{"id":3451,"date":"2025-12-24T17:21:22","date_gmt":"2025-12-24T08:21:22","guid":{"rendered":"https:\/\/math-travel.com\/?p=3451"},"modified":"2026-02-11T17:28:00","modified_gmt":"2026-02-11T08:28:00","slug":"real-number","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-1\/real-number\/","title":{"rendered":"\u5b9f\u6570\u3068\u306f\uff1f\u6709\u7406\u6570\u30fb\u7121\u7406\u6570\u306e\u9055\u3044\u3068\u300c\u865a\u6570\u300d\u3068\u306e\u898b\u5206\u3051\u65b9\u3092\u5177\u4f53\u4f8b\u3067\u89e3\u8aac"},"content":{"rendered":"\n

\u300c\u3069\u308c\u304c\u5b9f\u6570\u304b\u5206\u304b\u3089\u306a\u3044\u300d<\/span>
\u300c\u5b9f\u6570\u306e\u5177\u4f53\u4f8b\u3092\u6559\u3048\u3066\u6b32\u3057\u3044\u300d<\/span><\/p>\n\n\n\n

\u4eca\u56de\u306f\u5b9f\u6570\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u3069\u308c\u304c\u5b9f\u6570\u306a\u306e\u304b\u3088\u304f\u5206\u304b\u3063\u3066\u3044\u306a\u304f\u3066\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u6570\u5b66\u3067\u306f\u3001“\u5b9f\u6570”<\/span>\u3068\u3044\u3046\u8a00\u8449\u304c\u3088\u304f\u51fa\u3066\u304d\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

\u300c\u306a\u306b\u304c\u5b9f\u6570\u306b\u542b\u307e\u308c\u308b\u3093\u3060\u3063\u3051…\u300d<\/p>\n\n\n\n

\u9ad8\u6821\u751f\u306e\u50d5\u3082\u3042\u307e\u308a\u5206\u304b\u3063\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\u3002<\/p>\n\n\n\n

\u7d50\u8ad6\u304b\u3089\u8a00\u3046\u3068\u3001\u5b9f\u6570\u3068\u306f\u300c\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u7dcf\u79f0\u300d<\/span>\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u5b9f\u6570\u3068\u306f\uff1f\"
\u5b9f\u6570\u306b\u542b\u307e\u308c\u308b\u3082\u306e<\/figcaption><\/figure>\n<\/div>\n\n\n

\u9ad8\u6821\u751f\u6570\u5b66\u306e\u7bc4\u56f2\u3067\u8a00\u3046\u3068\u3001\u865a\u6570\u4ee5\u5916\u306f\u3059\u3079\u3066\u5b9f\u6570<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n

\u3068\u3066\u3082\u7c21\u6f54\u306b\u7d50\u8ad6\u3060\u3051\u3092\u8ff0\u3079\u307e\u3057\u305f\u304c\u3001\u307e\u3060\u5b8c\u5168\u306a\u7406\u89e3\u306b\u306f\u81f3\u3063\u3066\u3044\u306a\u3044\u65b9\u3082\u591a\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u5b9f\u6570\u306e\u5b9a\u7fa9\u3084\u5177\u4f53\u4f8b\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u5b9f\u6570\u3067\u306a\u3044\u3082\u306e\u306e\u4f8b\u3082\u7d39\u4ecb\u3057\u3066\u3044\u308b\u306e\u3067\u305c\u3072\u53c2\u8003\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u5b9f\u6570\u3068\u306f”\u6709\u7406\u6570”\u3068”\u7121\u7406\u6570”\u306e\u7dcf\u79f0<\/h2>\n\n\n\n

\u307e\u305a\u3001\u5b9f\u6570\u3068\u306f\u300c\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u7dcf\u79f0\u300d<\/span>\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u9ad8\u6821\u6570\u5b66\u3067\u7fd2\u3046\u7bc4\u56f2\u3067\u8a00\u3046\u3068\u3001\u865a\u6570\u4ee5\u5916\u306e\u6570\u306f\u3059\u3079\u3066\u5b9f\u6570\u306b\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u5b9f\u6570\u3068\u306f\uff1f\"<\/figure>\n<\/div>\n\n\n

\u306a\u306e\u3067\u3001\u5206\u6570\u3084\u30eb\u30fc\u30c8\u3001\u03c0\u306a\u3069\u3082\u5b9f\u6570\u306b\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

\u5b9f\u6570\u306e\u4f8b<\/span><\/div>
\n

\u30fb\u6574\u6570
\\[-3,-2,-1,0,1,2,3\\]<\/p>\n\n\n\n

\u30fb\u6709\u9650\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.125&=&\\frac{1}{8}\\\\
\\displaystyle 0.0001&=&\\frac{1}{10000}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u5faa\u74b0\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.3333…&=&\\frac{1}{3}\\\\
\\displaystyle 0.2525…&=&\\frac{25}{99}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u7121\u7406\u6570(\u5faa\u74b0\u3057\u306a\u3044\u5c0f\u6570)
\\begin{eqnarray}
\\sqrt{2}=1.41421356…\\\\
\\pi =3.14159265…
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u3063\u3066\u306a\u3093\u3067\u3057\u305f\u3063\u3051\uff1f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u3064\u304e\u306f\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u9055\u3044\u3092\u78ba\u8a8d\u3059\u308b\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u9055\u3044<\/h2>\n\n\n\n

