{"id":9473,"date":"2025-10-20T17:16:11","date_gmt":"2025-10-20T08:16:11","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9473"},"modified":"2025-10-21T16:07:06","modified_gmt":"2025-10-21T07:07:06","slug":"ch01-real-number-system","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-analysis\/ch01-real-number-system\/","title":{"rendered":"\uc2e4\uc218\uacc4\uc758 \uc131\uc9c8"},"content":{"rendered":"
<\/p>\n

<\/p>\n

\uc774 \uc7a5\uc5d0\uc11c\ub294 \uc2e4\uc218\uacc4\ub97c \uc644\ube44\uc21c\uc11c\uccb4\ub85c \uc815\uc758\ud558\uace0 \uadf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n

\uc21c\uc11c\uccb4<\/h3>\n

\uc9d1\ud569 \\(F\\)\uc5d0 \ub367\uc148\uacfc \uacf1\uc148\uc774 \uc815\uc758\ub418\uc5b4 \uc788\uace0, \uc774 \uc5f0\uc0b0\uc774 \ub2e4\uc74c \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0ac \ub54c, \\(F\\)\ub97c \uccb4<\/span>(field)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n

    \n
  1. \ub367\uc148: \uacb0\ud569\ubc95\uce59\uacfc \uad50\ud658\ubc95\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a4\uace0, \ub367\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0 0\uc774 \uc874\uc7ac\ud558\uba70, \uc784\uc758\uc758 \uc6d0\uc18c\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n
  2. \uacf1\uc148: \uacb0\ud569\ubc95\uce59\uacfc \uad50\ud658\ubc95\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a4\uace0, \uacf1\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0 1\uc774 \uc874\uc7ac\ud558\uba70, 0\uc774 \uc544\ub2cc \uc784\uc758\uc758 \uc6d0\uc18c\uc758 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n
  3. \ubd84\ubc30\ubc95\uce59: \uc784\uc758\uc758 \uc6d0\uc18c \\(a\\), \\(b\\), \\(c\\)\uc5d0 \ub300\ud558\uc5ec \\(a(b + c) = ab + ac\\)\uac00 \uc131\ub9bd\ud55c\ub2e4.<\/li>\n<\/ol>\n

    \\(b\\)\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \\(-b\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub610\ud55c \\(a+(-b)\\)\ub97c \uac04\ub2e8\ud788 \\(a-b\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.
    \n\\(b\\neq 0\\)\uc77c \ub54c, \\(b\\)\uc758 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \\(\\frac{1}{b}\\) \ub610\ub294 \\(1\/b\\) \ub610\ub294 \\(b^{-1}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub610\ud55c \\(a\\)\uc640 \\(\\frac{1}{b}\\)\uc758 \uacf1\uc744 \\(\\frac{a}{b}\\) \ub610\ub294 \\(a\/b\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n

    \n

    \ubb38\uc81c 1.1.<\/span>
    \n\\(F\\)\uac00 \uccb4\uc77c \ub54c \ub2e4\uc74c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n

      \n
    1. \\(F\\)\uc5d0\uc11c \ub367\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0\uacfc \uacf1\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0\uc774 \uac01\uac01 \uc720\uc77c\ud558\ub2e4.<\/li>\n
    2. \\(a\\in F\\)\uc77c \ub54c \\(a\\)\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \uc720\uc77c\ud558\ub2e4.<\/li>\n
    3. \\(b\\in F\\)\uc774\uace0 \\(b\\ne 0\\)\uc77c \ub54c \\(b\\)\uc758 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \uc720\uc77c\ud558\ub2e4.<\/li>\n<\/ol>\n<\/div>\n

      \uccb4 \\(F\\)\uc5d0 \uc21c\uc11c \uad00\uacc4 \\(\\leq\\)\uac00 \uc815\uc758\ub418\uc5b4 \uc788\uc73c\uba70 \ub2e4\uc74c \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0ac \ub54c \\(F\\)\ub97c \uc21c\uc11c\uccb4<\/span>(ordered field)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n

        \n
      1. \uc784\uc758\uc758 \\(a,\\, b \\in F\\)\uc5d0 \ub300\ud574 \\(a \\leq b\\) \ub610\ub294 \\(b \\leq a\\)\uc774\ub2e4.<\/li>\n
      2. \\(a \\leq b\\)\uc774\uace0 \\(b \\leq c\\)\uc774\uba74 \\(a \\leq c\\)\uc774\ub2e4.<\/li>\n
      3. \\(a \\leq b\\)\uc774\uace0 \\(b \\leq a\\)\uc774\uba74 \\(a = b\\)\uc774\ub2e4.<\/li>\n
      4. \\(a \\leq b\\)\uc774\uba74 \\(a + c \\leq b + c\\)\uc774\ub2e4.<\/li>\n
      5. \\(a \\leq b\\)\uc774\uace0 \\(0 \\leq c\\)\uc774\uba74 \\(ac \\leq bc\\)\uc774\ub2e4.<\/li>\n<\/ol>\n

