[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116011#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116011","headline":"\u5168\u5358\u5c04 &#8211; Wikipedia","name":"\u5168\u5358\u5c04 &#8211; Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0&#8220;\u5168\u5358\u5c04&#8221;\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082016\u5e741\u6708\uff09 \u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5168\u5358\u5c04\uff08\u305c\u3093\u305f\u3093\u3057\u3083\uff09\u3042\u308b\u3044\u306f\u53cc\u5c04\uff08\u305d\u3046\u3057\u3083\uff09(bijective function, bijection) \u3068\u306f\u3001\u5199\u50cf\u3067\u3042\u3063\u3066\u3001\u305d\u306e\u5199\u50cf\u306e\u7d42\u57df\u3068\u306a\u308b\u96c6\u5408\u306e\u4efb\u610f\u306e\u5143\u306b\u5bfe\u3057\u3001\u305d\u306e\u5143\u3092\u5199\u50cf\u306e\u50cf\u3068\u3059\u308b\u5143\u304c\u3001\u5199\u50cf\u306e\u5b9a\u7fa9\u57df\u3068\u306a\u308b\u96c6\u5408\u306b\u5e38\u306b\u305f\u3060\u4e00\u3064\u3060\u3051\u5b58\u5728\u3059\u308b\u3088\u3046\u306a\u3082\u306e\u3001\u3059\u306a\u308f\u3061\u5358\u5c04\u304b\u3064\u5168\u5c04\u3067\u3042\u308b\u3088\u3046\u306a\u5199\u50cf\u306e\u3053\u3068\u3092\u8a00\u3046\u3002\u4f8b\u3068\u3057\u3066\u306f\u3001\u7fa4\u8ad6\u3067\u6271\u308f\u308c\u308b\u7f6e\u63db\u304c\u6319\u3052\u3089\u308c\u308b\u3002 \u5168\u5358\u5c04\u3067\u3042\u308b\u3053\u3068\u30921\u5bfe1\u4e0a\u3078\u306e\u5199\u50cf[\u4e0a\u3078\u306e1\u5bfe1\u5199\u50cf] (one-to-one onto mapping)\u3042\u308b\u3044\u306f1\u5bfe1\u5bfe\u5fdc (one-to-one correspondence) \u3068\u3082\u3044\u3046\u304c\u3001\u7d1b\u3089\u308f\u3057\u3044\u306e\u3067\u3053\u3053\u3067\u306f\u4f7f\u7528\u3057\u306a\u3044\u3002","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116011","about":["Wiki"],"wordCount":2096,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0&#8220;\u5168\u5358\u5c04&#8221;\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082016\u5e741\u6708\uff09\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5168\u5358\u5c04\uff08\u305c\u3093\u305f\u3093\u3057\u3083\uff09\u3042\u308b\u3044\u306f\u53cc\u5c04\uff08\u305d\u3046\u3057\u3083\uff09(bijective function, bijection) \u3068\u306f\u3001\u5199\u50cf\u3067\u3042\u3063\u3066\u3001\u305d\u306e\u5199\u50cf\u306e\u7d42\u57df\u3068\u306a\u308b\u96c6\u5408\u306e\u4efb\u610f\u306e\u5143\u306b\u5bfe\u3057\u3001\u305d\u306e\u5143\u3092\u5199\u50cf\u306e\u50cf\u3068\u3059\u308b\u5143\u304c\u3001\u5199\u50cf\u306e\u5b9a\u7fa9\u57df\u3068\u306a\u308b\u96c6\u5408\u306b\u5e38\u306b\u305f\u3060\u4e00\u3064\u3060\u3051\u5b58\u5728\u3059\u308b\u3088\u3046\u306a\u3082\u306e\u3001\u3059\u306a\u308f\u3061\u5358\u5c04\u304b\u3064\u5168\u5c04\u3067\u3042\u308b\u3088\u3046\u306a\u5199\u50cf\u306e\u3053\u3068\u3092\u8a00\u3046\u3002\u4f8b\u3068\u3057\u3066\u306f\u3001\u7fa4\u8ad6\u3067\u6271\u308f\u308c\u308b\u7f6e\u63db\u304c\u6319\u3052\u3089\u308c\u308b\u3002  \u5168\u5358\u5c04\u3067\u3042\u308b\u3053\u3068\u30921\u5bfe1\u4e0a\u3078\u306e\u5199\u50cf[\u4e0a\u3078\u306e1\u5bfe1\u5199\u50cf] (one-to-one onto mapping)\u3042\u308b\u3044\u306f1\u5bfe1\u5bfe\u5fdc (one-to-one correspondence) \u3068\u3082\u3044\u3046\u304c\u3001\u7d1b\u3089\u308f\u3057\u3044\u306e\u3067\u3053\u3053\u3067\u306f\u4f7f\u7528\u3057\u306a\u3044\u3002\u5199\u50cf f \u304c\u5168\u5358\u5c04\u306e\u3068\u304d\u3001f \u306f\u53ef\u9006\u3067\u3042\u308b\u3068\u3082\u3044\u3046\u3002\u5199\u50cf f: A \u2192 B \u306b\u5bfe\u3057\u30012\u3064\u306e\u6761\u4ef6  \u5168\u5c04\u6027: f(A) = B\u5358\u5c04\u6027: \u4efb\u610f\u306e A \u306e\u5143 a1, a2 \u306b\u3064\u3044\u3066\u3001f(a1) = f(a2) \u306a\u3089\u3070 a1 = a2\u304c\u3068\u3082\u306b\u6210\u308a\u7acb\u3064\u3068\u304d\u3001\u5199\u50cf f \u306f\u5168\u5358\u5c04 (bijective) \u3067\u3042\u308b\u3068\u3044\u3046\u3002\u3053\u306e\u7528\u8a9e\u306f\u30d6\u30eb\u30d0\u30ad\u306b\u3088\u308b\u3002f: A \u2192 B \u304c\u5168\u5358\u5c04\u3067\u3042\u308b\u3053\u3068\u306f\u3001\u2200\u00a0b\u2208B,\u2203\u00a0!\u00a0a\u2208A\u00a0s.t.\u00a0b=f(a){displaystyle forall  bin B,,exists  ! ain A{text{ s.t. }}b=f(a)}\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3002\u5b9f\u969b\u3001\u5168\u5c04\u3068\u5358\u5c04\u306e\u5b9a\u7fa9\u3092\u5408\u308f\u305b\u308c\u3070\u3001\u5168\u5c04\u306e\u5b9a\u7fa9\u306b\u304a\u3051\u308b\u5b58\u5728\u8a18\u53f7   \u2203{displaystyle exists } \u3092\u552f\u4e00\u5b58\u5728\u8a18\u53f7 \u2203\u00a0!{displaystyle exists  !} \u306b\u7f6e\u304d\u63db\u3048\u308c\u3070\u3088\u3044\u3053\u3068\u304c\u3059\u3050\u306b\u5206\u304b\u308b\u3002\u5168\u5c04\u3067\u3082\u5358\u5c04\u3067\u3082\u306a\u3044\u5358\u5c04\u3067\u3042\u308a\u5168\u5c04\u3067\u306a\u3044\u5168\u5c04\u3067\u3042\u308a\u5358\u5c04\u3067\u306a\u3044\u5168\u5358\u5c04f: R \u2192 (0, \u221e); f(x)\u00a0:= ex \u306f\u5168\u5358\u5c04\u3067\u3042\u308b\u3002f: (0, \u221e) \u2192 R; f(x)\u00a0:= log x \u306f\u5168\u5358\u5c04\u3067\u3042\u308b\u3002f: (\u2212\u03c0\/2, \u03c0\/2) \u2192 R; f(x)\u00a0:= tan x \u306f\u5168\u5358\u5c04\u3067\u3042\u308b\u3002\u5b58\u5728\u306e\u4f8b[\u7de8\u96c6]\u51aa\u96c6\u5408 P(N){displaystyle {mathcal {P}}(mathbb {N} )} \u304b\u3089 R \u3078\u306e\u5168\u5358\u5c04\u304c\u5b58\u5728\u3059\u308b\uff0eN, Z, Q, P \u306e\u9593\u306e\u5168\u5358\u5c04\u304c\u5b58\u5728\u3059\u308b\uff0e\u3053\u3053\u3067 P \u306f\u7d20\u6570\u306e\u5168\u4f53\u3067\u3042\u308b\uff0eR, C \u306e\u9593\u306e\u5168\u5358\u5c04\u304c\u5b58\u5728\u3059\u308b\uff0e\u307e\u305f\uff0ca < b \u306b\u5bfe\u3059\u308b\u9589\u533a\u9593 [a, b], \u534a\u958b\u533a\u9593 (a, b], [a, b), \u958b\u533a\u9593 (a, b) \u3084\u7121\u9650\u533a\u9593\u3068 R \u306e\u9593\u306e\u5168\u5358\u5c04\u304c\u5b58\u5728\u3059\u308b\uff0e\u5168\u5358\u5c04\u306f\u9006\u5199\u50cf\u3092\u6301\u3064\u3002\u5b9f\u969b\u3001f: A \u2192 B \u304c\u5168\u5358\u5c04\u3067\u3042\u308c\u3070\u3001B \u306e\u4efb\u610f\u306e\u5143 