\u5b9f\u6570\u306f\u300c\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u7dcf\u79f0<\/span>\u300d\u3067\u3059\u3002<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001\u300c\u305d\u3082\u305d\u3082”\u6709\u7406\u6570”\u3068”\u7121\u7406\u6570”\u3063\u3066\u4f55\uff1f\u300d\u3068\u3044\u3046\u65b9\u3082\u3044\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n

\n
\"\u6709\u7406\u6570\u3068\u7121\u7406\u6570\"<\/figure>\n<\/div>\n\n\n

\u5b9f\u6570\u3092\u30d0\u30c3\u30c1\u30ea\u3068\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306b\u3064\u3044\u3066\u3082\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u6709\u7406\u6570\u3068\u306f\uff1f<\/h3>\n\n\n\n

\u6709\u7406\u6570\u3068\u306f\u300c\u5206\u6570\u306e\u5f62\u3067\u8868\u305b\u308b\u6570\u300d<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u4f8b\u3068\u3057\u3066\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u9055\u3044\"<\/figure>\n<\/div>\n\n\n

\u6574\u6570\u306a\u3089\u3070\u3069\u3093\u306a\u6570\u3067\u3082\u5206\u6570\u306b\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u306d\u3002<\/p>\n\n\n\n

\n

\\[\\displaystyle 3=\\frac{3}{1},-2=-\\frac{2}{1}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u6b21\u306b\u30010,5\u30840,125\u306e\u3088\u3046\u306a\u6709\u9650\u306a\u5c0f\u6570\u3092\u6709\u9650\u5c0f\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u6709\u9650\u5c0f\u6570\u306f\\(10^{n}\\)\u3092\u5206\u6bcd\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u5206\u6570\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\n

\\[\u6709\u9650\u5c0f\u6570\\displaystyle =\\frac{\u6574\u6570}{10^{n}}\\]
\\[\\displaystyle 0.05=\\frac{5}{100}\\]<\/p>\n\n\n\n

\\[\\displaystyle 0.1234=\\frac{1234}{10000}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u7121\u9650\u5c0f\u6570\u306e\u306a\u304b\u3067\u3082\u3001\u540c\u3058\u6570\u5b57\u3092\u7e70\u308a\u8fd4\u3059\u3082\u306e\u3092\u5faa\u74b0\u5c0f\u6570\u3068\u3044\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u5faa\u74b0\u5c0f\u6570\u3092\u5206\u6570\u306b\u76f4\u3059\u306b\u306f\u3001\u3072\u3068\u624b\u9593\u52a0\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u5faa\u74b0\u5c0f\u6570\\(0.3333\\cdots\\)\u3092\u4f8b\u306b\u3059\u308b\u3068\u3001<\/p>\n\n\n

\n
\"\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u9055\u3044\"<\/figure>\n<\/div>\n\n
\n
\"\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u9055\u3044\"<\/figure>\n<\/div>\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
9x=3\\\\
\\displaystyle x=\\frac{1}{3}
\\end{eqnarray}<\/p>\n\n\n\n

\u5faa\u74b0\u5c0f\u6570\u3092\u5206\u6570\u306b\u76f4\u3059\u65b9\u6cd5\u306f\u300c\u5faa\u74b0\u5c0f\u6570\u306e\u4f8b\u3068\u5206\u6570\u306b\u76f4\u3059\u65b9\u6cd5\u300d\u306b\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u7121\u7406\u6570\u3068\u306f\uff1f<\/h3>\n\n\n\n

\u4e00\u65b9\u3067\u3001\u300c\u5206\u6570\u3067\u8868\u305b\u306a\u3044\u6570\u300d<\/span>\u3092\u7121\u7406\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u7121\u7406\u6570\u3060\u3068\u5224\u65ad\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3001\u30eb\u30fc\u30c8\u3084\\(\\pi\\)\u306a\u3069\u306e\u5faa\u74b0\u3057\u306a\u3044\u5c0f\u6570\u304c\u7121\u7406\u6570\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u6709\u7406\u6570\u3068\u7121\u7406\u6570\"<\/figure>\n<\/div>\n\n\n
\u7121\u7406\u6570\u3068\u306f\uff1f<\/span><\/div>
\n