        \\(a\\le b\\)\uc774\uba74\uc11c \\(a\\neq b\\)\uc778 \uac83\uc744 \\(a0\\)\uc77c \ub54c \\(a\\)\ub97c \uc591\uc218<\/span>\ub77c\uace0 \ubd80\ub974\uace0, \\(a<0\\)\uc77c \ub54c \\(a\\)\ub97c \uc74c\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4. \uc21c\uc11c\uccb4\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\ub294 \uc591\uc218, \\(0\\), \uc74c\uc218 \uc911 \ud558\ub098\ub85c \uacb0\uc815\ub41c\ub2e4.<\/p>\n

        \uc21c\uc11c\uccb4 \\(F\\)\uc758 \uc6d0\uc18c \\(a\\)\uc758 \uc808\ub313\uac12<\/span> \\(\\lvert a \\rvert\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.
        \n\\[\\lvert a \\rvert =
        \n\\begin{cases}
        \na & \\text{ if }\\, a\\ge 0 ,\\\\[6pt]
        \n-a & \\text{ if }\\, a < 0 .\n\\end{cases}\\]<\/p>\n

        \n

        \ubb38\uc81c 1.2.<\/span>
        \n\uccb4 \\(F\\)\uc758 \uc6d0\uc18c \\(a\\), \\(b\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n

          \n
        1. \\(0\\cdot a = 0\\)<\/li>\n
        2. \\(-a = (-1)\\cdot a\\)<\/li>\n
        3. \\(-(-a)=a\\)<\/li>\n
        4. \\((-a)(-b)=ab\\)<\/li>\n<\/ol>\n<\/div>\n
          \n

          \ubb38\uc81c 1.3.<\/span>
          \n\uc21c\uc11c\uccb4 \\(F\\)\uc758 \uc6d0\uc18c \\(a\\), \\(b\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n

            \n
          1. \\(\\lvert ab \\rvert = \\lvert a \\rvert \\lvert b \\rvert\\).<\/li>\n
          2. \\(\\lvert a+b \\rvert \\le \\lvert a \\rvert + \\lvert b \\rvert\\). (\uc0bc\uac01\ubd80\ub4f1\uc2dd)<\/li>\n
          3. \\(\\lvert \\lvert a \\rvert – \\lvert b \\rvert \\rvert \\le \\lvert a-b \\rvert\\).<\/li>\n<\/ol>\n<\/div>\n
            \n

            \ubb38\uc81c 1.4.<\/span>
            \n\uc21c\uc11c\uccb4\uc758 \uc6d0\uc18c \\(x\\), \\(y\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n

              \n
            1. \\(x \\le y\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uc784\uc758\uc758 \\(\\varepsilon > 0\\)\uc5d0 \ub300\ud558\uc5ec \\(x < y+\\varepsilon\\)\uc778 \uac83\uc774\ub2e4.<\/li>\n
            2. \\(x=0\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uc784\uc758\uc758 \\(\\varepsilon > 0\\)\uc5d0 \ub300\ud558\uc5ec \\(\\lvert x \\rvert < \\varepsilon\\)\uc778 \uac83\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n

              \uc218\ud559\uc5d0\uc11c \uc790\uc8fc \ub2e4\ub8e8\ub294 \ub300\ud45c\uc801\uc778 \uccb4\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uac83\ub4e4\uc774 \uc788\ub2e4.<\/p>\n

                \n
              • \uc720\ub9ac\uc218\uccb4 \\(\\mathbb{Q}\\), \uc2e4\uc218\uccb4 \\(\\mathbb{R}\\), \ubcf5\uc18c\uc218\uccb4 \\(\\mathbb{C}\\)\ub294 \ubaa8\ub450 \uccb4\uc774\ub2e4. \ud2b9\ud788 \\(\\mathbb{Q}\\)\uc640 \\(\\mathbb{R}\\)\uc740 \uc21c\uc11c\uccb4\uc774\ub2e4.<\/li>\n
              • \\(p\\)\uac00 \uc18c\uc218(prime number)\uc774\uace0 \\(\\mathbb{Z}_p = \\left\\{ 0,\\,1,\\,2,\\,\\cdots,\\,p-1 \\right\\}\\)\uc774\ub77c\uace0 \ud558\uc790. \uc5ec\uae30\uc11c \ub367\uc148\uacfc \uacf1\uc148\uc744 \ud1b5\uc0c1\uc801\uc778 \uc815\uc218\uc758 \uc5f0\uc0b0\uc758 \uacb0\uacfc\ub97c \\(p\\)\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub85c \uc815\uc758\ud558\uc790. \uc608\ub97c \ub4e4\uba74 \\(p=5\\)\uc77c \ub54c
                \n\\[\\begin{gathered}
                \n1+0=1,\\quad 1+2=3,\\quad 3+2=0,\\quad 3+4=2,\\quad \\cdots, \\\\[6pt]
                \n1\\cdot 0=0,\\quad 1\\cdot 2=2,\\quad 3\\cdot 2=1,\\quad 3\\cdot 4=2,\\quad \\cdots
                \n\\end{gathered}\\]
                \n\uc774\ub2e4. \uadf8\ub7ec\uba74 \\(\\mathbb{Z}_p\\)\ub294 \uccb4\uc774\ub2e4.<\/li>\n<\/ul>\n