b \u306b\u5bfe\u3057\u3001f \u306e\u5168\u5c04\u6027\u304b\u3089 f(a) = b \u3068\u306a\u308b a \u304c\u5b58\u5728\u3059\u308b\u304c\u3001f \u306e\u5358\u5c04\u6027\u304b\u3089\u3053\u306e\u3088\u3046\u306a a \u306f b \u306b\u5bfe\u3057\u3066\u305f\u3060\u4e00\u3064\u3057\u304b\u306a\u3044\u306e\u3067\u3001\u5199\u50cf g: B \u2192 A; f(a) \u21a6 a \u304c\u4f5c\u308c\u308b\u3002\u9006\u306b\u3001\u9006\u5199\u50cf\u3092\u6301\u3064\u5199\u50cf\u306f\u5168\u5358\u5c04\u306b\u9650\u308b\u306e\u3067\u3001\u5199\u50cf\u304c\u5168\u5358\u5c04\u3067\u3042\u308b\u3053\u3068\u3068\u9006\u5199\u50cf\u3092\u6301\u3064\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001f: A \u2192 B \u304c\u5168\u5358\u5c04\u3067\u3042\u308b\u3053\u3068\u3068\u3001g: B \u2192 A \u304c\u5b58\u5728\u3057\u3066 g\u2218f=idA{displaystyle gcirc f=mathrm {id} _{A}} \u304b\u3064 f\u2218g=idB{displaystyle fcirc g=mathrm {id} _{B}} \u3068\u306a\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u30022\u3064\u306e\u5199\u50cf f: A \u2192 B, g: B \u2192 C \u306e\u5408\u6210\u5199\u50cf g\u2218f:A\u2192C{displaystyle gcirc fcolon Ato C} \u304c\u5168\u5358\u5c04\u306a\u3089\u3070 f \u306f\u5358\u5c04\u3067\u3001g \u306f\u5168\u5c04\u3067\u3042\u308b\u30022\u3064\u306e\u5168\u5358\u5c04\u304c\u5408\u6210\u3067\u304d\u308b\u306a\u3089\u3070\u3001\u305d\u306e\u5408\u6210\u5199\u50cf\u3082\u5168\u5358\u5c04\u3067\u3042\u308b\u3002\u96c6\u5408 X \u4e0a\u306e\u5168\u5358\u5c04\u5168\u4f53\u306e\u6210\u3059\u96c6\u5408\u3092 SX \u3068\u3059\u308b\u3068\u3001SX \u306f\u5199\u50cf\u306e\u5408\u6210\u306b\u95a2\u3057\u3066\u7fa4\u3092\u6210\u3059\u3002\u3053\u308c\u3092 X \u4e0a\u306e\u7f6e\u63db\u7fa4\u3042\u308b\u3044\u306f\u5bfe\u79f0\u7fa4\u3068\u547c\u3076\u3002\u96c6\u5408\u5168\u4f53\u306e\u3064\u304f\u308b\u30af\u30e9\u30b9\uff08\u985e\uff09\u306b\u304a\u3044\u3066\u3001\u300c2\u3064\u306e\u96c6\u5408\u306e\u9593\u306b\u5168\u5358\u5c04\u304c\u5b58\u5728\u3059\u308b\u300d \u3068\u3044\u3046\u95a2\u4fc2\u306f\u540c\u5024\u95a2\u4fc2\u3092\u5b9a\u3081\u308b\u3002\u3053\u306e\u540c\u5024\u95a2\u4fc2\u306b\u3088\u308a\u96c6\u5408\u5168\u4f53\u306e\u6210\u3059\u30af\u30e9\u30b9\u3092\u985e\u5225\u3057\u3066\u6fc3\u5ea6\u306e\u6982\u5ff5\u304c\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u96c6\u5408\u9593\u3067\u5168\u5358\u5c04\u304c\u5b9a\u7fa9\u53ef\u80fd\u306a\u5834\u5408\u3001\u305d\u308c\u3089\u306e\u96c6\u5408\u306f\u57fa\u6570\u304c\u7b49\u3057\u3044\u3002X, Y \u304c\u540c\u6570\u306e\u5143\u3092\u6301\u3064\u6709\u9650\u96c6\u5408\u306e\u5834\u5408\u3001\u5199\u50cf f: X \u2192 Y \u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306f\u540c\u5024\u3067\u3042\u308b:f \u306f\u5168\u5358\u5c04\u3067\u3042\u308b\u3002f \u306f\u5168\u5c04\u3067\u3042\u308b\u3002f \u306f\u5358\u5c04\u3067\u3042\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/116011#breadcrumbitem","name":"\u5168\u5358\u5c04 &#8211; Wikipedia"}}]}]