\u7121\u7406\u6570\u21d2\u5faa\u74b0\u3057\u306a\u3044\u5c0f\u6570
\\(\\sqrt{2},-\\sqrt{5},\\pi\\)\u306a\u3069<\/p>\n<\/div><\/div>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u3092\u5408\u308f\u305b\u3066\u5b9f\u6570\u3068\u3044\u3046\u3093\u3060\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u305d\u3046\u3044\u3046\u3053\u3068\uff01\u305d\u308c\u305e\u308c\u306e\u8a00\u8449\u306e\u5b9a\u7fa9\u306f\u899a\u3048\u3066\u304a\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5b9f\u6570\u306e\u4f8b<\/h2>\n\n\n\n

\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3057\u305f\u304c\u3001\u6539\u3081\u3066\u5b9f\u6570\u306e\u5177\u4f53\u4f8b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\n

\u30fb\u6574\u6570
\\[-3,-2,-1,0,1,2,3\\]<\/p>\n\n\n\n

\u30fb\u6709\u9650\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.125&=&\\frac{1}{8}\\\\
\\displaystyle 0.0001&=&\\frac{1}{10000}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u5faa\u74b0\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.3333…&=&\\frac{1}{3}\\\\
\\displaystyle 0.2525…&=&\\frac{25}{99}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u7121\u7406\u6570(\u5faa\u74b0\u3057\u306a\u3044\u5c0f\u6570)
\\begin{eqnarray}
\\sqrt{2}=1.41421356…\\\\
\\pi =3.14159265…
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u5b9f\u6570\u3067\u306a\u3044\u3082\u306e\u306e\u4f8b<\/h2>\n\n\n\n

\u5b9f\u6570\u306e\u5177\u4f53\u4f8b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u304c\u3001\u9006\u306b\u5b9f\u6570\u3067\u306a\u3044\u3082\u306e\u306e\u4f8b\u3082\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u5b9f\u6570\u3067\u306a\u3044\u6570\u306b\u306f\u3001\u865a\u6570<\/span>\u3084\u56db\u6b21\u5143\u6570<\/span>\u306a\u3069\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

\n

\u30fb\u865a\u6570
\\[2\u22125i,5+7i\\]<\/p>\n\n\n\n

\u30fb\u56db\u6b21\u5143\u6570
\\[a+bi+cj+dk\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u865a\u6570\u3068\u306f\u8907\u7d20\u6570\u3092\u8868\u3059\u6570\u3067\u3001\\(i^{2}=\u22121\\)\u3092\u6e80\u305f\u3059\\(i\\)\u3092\u6301\u3064\u6570\u3067\u3059\u3002<\/p>\n\n\n\n

\n

\u8907\u7d20\u6570\u306e\u4f8b\uff1a\\(2\u22125i,5+7i\\)<\/p>\n<\/div><\/div>\n\n\n\n

\u56db\u6b21\u5143\u6570\u3068\u306f\u8907\u7d20\u6570\u3092\u3055\u3089\u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

\u56db\u6b21\u5143\u6570\u306e\u4e00\u822c\u9805\uff1a\\(a+bi+cj+dk\\)\uff08\\(a,b,c,d\\)\u306f\u5b9f\u6570\uff09<\/p>\n\n\n\n

\u5b9f\u6570\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

\u4eca\u56de\u306f\u5b9f\u6570\u306e\u5b9a\u7fa9\u3068\u5177\u4f53\u4f8b\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n

\n
\"\u5b9f\u6570\u3068\u306f\uff1f\"<\/figure>\n<\/div>\n\n\n

\u5b9f\u6570\uff1a\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u7dcf\u79f0<\/span><\/p>\n\n\n\n

\u6709\u7406\u6570<\/span>\uff1a\u5206\u6570\u3067\u8868\u305b\u308b\u6570
\u7121\u7406\u6570<\/span>\uff1a\u5206\u6570\u3067\u8868\u305b\u306a\u3044\u6570<\/p>\n\n\n\n

\u5b9f\u6570\u306e\u4f8b<\/span><\/div>
\n

\u30fb\u6574\u6570
\\[-3,-2,-1,0,1,2,3\\]<\/p>\n\n\n\n

\u30fb\u6709\u9650\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.125&=&\\frac{1}{8}\\\\
\\displaystyle 0.0001&=&\\frac{1}{10000}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u5faa\u74b0\u5c0f\u6570
\\begin{eqnarray}
\\displaystyle 0.3333…&=&\\frac{1}{3}\\\\
\\displaystyle 0.2525…&=&\\frac{25}{99}
\\end{eqnarray}<\/p>\n\n\n\n

\u30fb\u7121\u7406\u6570(\u5faa\u74b0\u3057\u306a\u3044\u5c0f\u6570)
\\begin{eqnarray}
\\sqrt{2}=1.41421356…\\\\
\\pi =3.14159265…
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u5b9f\u6570\u306f\u3053\u308c\u304b\u3089\u3082\u305a\u3063\u3068\u4f7f\u3046\u8a00\u8449\u306a\u306e\u3067\u3001\u5fc5\u305a\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u305d\u308c\u3067\u306f\u6700\u5f8c\u307e\u3067\u8aad\u3093\u3067\u304f\u3060\u3055\u308a\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

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