                \uc720\ub9ac\uc218 \uc9d1\ud569 \\(\\mathbb{Q}\\)\ub294 \uc21c\uc11c\uccb4\uc774\ub2e4. \uadf8\ub7ec\ub098 \uc720\ub9ac\uc218 \uc9d1\ud569\uc5d0\uc11c\ub294 \uc720\ub9ac\uc218 \uc218\uc5f4\uc758 \uadf9\ud55c\uc774 \uc720\ub9ac\uc218\uac00 \uc544\ub2d0 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \ud55c\uacc4\ub97c \uadf9\ubcf5\ud558\uae30 \uc704\ud574 \uc644\ube44\uc131<\/span>(completeness)\uc774\ub77c\ub294 \uac1c\ub150\uc774 \ud544\uc694\ud558\ub2e4.<\/p>\n

                \uc0c1\ud55c\uacfc \uc644\ube44\uc131<\/h3>\n

                \uc9d1\ud569 \\(A \\subseteq \\mathbb{R}\\)\uacfc \uc2e4\uc218 \\(M\\), \\(m\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n

                  \n
                • \ubaa8\ub4e0 \\(x \\in A\\)\uc5d0 \ub300\ud574 \\(x \\leq M\\)\uc774\uba74 \\(M\\)\uc744 \\(A\\)\uc758 \uc0c1\uacc4<\/span>(upper bound)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                • \ubaa8\ub4e0 \\(x \\in A\\)\uc5d0 \ub300\ud574 \\(x \\geq m\\)\uc774\uba74 \\(m\\)\uc744 \\(A\\)\uc758 \ud558\uacc4<\/span>(lower bound)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                • \uc9d1\ud569 \\(A\\)\uc758 \uc0c1\uacc4\uac00 \uc874\uc7ac\ud560 \ub54c, “\\(A\\)\ub294 \uc704\ub85c \uc720\uacc4<\/span>\uc774\ub2e4(bounded above)”\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/li>\n
                • \uc9d1\ud569 \\(A\\)\uc758 \ud558\uacc4\uac00 \uc874\uc7ac\ud560 \ub54c, “\\(A\\)\ub294 \uc544\ub798\ub85c \uc720\uacc4<\/span>\uc774\ub2e4(bounded below)”\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/li>\n
                • \uc9d1\ud569 \\(A\\)\uac00 \uc704\ub85c \uc720\uacc4\uc774\uba74\uc11c \uc544\ub798\ub85c \uc720\uacc4\uc77c \ub54c, “\\(A\\)\ub294 \uc720\uacc4<\/span>\uc774\ub2e4(bounded)”\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/li>\n<\/ul>\n

                  \uc9d1\ud569 \\(A\\)\uac00 \uc704\ub85c \uc720\uacc4\uc77c \ub54c, \\(A\\)\uc758 \uc0c1\uacc4\uc758 \ucd5c\uc19f\uac12\uc744 \\(A\\)\uc758 \uc0c1\ud55c<\/span>(supremum) \ub610\ub294 \ucd5c\uc18c\uc0c1\uacc4<\/span>(least upper bound)\ub77c\uace0 \ubd80\ub974\uace0 \\(\\sup A\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc9d1\ud569 \\(A\\)\uac00 \uc544\ub798\ub85c \uc720\uacc4\uc77c \ub54c, \\(A\\)\uc758 \ud558\uacc4\uc758 \ucd5c\ub313\uac12\uc744 \\(A\\)\uc758 \ud558\ud55c<\/span>(infimum) \ub610\ub294 \ucd5c\ub300\ud558\uacc4<\/span>(greatest lower bound)\ub77c\uace0 \ubd80\ub974\uace0 \\(\\inf A\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n

                  \uc989 \uc2e4\uc218 \\(\\alpha\\)\uac00 \uc9d1\ud569 \\(A\\)\uc758 \uc0c1\ud55c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\uc774\ub2e4.<\/p>\n

                    \n
                  • \\(\\alpha\\)\uac00 \\(A\\)\uc758 \uc0c1\uacc4\uc774\ub2e4.<\/li>\n
                  • \\(\\beta\\)\uac00 \\(A\\)\uc758 \uc0c1\uacc4\uc774\uba74, \\(\\alpha \\le \\beta\\)\uc774\ub2e4.<\/li>\n<\/ul>\n

                    \uc2e4\uc218 \\(\\alpha\\)\uac00 \uc9d1\ud569 \\(A\\)\uc758 \uc0c1\ud55c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc744 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\uc73c\ub85c \uc9c4\uc220\ud560 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n

                      \n
                    • \uc784\uc758\uc758 \\(x \\in A\\)\uc5d0 \ub300\ud574 \\(x \\leq \\alpha\\)\uc774\ub2e4.<\/li>\n
                    • \uc784\uc758\uc758 \\(\\varepsilon > 0\\)\uc5d0 \ub300\ud574 \\(\\alpha – \\varepsilon < x\\)\uc778 \\(x \\in A\\)\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<\/ul>\n
                      \n

                      \ubb38\uc81c 1.5.<\/span>
                      \n\uc0c1\ud55c\uc758 \uc720\uc77c\uc131\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc989 \uc9d1\ud569 \\(A\\)\uac00 \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\uace0 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uba70 \\(\\alpha_1\\)\uacfc \\(\\alpha_2\\)\uac00 \\(A\\)\uc758 \uc0c1\ud55c\uc774\uba74 \\(\\alpha_1 = \\alpha_2\\)\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n

