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\u30ea\u30b9\u30c8\u3055\u308c\u3066\u3044\u308b4\u3064\u306e\u6bd4\u8f03\u306f\u72ec\u7acb\u3057\u305f\u95a2\u4fc2\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u308c\u3089\u306e\u305d\u308c\u305e\u308c\u306f\u4ed6\u306e\u3044\u305a\u308c\u304b\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\u306e\u3067\u3001\u306e\u7570\u306a\u308b\u6bd4\u8f03\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u6b63\u5f53\u5316\u3055\u308c\u307e\u3059 \u81ea\u7136\u3001\u672c\u7269\u306a\u3069\u306e\u9806\u5e8f\u3002\u305f\u3068\u3048\u3070\u3001\u4ed6\u306e\u6bd4\u8f03\u306f\u3001\u95a2\u4fc2\u306b\u3088\u3063\u3066\u6b21\u306e\u3088\u3046\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059 after-content-x4 < {displaystyle {displaystyle leq} \u5f8c\u7d99\u95a2\u6570\u306b\u3088\u3063\u3066 a \u21a6 a 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    (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u5b9f\u6570\u306e\u9806\u5e8f\u306f\u3001\u6570\u5024\u306e\u6570\u3067\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u53f3\u5074\u306b\u306f\u3001\u6570\u5b57\u304c\u5927\u304d\u304f\u306a\u308a\u3001\u5de6\u304c\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u3002 \u6570\u5b66\u3067\u306f\u3001\u81ea\u7136\u3001\u5168\u4f53\u3001\u5408\u7406\u7684\u3001\u307e\u305f\u306f\u5b9f\u6570\u306e\u3088\u3046\u306a\u7279\u5b9a\u306e\u6570\u9818\u57df\u304b\u3089\u306e\u6570\u5024\u304b\u3089 \u6bd4\u8f03 \u3002\u6bd4\u8f03\u30b5\u30a4\u30f3\u306f\u6570\u5b66\u7684\u306a\u5f0f\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 1\u3064\u306f\u66f8\u3044\u3066\u3044\u307e\u3059\uff1a        (adsbygoogle = window.adsbygoogle || 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\u307e\u305f\u306f\u8a00\u3044\u63db\u3048\u308c\u3070\uff1a a {displaystyle a} \u305d\u308c\u3088\u308a\u3082\u5927\u304d\u304f\u3042\u308a\u307e\u305b\u3093 b {displaystyle b} \u3001 \u3082\u3057\u3082 b {displaystyle b} \u304b\u3089 a {displaystyle a} \u5f8c\u7d99\u95a2\u6570\u306e\u4f7f\u7528\u304b\u3089\u5230\u9054\u3067\u304d\u307e\u3059\u3002 Von Neumann\u306e\u81ea\u7136\u6570\u306e\u30e2\u30c7\u30eb\u3067 a < b {displaystyle a as\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 a \u2208 b {displaystyle ain b} \uff08\u3064\u307e\u308a\u3001\u7fa4\u8846 a {displaystyle a} \u306e\u8981\u7d20\u3067\u3059 b {displaystyle b} \uff09 \u3068 a \u2264 b {displaystyle aleq b} \u7d42\u3048\u305f a \u2286 b {displaystyle asubseteq b} \uff08d\u3002h\u3002\u3001 a {displaystyle a} \u306e\u4e00\u90e8\u3067\u3059 b {displaystyle b} \uff09\u3002 \u6b21\u306e\u5b9a\u7fa9 a \u2264 b {displaystyle aleq b} \u53ef\u80fd\uff1a \u5408\u7406\u7684\u306a\u6570\u5b57\u306f\u4f11\u61a9\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f11\u61a9\u3092\u901a\u3058\u30662\u3064\u306e\u5408\u7406\u7684\u306a\u6570\u5b57\u3082\u540c\u69d8\u3067\u3059 a0a1{displaystyle textStyle {frac {a_ {0}} {a_ {1}}}}}} \u3068 b0b1{displaystyle\u30c6\u30ad\u30b9\u30c8\u30b9\u30bf\u30a4\u30eb{frac {b_ {0}} {b_ {1}}}}} \u4e0e\u3048\u3089\u308c\u307e\u3059\uff08\u3042\u308a\u307e\u3059 a 0 \u3001 b 0 {displaystyle a_ {0}\u3001b_ {0}} \u6574\u6570\u3068 a \u521d\u3081 \u3001 b \u521d\u3081 {displaystyle a_ {1}\u3001b_ {1}} \u30dd\u30b8\u30c6\u30a3\u30d6\u3001\u81ea\u7136\u6570\uff09\u3002\u305d\u308c\u304b\u3089 a0a1\u2264 b0b1{displaystyle textStyle {frac {a_ {0}} {a_ {1}} leq text style {frac {b_ {0}} {b_ {1}}}}} \u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059 a 0 de b \u521d\u3081 \u2264 b 0 de a \u521d\u3081 {displaystyle a_ {0} cdot b_ {1} leq b_ {0} cdot a_ {1}} \u3002 \u79e9\u5e8f\u7406\u8ad6\u306f\u3001Dedekind\u306e\u5408\u7406\u7684\u306a\u6570\u306e\u30ab\u30c3\u30c8\u3068\u3057\u3066\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u306f a \u3001 b {displaystyle alpha\u3001beta} \u3001\u5408\u7406\u7684\u306a\u6570\u306e\u90e8\u5206\u91cf\u3001\u5b9f\u6570\u3078\u306e\u6df7\u5408 a \u3001 b {displaystyle a\u3001b} \uff08\u305d\u308c\u306f\u610f\u5473\u3057\u307e\u3059 a {displaystyle alpha} \u307e\u305f\u3002 b {displaystyle\u30d9\u30fc\u30bf} \u3059\u3079\u3066\u306e\u5408\u7406\u7684\u306a\u6570\u5024\u306e\u91cf\u306f\u3088\u308a\u5c11\u306a\u3044 a {displaystyle a} \u307e\u305f\u3002 b {displaystyle b} \uff09\u3001\u305d\u3046\u3067\u3059 a \u2264 b {displaystyle aleq b} \u6b63\u78ba\u306b\u3044\u3064 a {displaystyle alpha} \u306e\u4e3b\u984c b {displaystyle\u30d9\u30fc\u30bf} \u306f\u3002 \u5b9f\u969b\u306e\u6570\u5b57\u306f\u3001\u5408\u7406\u7684\u306a\u6570\u5b57\u306e\u30b3\u30fc\u30b7\u30fc\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u306a\u308c \uff08 a n \uff09\uff09 {displaystyle\uff08a_ {n}\uff09} \u3068 \uff08 b n \uff09\uff09 {displaystyle\uff08b_ {n}\uff09} \u5b9f\u6570\u306e\u5408\u7406\u7684\u306a\u30b3\u30fc\u30b7\u30fc\u30a8\u30d4\u30bd\u30fc\u30c9 a {displaystyle a} \u307e\u305f\u3002 b {displaystyle b} \u4ee3\u8868\u3059\u308b\u3002\u305d\u306e\u5f8c\u3001\u9069\u7528\u3055\u308c\u307e\u3059 a \u2264 b {displaystyle aleq b} \u6b63\u78ba\u306b\u3044\u3064 a = b {displaystyle a = b} \uff08\u3059\u306a\u308f\u3061\u30012\u3064\u306e\u30b3\u30fc\u30b7\u30fc\u30a8\u30d4\u30bd\u30fc\u30c9\u306e\u540c\u7b49\u6027\uff09\u307e\u305f\u306f\u3059\u3079\u3066\u306e\u4eba\u306e\u305f\u3081\u306b n \u2208 n {displaystyle nin mathbb {n}} \u6700\u7d42\u7684\u306b\u591a\u304f\u3092\u9664\u3044\u3066 a n \u2264 b n {displaystyle a_ {n} leq b_ {n}}} \u9069\u7528\u53ef\u80fd\u3067\u3059\u3002 \u6570\u5b57\u306e\u5834\u5408 \u30d0\u30c4 \u3001 \u3068 \u3001 \u3068 {displaystyle x\u3001y\u3001z} \u3068 \u30d0\u30c4 < \u3068 {displaystyle x \u3068 \u3068 < \u3068 {displaystyle y \u5e38\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 < \u3068 {displaystyle x \u3002\u3053\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u305d\u3046\u3057\u307e\u3059 \u63a8\u79fb\u6027 \u304b\u3089 < {displaystyle &#8220;>\u53b3\u5bc6\u306a\u5408\u8a08\u9806\u5e8f\u3002\u4e0d\u6a5f\u5acc\u3055\u306f\u3053\u308c\u3089\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304b\u3089\u3082\u7d9a\u304d\u307e\u3059\uff1a\u6570\u306e\u305f\u3081\u306b \u30d0\u30c4 {displaystyle x} \u305d\u308c\u305e\u308c\u306e\u6570\u5024\u304b\u3089\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 < \u30d0\u30c4 {displaystyle x \u3002\u975e\u5bfe\u79f0\u6027\u3082\u7d9a\u304d\u307e\u3059\uff1a\u9069\u7528 \u30d0\u30c4 < \u3068 {displaystyle x \u9069\u7528\u3055\u308c\u307e\u3059 \u3068 < \u30d0\u30c4 {displaystyle y \u3044\u3044\u3048\u3002 \u307e\u305f \u2264 {displaystyle leq} \u900f\u904e\u7387\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff1aif \u30d0\u30c4 \u2264 \u3068 {displaystyle xleq y} \u3068 \u3068 \u2264 \u3068 {disspastyle yleq with} \u3057\u305f\u304c\u3063\u3066\u3001\u5e38\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 \u2264 \u3068 {disspastyle xleq\u3068} \u3002\u5225\u306e\u7279\u6027\u306f\u53cd\u5c04\u6027\u3067\u3059\uff1a\u4efb\u610f\u306e\u6570 \u30d0\u30c4 {displaystyle x} \u305d\u308c\u305e\u308c\u306e\u6570\u5024\u304b\u3089\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 \u2264 \u30d0\u30c4 {displaystyle xleq x} \u3002\u30c0\u30a4\u95a2\u4fc2 \u2264 {displaystyle leq} \u53cd\u5bfe\u79f0\u3067\u3059\uff1afor \u30d0\u30c4 \u2260 \u3068 {displaystyle xneq y} \u540c\u6642\u306b\u3067\u304d\u307e\u305b\u3093 \u30d0\u30c4 \u2264 \u3068 {displaystyle xleq y} \u3068 \u3068 \u2264 \u30d0\u30c4 {displaystyle yleq x} \u6709\u52b9\u3067\u3059\u3002\u305d\u308c\u305e\u308c2\u3064\u306e\u6570\u5b57\u306e\u30d7\u30ed\u30d1\u30c6\u30a3 \u30d0\u30c4 \u3001 \u3068 {displaystyle x\u3001y} \u5c11\u306a\u304f\u3068\u3082 \u30d0\u30c4 \u2264 \u3068 {displaystyle xleq y} \u307e\u305f \u3068 \u2264 \u30d0\u30c4 {displaystyle yleq x} Apply\u306fTotality\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u7e70\u308a\u8fd4\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e\u95a2\u4fc2\u306f Totalordnung \u547c\u3073\u51fa\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u3001\u540c\u69d8\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u2265 {displaystylegeq} \u3001\u5408\u8a08\u9806\u5e8f\u3082\u5f62\u6210\u3057\u307e\u3059\u3002  out \u30d0\u30c4 < \u3068 {displaystyle x \u7d9a\u304d\u307e\u3059 \u30d0\u30c4 + a < \u3068 + a {displaystyle x+a \u81ea\u7136\u3001\u672c\u7269\u306a\u3069\u306e\u9806\u5e8f \u4e92\u63db\u6027 \u8ffd\u52a0\u3067\uff1a\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 < \u3068 {displaystyle x \u305d\u3057\u3066 a {displaystyle a} \u305d\u306e\u3088\u3046\u306a\u6570\u306e\u6570\u3082\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 + a < \u3068 + a {displaystyle x+a \u3002\u9006\u306b\u3001\u7d9a\u304d\u307e\u3059 \u30d0\u30c4 + a < \u3068 + a {displaystyle x+a \u307e\u305f \u30d0\u30c4 + a + \uff08  &#8211;  a \uff09\uff09 < \u3068 + a + \uff08  &#8211;  a \uff09\uff09 {displaystyle x+a+\uff08 &#8211;  a\uff09 \u3057\u305f\u304c\u3063\u3066 \u30d0\u30c4 < \u3068 {displaystyle x \u3002\u6e1b\u7b97\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u5834\u5408\uff08\u3053\u308c\u306f\u81ea\u7136\u6570\u306e\u5834\u5408\u3067\u306f\u306a\u304f\u3001\u305f\u3068\u3048\u3070\u5168\u4f53\u306b\u3001\u5408\u7406\u7684\u306a\u6570\u3068\u5b9f\u6570\uff09\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 < \u3068 {displaystyle x \u6b63\u78ba\u306b\u3044\u3064 "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/7130#breadcrumbitem","name":"\u6bd4\u8f03\uff08\u6570\u5b57\uff09 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]