 \\(\\{5,\\,2,\\,8,\\,3\\}\\)\uc758 \ucd5c\uc18c\uc6d0\uc18c\ub97c \uad6c\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 6.17.<\/span><br \/>\n\uc815\ub9ac 6.8\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \ud2b9\ud788 \uc815\ub82c\uc131\uc740 \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 6.18.<\/span><br \/>\n\\(\\mathbb N\\times\\mathbb N\\) \uc704\uc758 \uad00\uacc4 \\(\\sim\\)\ub97c<br \/>\n\\[(a,b)\\sim(c,d)\\quad\\Longleftrightarrow\\quad a+d=b+c\\]<br \/>\n\ub85c \uc815\uc758\ud558\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\sim\\)\uac00 \ub3d9\uce58\uad00\uacc4\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/li>\n<li>\ubaab\uc9d1\ud569 \\(\\mathbb Z=(\\mathbb N\\times\\mathbb N)\/\\sim\\)\ub97c \uc0dd\uac01\ud558\uc790. \ub3d9\uce58\ub958 \\([(a,b)]\\)\ub97c \ud615\uc2dd\uc801\uc778 \ucc28 \\(a-b\\)\ub85c \ud574\uc11d\ud560 \uc218 \uc788\uc74c\uc744 \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<li>\\(i\\colon\\mathbb N\\to\\mathbb Z\\), \\(i(n)=[(n,0)]\\)\uc774 \uc77c\ub300\uc77c\ud568\uc218\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/li>\n<li>\ub2e4\uc74c \uc5f0\uc0b0\uc774 \ub300\ud45c\uc6d0\uc758 \uc120\ud0dd\uacfc \ubb34\uad00\ud558\uac8c \uc798 \uc815\uc758\ub428\uc744 \ubcf4\uc774\uc2dc\uc624.<br \/>\n\\[[(a,b)]+[(c,d)]=[(a+c,b+d)],\\]<br \/>\n\\[[(a,b)]\\cdot[(c,d)]=[(ac+bd,ad+bc)].\\]\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"contentbottombox\">\n<p class=\"contentbottomboxtitle\"><a href=\"\/blog\/invitation-to-mathematical-logic\/\">\uc9d1\ud569\uacfc \uc218\ub9ac\ub17c\ub9ac \uccab\uac78\uc74c \ubaa9\ucc28 \ubcf4\uae30<\/a><\/p>\n<p><span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch01-naive-logic\/\">\uba85\uc81c\uc640 \ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch02-sets\">\uc9d1\ud569\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch03-algebra-of-classes\">\ub2e4\uc591\ud55c \uc9d1\ud569\uc758 \uc5f0\uc0b0<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch04-relations-and-functions\">\uad00\uacc4\uc640 \ud568\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch05-infinite-sets\">\uc720\ud55c\uc9d1\ud569\uacfc \ubb34\ud55c\uc9d1\ud569<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch06-natural-numbers\">\uc790\uc5f0\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch07-cardinal-numbers\">\uc9d1\ud569\uc758 \uae30\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch08-ordinal-numbers\">\uc9d1\ud569\uc758 \uc11c\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch09-axiomatic-set-theory\">\uc9d1\ud569\ub860\uc758 \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch10-axiom-of-choice\">\uc120\ud0dd \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch11-formal-logic\">\ud615\uc2dd\ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch12-propositional-logic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch13-soundness-completeness-proplogic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch14-syntax-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch15-semantics-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uc758\ubbf8\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch16-inference-rule-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch17-compactness-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch18-peano-arithmetics\">\ud398\uc544\ub178 \uc0b0\uc220<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch19-incompleteness-theorem\">\ubd88\uc644\uc804\uc131 \uc815\ub9ac<\/a><\/span>\n<\/div>\n<\/div>\n<p><!-- ################## --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc9d1\ud569\uc758 \uae30\ubcf8 \uc131\uc9c8 \uc911 \ud558\ub098\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\uc758 \uac1c\uc218\uc774\ub2e4. \uc720\ud55c\uc9d1\ud569\uc758 \uacbd\uc6b0 \uc6d0\uc18c\uc758 \uac1c\uc218\ub97c \uc790\uc5f0\uc218\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uc9c0\ub9cc, \ubb34\ud55c\uc9d1\ud569\uc758 \ud06c\uae30\ub97c \ub2e4\ub8e8\ub824\uba74 \ub354 \uc815\uad50\ud55c \uac1c\ub150\uc774 \ud544\uc694\ud558\ub2e4. \uce78\ud1a0\uc5b4\ub294 19\uc138\uae30 \ub9d0 \ubb34\ud55c\uc758 \ud06c\uae30\ub97c \uccb4\uacc4\uc801\uc73c\ub85c \uc5f0\uad6c\ud558\uba74\uc11c \uae30\uc218\uc640 \uc11c\uc218\ub77c\ub294 \ud601\uc2e0\uc801\uc778 \uac1c\ub150\uc744 \ub3c4\uc785\ud588\ub2e4. \uc774\uac83\uc740 \uc218\ud559\uc5d0\uc11c \ubb34\ud55c\uc744 \ub2e4\ub8e8\ub294 \ubc29\uc2dd\uc744 \uc644\uc804\ud788 \ubc14\uafb8\uc5b4 \ub193\uc558\ub2e4. \uae30\uc218(cardinal number)\ub294 \uc9d1\ud569\uc758 \ud06c\uae30 \ub610\ub294 \uc6d0\uc18c\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uac1c\ub150\uc774\ub2e4. \ub450 \uc9d1\ud569 \uc0ac\uc774\uc5d0 \uc77c\ub300\uc77c\ub300\uc751\uc774 \uc874\uc7ac\ud558\uba74 \uac19\uc740 \uae30\uc218\ub97c \uac00\uc9c4\ub2e4\uace0 \ub9d0\ud55c\ub2e4. \uc774\uac83\uc740 \uc720\ud55c\uc9d1\ud569\ubfd0\ub9cc \uc544\ub2c8\ub77c&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9246,"menu_order":106,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9256","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9256","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9256"}],"version-history":[{"count":10,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9256\/revisions"}],"predecessor-version":[{"id":10081,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9256\/revisions\/10081"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9246"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}