                      \n

                      \ubb38\uc81c 1.6.<\/span>
                      \n\\(A\\subseteq\\mathbb{R}\\), \\(A\\ne\\varnothing\\)\uc774\uace0 \\(-A = \\left\\{ -x \\mid x\\in A\\right\\}\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(\\alpha\\)\uac00 \\(A\\)\uc758 \uc0c1\ud55c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(-\\alpha\\)\uac00 \\(-A\\)\uc758 \ud558\ud55c\uc778 \uac83\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n

                      \n

                      \ubb38\uc81c 1.7.<\/span>
                      \n\\(A\\)\uc640 \\(B\\)\uac00 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uace0 \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\uba70 \uc704\ub85c \uc720\uacc4\uc774\uace0, \\(\\alpha = \\sup A\\), \\(\\beta = \\sup B\\)\ub77c\uace0 \ud558\uc790. \ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/p>\n

                        \n
                      1. \\(A+B = \\left\\{ x+y \\mid x\\in A,\\, y\\in B\\right\\}\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(\\sup (A+B) = \\alpha + \\beta\\)\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/li>\n
                      2. \\(A\\)\uc640 \\(B\\)\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\uac00 \\(0\\) \uc774\uc0c1\uc774\uace0 \\(AB = \\left\\{ xy \\mid x\\in A,\\, y\\in B\\right\\}\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(\\sup (AB)=\\alpha \\beta\\)\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n

                        \ub2e4\uc74c \uacf5\ub9ac\ub294 \uc2e4\uc218\uacc4\uc640 \uc720\ub9ac\uc218\uacc4\uc758 \ubcf8\uc9c8\uc801\uc778 \ucc28\uc774\ub97c \uc124\uba85\ud558\ub294 \uc9c4\uc220\uc774\ub2e4.<\/p>\n

                        \n

                        \uacf5\ub9ac (\uc2e4\uc218\uacc4\uc758 \uc644\ube44\uc131).<\/span><\/p>\n

                        \\(A\\)\uac00 \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(A\\)\uac00 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uace0 \uc704\ub85c \uc720\uacc4\uc774\uba74, \\(A\\)\uc758 \uc0c1\ud55c\uc774 \\(\\mathbb{R}\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<\/div>\n

                        \uc644\ube44\uc131\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uccb4\ub97c \uc644\ube44\uccb4<\/span>(complete field)\ub77c\uace0 \ubd80\ub978\ub2e4. \uc644\ube44\uc778 \uc21c\uc11c\uccb4\uac00 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud568\uc774 \uc54c\ub824\uc838 \uc788\ub2e4. \uc644\ube44\uc778 \uc21c\uc11c\uccb4\ub97c \uc2e4\uc218\uacc4<\/span>(real number system)\ub77c\uace0 \ubd80\ub974\uace0 \\(\\mathbb{R}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n

                        \n

                        \ubb38\uc81c 1.8.<\/span>
                        \n\\(B\\)\uac00 \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(B\\)\uac00 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uace0 \uc544\ub798\ub85c \uc720\uacc4\uc774\uba74, \\(B\\)\uc758 \ud558\ud55c\uc774 \\(\\mathbb{R}\\)\uc5d0 \uc874\uc7ac\ud568\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                        \uc9d1\ud569 \\(A\\)\uac00 \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2d0 \ub54c\ub294 \\(A\\)\uc758 \uc0c1\ud55c\uc744 \\(\\infty\\)\ub85c \uc815\uc758\ud55c\ub2e4. \ub610\ud55c \\(A\\)\uac00 \uc544\ub798\ub85c \uc720\uacc4\uac00 \uc544\ub2d0 \ub54c\ub294 \\(A\\)\uc758 \ud558\ud55c\uc744 \\(-\\infty\\)\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\n

                        \uacf5\uc9d1\ud569\uc758 \uc0c1\ud55c\uc740 \ucc45\uc5d0 \ub530\ub77c\uc11c \\(-\\infty\\)\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud558\uace0, \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uac83\uc73c\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud55c\ub2e4. \uacf5\uc9d1\ud569\uc758 \ud558\ud55c \ub610\ud55c \ucc45\uc5d0 \ub530\ub77c\uc11c \\(\\infty\\)\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud558\uace0, \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uac83\uc73c\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n

                        \n

                        \ubb38\uc81c 1.9.<\/span>
                        \n\ub2e4\uc74c \uc9d1\ud569\uc758 \uc0c1\ud55c\uacfc \ud558\ud55c\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n

                          \n
                        1. \\(\\left\\{ 2,\\, 4,\\, 6,\\, 8 \\right\\}\\)<\/li>\n
                        2. \uc5f4\ub9b0\uad6c\uac04 \\((1,\\,3)\\)<\/li>\n
                        3. \\(A = \\{1 – \\frac{1}{n} \\mid n \\in \\mathbb{N}\\}\\)<\/li>\n
                        4. \\(B = (1,\\,3)\\setminus \\mathbb{Q}\\)<\/li>\n<\/ol>\n<\/div>\n

                          \uc790\uc5f0\uc218, \uc815\uc218, \uc720\ub9ac\uc218<\/h3>\n

                          \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(N\\)\uc774 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0ac \ub54c, \\(N\\)\uc744 \uadc0\ub0a9\uc801 \uc9d1\ud569<\/span>(inductive set)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n

                            \n
                          1. \\(1\\in N\\)\uc774\ub2e4.<\/li>\n
                          2. \\(n\\in N\\)\uc774\uba74 \\(n+1\\in N\\)\uc774\ub2e4.<\/li>\n<\/ol>\n

                            \ub610\ud55c \ubaa8\ub4e0 \uadc0\ub0a9\uc801 \uc9d1\ud569\uc758 \uad50\uc9d1\ud569\uc744 \uc790\uc5f0\uc218<\/span> \uc9d1\ud569\uc774\ub77c\uace0 \ubd80\ub974\uace0 \\(\\mathbb{N}\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4. [\ucc45\uc5d0 \ub530\ub77c\uc11c\ub294 \\(0\\) \uc774\uc0c1\uc778 \uc815\uc218\ub97c \uc790\uc5f0\uc218\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4. \uc774 \ub178\ud2b8\uc5d0\uc11c\ub294 \\(1\\) \uc774\uc0c1\uc778 \uc815\uc218\ub97c \uc790\uc5f0\uc218\ub77c\uace0 \ubd80\ub974\uaca0\ub2e4.]<\/p>\n

                            \n

                            \ubb38\uc81c 1.10.<\/span>
                            \n\\(\\phi\\)\uac00 \uc815\uc758\uc5ed\uc774 \\(\\mathbb{N}\\)\uc778 \uba85\uc81c\ud568\uc218\ub77c\uace0 \ud558\uc790. \uc989 \\(\\phi(n)\\)\uc740 \uc790\uc5f0\uc218 \\(n\\)\uc758 \uac12\uc5d0 \ub530\ub77c \ucc38 \ub610\ub294 \uac70\uc9d3\uc774 \uacb0\uc815\ub418\ub294 \uc9c4\uc220\uc774\ub2e4. \\(\\phi\\)\uac00 \ub2e4\uc74c \ub450 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \uac00\uc815\ud558\uc790.<\/p>\n

                              \n
                            1. \\(\\phi(1)\\)\uc774 \ucc38\uc774\ub2e4.<\/li>\n
                            2. \\(\\phi(k)\\)\uac00 \ucc38\uc774\uba74 \\(\\phi(k+1)\\)\ub3c4 \ucc38\uc774\ub2e4.<\/li>\n<\/ol>\n

                              \uc774\ub54c \uc784\uc758\uc758 \uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(\\phi(n)\\)\uc774 \ucc38\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                              \\(n\\)\uc774 \uc790\uc5f0\uc218\uc77c \ub54c \\(-n\\)\uc744 \uc74c\uc758 \uc815\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4. \uc774\ub7ec\ud55c \uad00\uc810\uc5d0\uc11c \uc790\uc5f0\uc218\ub97c \uc591\uc758 \uc815\uc218<\/span>\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4. \uc591\uc758 \uc815\uc218\uc640 \uc74c\uc758 \uc815\uc218, \uadf8\ub9ac\uace0 \\(0\\)\uc744 \ud1b5\ud2c0\uc5b4 \uc815\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4. \ubaa8\ub4e0 \uc815\uc218\uc758 \uc9d1\ud569\uc744 \\(\\mathbb{Z}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n

                              \ub450 \uc815\uc218\uc758 \ube44\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub294 \uc218\ub97c \uc720\ub9ac\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4. \ubb3c\ub860 \\(0\\)\uc758 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc73c\ubbc0\ub85c, \ubd84\ubaa8\uac00 \\(0\\)\uc778 \ube44\ub294 \uc0dd\uac01\ud558\uc9c0 \uc54a\ub294\ub2e4. \ubaa8\ub4e0 \uc720\ub9ac\uc218\uc758 \uc9d1\ud569\uc744 \\(\\mathbb{Q}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \uc989
                              \n\\[\\mathbb{Q} = \\left\\{ \\frac{m}{k} \\,\\Big\\vert\\, m\\in \\mathbb{Z} ,\\, k\\in\\mathbb{Z} ,\\, k\\neq 0 \\right\\} .\\]<\/p>\n

                              \n

                              \ubb38\uc81c 1.11.<\/span>
                              \n\uc790\uc5f0\uc218 \uc9d1\ud569\uc774 \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2d8\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                              \n

                              \ubb38\uc81c 1.12.<\/span>
                              \n\\(A\\)\uac00 \\(\\mathbb{Z}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\uace0 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uba70 \uc704\ub85c \uc720\uacc4\uc77c \ub54c, \\(A\\)\uc758 \uc0c1\ud55c\uc774 \\(\\mathbb{Z}\\)\uc5d0 \uc874\uc7ac\ud568\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                              \n

                              \ubb38\uc81c 1.13.<\/span>
                              \n\ubcf5\uc18c\uc218\uacc4(complex number system)\uc758 \uc815\uc758\ub97c \uc870\uc0ac\ud558\uc2dc\uc624.<\/p>\n<\/div>\n

                              \uc2e4\uc218\uc5f4\uc758 \uadf9\ud55c<\/h3>\n

                              \uc2e4\uc218\uc5f4 \\(\\{a_n\\}\\)\uc774 \uc2e4\uc218 \\(L\\)\ub85c \uc218\ub834<\/span>\ud55c\ub2e4(converge)\ub294 \uac83\uc740, \uc784\uc758\uc758 \\(\\varepsilon > 0\\)\uc5d0 \ub300\ud574 \uc790\uc5f0\uc218 \\(N\\)\uc774 \uc874\uc7ac\ud558\uc5ec \\(n > N\\)\uc77c \ub54c \\(|a_n – L| < \\varepsilon\\)\uc774 \uc131\ub9bd\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc774\uac83\uc744 \uae30\ud638\ub85c \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.\n\\[\\lim_{n \\to \\infty} a_n = L \\quad\\text{ \ub610\ub294 }\\quad a_n \\to L.\\]<\/p>\n

                              \uc218\ub834\ud558\ub294 \uc218\uc5f4\uc758 \uadf9\ud55c\uc740 \uc720\uc77c\ud558\ub2e4. \uc989 \\(a_n \\to L\\)\uc774\uace0 \\(a_n \\to M\\)\uc774\ub77c\uace0 \ud558\uc790. \uc784\uc758\uc758 \\(\\varepsilon > 0\\)\uc5d0 \ub300\ud574, \ucda9\ubd84\ud788 \ud070 \\(n\\)\uc774 \uc874\uc7ac\ud558\uc5ec \\(|a_n – L| < \\frac{\\varepsilon}{2}\\)\uc774\uace0 \\(|a_n - M| < \\frac{\\varepsilon}{2}\\)\uc774\ub2e4. \uc774\ub54c \uc0bc\uac01\ubd80\ub4f1\uc2dd\uc5d0 \uc758\ud574\n\\[|L - M| \\leq |L - a_n| + |a_n - M| < \\varepsilon\\]\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \uc5ec\uae30\uc11c \\(\\varepsilon\\)\uc774 \uc784\uc758\uc758 \uc591\uc218\uc774\ubbc0\ub85c \\(L = M\\)\uc774\ub2e4.<\/p>\n

                              \uc2e4\uc218 \\(M\\)\uc774 \uc874\uc7ac\ud558\uc5ec \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\le M\\)\uc77c \ub54c, “\\(\\left\\{ a_n \\right\\}\\)\uc774 \uc704\ub85c \uc720\uacc4<\/span>\uc774\ub2e4(bounded above)”\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc2e4\uc218 \\(m\\)\uc774 \uc874\uc7ac\ud558\uc5ec \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\ge m\\)\uc77c \ub54c, “\\(\\left\\{ a_n \\right\\}\\)\uc774 \uc544\ub798\ub85c \uc720\uacc4<\/span>\uc774\ub2e4(bounded below)”\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc218\uc5f4\uc774 \uc704\ub85c \uc720\uacc4\uc774\uba74\uc11c \uc544\ub798\ub85c \uc720\uacc4\uc77c \ub54c “\uc218\uc5f4\uc774 \uc720\uacc4\uc774\ub2e4”\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc989 \uc218\uc5f4\uc774 \uc720\uacc4\ub77c\ub294 \uac83\uc740 \uadf8 \uc218\uc5f4\uc758 \ubaa8\ub4e0 \ud56d\uc744 \uc6d0\uc18c\ub85c \uac16\uace0 \uae38\uc774\uac00 \uc720\ud55c\uc778 \uad6c\uac04\uc774 \uc874\uc7ac\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n

                              \n

                              \ubb38\uc81c 1.14.<\/span>
                              \n\uc218\ub834\ud558\ub294 \uc218\uc5f4\uc774 \uc720\uacc4\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                              \uc0ac\uce59\uacc4\uc0b0 \ubc0f \uc21c\uc11c\uad00\uacc4\uc640 \uad00\ub828\ud558\uc5ec, \uc218\uc5f4\uc758 \uadf9\ud55c\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc131\uc9c8\uc744 \uac00\uc9c4\ub2e4.<\/p>\n

                                \n
                              • \uc120\ud615\uc131: \\(c\\)\uc640 \\(d\\)\uac00 \uc0c1\uc218\uc774\uace0 \\(a_n \\to A\\), \\(b_n \\to B\\)\uc774\uba74 \\(ca_n + db_n \\to cA + dB\\)\uc774\ub2e4.<\/li>\n
                              • \uacf1\uc758 \uadf9\ud55c: \\(a_n \\to A\\), \\(b_n \\to B\\)\uc774\uba74 \\(a_n b_n \\to AB\\)\uc774\ub2e4.<\/li>\n
                              • \ubaab\uc758 \uadf9\ud55c: \\(a_n \\to A\\), \\(b_n \\to B \\neq 0\\)\uc774\uba74 \\(a_n\/b_n \\to A\/B\\)\uc774\ub2e4.<\/li>\n
                              • \uc21c\uc11c \ubcf4\uc874: \\(a_n \\leq b_n\\)\uc774\uace0 \\(a_n \\to A\\), \\(b_n \\to B\\)\uc774\uba74 \\(A \\leq B\\)\uc774\ub2e4.<\/li>\n
                              • \uc0cc\ub4dc\uc704\uce58 \uc815\ub9ac: \\(a_n \\leq b_n \\leq c_n\\)\uc774\uace0 \\(a_n \\to L\\), \\(c_n \\to L\\)\uc774\uba74 \\(b_n \\to L\\)\uc774\ub2e4.<\/li>\n<\/ul>\n
                                \n

                                \ubb38\uc81c 1.15.<\/span>
                                \n\uc704 \uc131\uc9c8\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc989 \uadf9\ud55c \uc120\ud615\uc131, \uacf1\uc758 \uadf9\ud55c, \ubaab\uc758 \uadf9\ud55c, \uc21c\uc11c \ubcf4\uc874 \uc131\uc9c8\uacfc \uc0cc\ub4dc\uc704\uce58 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\n<\/div>\n

                                \uc218\uc5f4 \\(\\left\\{ a_n \\right\\}\\)\uc774 \uc5b4\ub5a0\ud55c \uc2e4\uc218\uc5d0\ub3c4 \uc218\ub834\ud558\uc9c0 \uc54a\uc744 \ub54c, “\\(\\left\\{ a_n \\right\\}\\)\uc774 \ubc1c\uc0b0<\/span>\ud55c\ub2e4(diverge)”\ub77c\uace0 \ub9d0\ud55c\ub2e4. \ubc1c\uc0b0\ud558\ub294 \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \ubd84\ub958\ud55c\ub2e4.<\/p>\n

                                  \n
                                • \uc784\uc758\uc758 \\(M > 0\\)\uc5d0 \ub300\ud574 \uc790\uc5f0\uc218 \\(N\\)\uc774 \uc874\uc7ac\ud558\uc5ec \\(n > N\\)\uc77c \ub54c \\(a_n > M\\)\uc774\uba74 “\\(\\left\\{ a_n \\right\\}\\)\uc774 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0<\/span>\ud55c\ub2e4”\ub77c\uace0 \ub9d0\ud558\uace0, \uc774\uac83\uc744 \\(\\displaystyle\\lim_{n\\rightarrow\\infty} a_n = \\infty\\) \ub610\ub294 \\(a_n \\rightarrow \\infty\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n
                                • \uc784\uc758\uc758 \\(M > 0\\)\uc5d0 \ub300\ud574 \uc790\uc5f0\uc218 \\(N\\)\uc774 \uc874\uc7ac\ud558\uc5ec \\(n > N\\)\uc77c \ub54c \\(a_n < -M\\)\uc774\uba74 \"\\(\\left\\{ a_n \\right\\}\\)\uc774 \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0<\/span>\ud55c\ub2e4”\ub77c\uace0 \ub9d0\ud558\uace0, \uc774\uac83\uc744 \\(\\displaystyle\\lim_{n\\rightarrow\\infty} a_n = -\\infty\\) \ub610\ub294 \\(a_n \\rightarrow -\\infty\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n
                                • \uc218\uc5f4\uc774 \uc218\ub834\ud558\uc9c0 \uc54a\uace0, \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0 \uc54a\uace0, \uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\uc9c0\ub3c4 \uc54a\uc744 \ub54c, “\uc218\uc5f4\uc774 \uc9c4\ub3d9<\/span>\ud55c\ub2e4(oscillate)”\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/li>\n<\/ul>\n

                                  \uc644\ube44\uc131\uacfc \uad00\ub828 \uc815\ub9ac\ub4e4<\/h3>\n

                                  \uc720\uacc4\uc778 \uc218\uc5f4\uc774 \ud56d\uc0c1 \uc218\ub834\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \ub2e8\uc870\uc774\uba74\uc11c \uc720\uacc4\uc778 \uc218\uc5f4\uc740 \ubc18\ub4dc\uc2dc \uc218\ub834\ud55c\ub2e4.<\/p>\n

                                  \uc218\uc5f4 \\(\\left\\{ a_n \\right\\}\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n

                                    \n
                                  • \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\le a_{n+1}\\)\uc774 \uc131\ub9bd\ud558\uba74 \\(\\left\\{ a_n \\right\\}\\)\uc744 \ub2e8\uc870\uc99d\uac00<\/span>\ud558\ub294 \uc218\uc5f4\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                                  • \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n < a_{n+1}\\)\uc774 \uc131\ub9bd\ud558\uba74 \\(\\left\\{ a_n \\right\\}\\)\uc744 \uc21c\uc99d\uac00<\/span>\ud558\ub294 \uc218\uc5f4\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                                  • \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\ge a_{n+1}\\)\uc774 \uc131\ub9bd\ud558\uba74 \\(\\left\\{ a_n \\right\\}\\)\uc744 \ub2e8\uc870\uac10\uc18c<\/span>\ud558\ub294 \uc218\uc5f4\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                                  • \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n > a_{n+1}\\)\uc774 \uc131\ub9bd\ud558\uba74 \\(\\left\\{ a_n \\right\\}\\)\uc744 \uc21c\uac10\uc18c<\/span>\ud558\ub294 \uc218\uc5f4\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n
                                  • \ub2e8\uc870\uc99d\uac00\ud558\ub294 \uc218\uc5f4\uacfc \ub2e8\uc870\uac10\uc18c\ud558\ub294 \uc218\uc5f4\uc744 \ud1b5\ud2c0\uc5b4 \ub2e8\uc870\uc218\uc5f4<\/span>(monotone sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<\/ul>\n
                                    \n

                                    \uc815\ub9ac 1.1. (\ub2e8\uc870\uc218\ub834 \uc815\ub9ac)<\/span><\/p>\n

                                    \uc218\uc5f4 \\(\\left\\{ a_n \\right\\}\\)\uc774 \ub2e8\uc870\uc218\uc5f4\uc774\uace0 \uc720\uacc4\uc774\uba74, \\(\\left\\{ a_n \\right\\}\\)\uc740 \uc218\ub834\ud55c\ub2e4.<\/p>\n<\/div>\n

                                    \n

                                    \uc99d\uba85<\/p>\n

                                    \\(\\left\\{ a_n \\right\\}\\)\uc774 \ub2e8\uc870\uc99d\uac00\ud558\ub294 \uacbd\uc6b0\ub9cc \uc99d\uba85\ud574\ub3c4 \ucda9\ubd84\ud558\ub2e4.<\/p>\n

                                    \uc9d1\ud569 \\(A = \\{a_n \\mid n \\in \\mathbb{N}\\}\\)\uc774 \uc704\ub85c \uc720\uacc4\uc774\ubbc0\ub85c \uc0c1\ud55c \\(\\alpha = \\sup A\\)\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n

                                    \\(\\varepsilon > 0\\)\uc774\ub77c\uace0 \ud558\uc790. \uc0c1\ud55c\uc758 \uc131\uc9c8\uc5d0 \uc758\ud574 \uc790\uc5f0\uc218 \\(N\\)\uc774 \uc874\uc7ac\ud558\uc5ec \\(\\alpha – \\varepsilon < a_N \\le \\alpha\\)\uc774\ub2e4. \\(\\left\\{ a_n \\right\\}\\)\uc774 \ub2e8\uc870\uc99d\uac00\ud558\ubbc0\ub85c \\(n > N\\)\uc77c \ub54c \\(\\alpha – \\varepsilon < a_N \\leq a_n \\leq \\alpha\\) \uc989 \\( | a_n - \\alpha | < \\varepsilon\\)\uc774\ub2e4. \ub530\ub77c\uc11c \\(a_n \\to \\alpha\\)\uc774\ub2e4.<\/p>\n

                                    \ub9cc\uc57d \\(\\left\\{a_n\\right\\}\\)\uc774 \ub2e8\uc870\uac10\uc18c\ud558\ub294 \uc218\uc5f4\uc774\ub77c\uba74 \\(b_n = -a_n\\)\uc73c\ub85c \uc815\uc758\ub41c \\(\\left\\{ b_n \\right\\}\\)\uc774 \ub2e8\uc870\uc99d\uac00\ud558\uace0 \uc720\uacc4\uc778 \uc218\uc5f4\uc774\ubbc0\ub85c \uc218\ub834\ud55c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(\\left\\{ a_n \\right\\}\\)\ub3c4 \uc218\ub834\ud55c\ub2e4.<\/span><\/p>\n<\/div>\n

                                    \ub2e8\uc870\uc218\ub834 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc790\uc5f0\uc0c1\uc218<\/span> \\(e\\)\ub97c \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \uc989 \\(e_n = \\left(1 + \\frac{1}{n}\\right)^n\\)\uc774\ub77c\uace0 \uc815\uc758\ub41c \uc218\uc5f4 \\(\\left\\{ e_n \\right\\}\\)\uc740 \ub2e8\uc870\uc99d\uac00\ud558\uace0 \uc704\ub85c \uc720\uacc4\uc774\ubbc0\ub85c \uc218\ub834\ud55c\ub2e4. \uc774 \uadf9\ud55c\uc744 \\(e\\)\ub85c \uc815\uc758\ud55c\ub2e4. \uc989
                                    \n\\[e = \\lim_{n \\to \\infty} \\left(1 + \\frac{1}{n}\\right)^n = 2.718281828459045\\cdots .\\]<\/p>\n

                                    \n

                                    \ubb38\uc81c 1.16.<\/span>
                                    \n\\(e_n = \\left(1 + \\frac{1}{n}\\right)^n\\)\uc774\ub77c\uace0 \uc815\uc758\ub41c \uc218\uc5f4 \\(\\left\\{ e_n \\right\\}\\)\uc774 \ub2e8\uc870\uc774\uace0 \uc720\uacc4\uc784\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<\/div>\n

                                    \ub2e4\uc74c \uc815\ub9ac\ub294 \uae38\uc774\uac00 \\(0\\)\uc73c\ub85c \uc218\ub834\ud558\ub294 \ub2eb\ud78c \ucd95\uc18c\uad6c\uac04\uc758 \uc5f4\uc758 \uad50\uc9d1\ud569\uc774 \ub2e8 \ud558\ub098\uc758 \uc6d0\uc18c\ub97c \uac00\uc9c4\ub2e4\ub294 \uc131\uc9c8\uc744 \uc124\uba85\ud55c\ub2e4.<\/p>\n

                                    \n

                                    \uc815\ub9ac 1.2. (\ucd95\uc18c\uad6c\uac04 \uc815\ub9ac)<\/span><\/p>\n

                                    \ub2eb\ud78c\uad6c\uac04\uc758 \uc218\uc5f4 \\(\\{[a_n,\\, b_n]\\}\\)\uc774 \ub2e4\uc74c\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ud558\uc790.<\/p>\n