[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/18000#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/18000","headline":"Indukive Menge  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Indukive Menge  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u3044\u3064 \u5e30\u7d0d\u7684\u91cf \u6570\u5b66\u306e\u91cf\u306b\u306a\u308a\u307e\u3059 m {displaystyle m} after-content-x4 \u7a7a\u306e\u91cf\u3092\u8aac\u660e\u3057\u307e\u3057\u305f \u2205 {displaystyle emptySet} \u5c01\u3058\u8fbc\u3081\u3089\u308c\u3001\u3069\u3053\u306b\u3044\u307e\u3059\u304b \u30d0\u30c4 {displaystyle x} \u307e\u305f\u3001\u5f7c\u3089\u306e\u5f8c\u7d99\u8005 after-content-x4 \u30d0\u30c4 ‘","datePublished":"2023-09-08","dateModified":"2023-09-08","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/18000","wordCount":3305,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u3044\u3064 \u5e30\u7d0d\u7684\u91cf \u6570\u5b66\u306e\u91cf\u306b\u306a\u308a\u307e\u3059 m {displaystyle m}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u7a7a\u306e\u91cf\u3092\u8aac\u660e\u3057\u307e\u3057\u305f \u2205 {displaystyle emptySet} \u5c01\u3058\u8fbc\u3081\u3089\u308c\u3001\u3069\u3053\u306b\u3044\u307e\u3059\u304b \u30d0\u30c4 {displaystyle x} \u307e\u305f\u3001\u5f7c\u3089\u306e\u5f8c\u7d99\u8005        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 ‘ = \u30d0\u30c4 \u222a { \u30d0\u30c4 } {displaystyle x ‘= xcup {x}} \u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 Infinity Axiom\u306f\u3001\u8a98\u5c0e\u91cf\u304c\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002 \u591a\u304f\u306e m {displaystyle m} \u3042\u306a\u305f\u304c\u6b21\u306e2\u3064\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3067\u3042\u308b\u5834\u5408\u3001\u307e\u3055\u306b\u5e30\u7d0d\u7684\u91cf\u3067\u3059 \u2205 \u2208 m {displaystyle emptyset in m} \u2200 \u30d0\u30c4 \u2208 m \uff1a x\u2032\u2208 m {displaystyle forall xin m\uff1ax’in m} \u305d\u308c\u306b\u3088\u3063\u3066\u6e80\u305f\u3055\u308c\u305f        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 ‘ \uff1a= \u30d0\u30c4 \u222a { \u30d0\u30c4 } {displaystyle x ‘\uff1a= xcup {x}}} \u306e\u5f8c\u7d99\u8005 \u30d0\u30c4 {displaystyle x} \u5c02\u7528\u3002 \u81ea\u7136\u6570 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8a98\u5c0e\u91cf\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u30ea\u30c1\u30e3\u30fc\u30c9\u30fb\u30c7\u30c7\u30ad\u30f3\u30c9\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u5f93\u3063\u3066\u3001\u81ea\u7136\u6570\u306e\u91cf\u306f\u91cf\u7406\u8ad6\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 [\u521d\u3081] N:=\u22c2{x\u2223xinduktiv}.{displaystyle {begin {aligned} mathbb {n}\uff1a= bigcap {xmid x; {text {induktiv}}}\u3002end {aligned}}}}} \u8a98\u5c0e\u91cf\u306e\u524a\u6e1b\u306f\u518d\u3073\u8a98\u5c0e\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u81ea\u7136\u6570\u306e\u91cf\u306f\u6700\u5c0f\u306e\u8a98\u5c0e\u91cf\u3067\u3059\u3002 n {displaystyle mathbb {n}} \u3057\u305f\u304c\u3063\u3066\u3001\u7a7a\u306e\u6570\u91cf\u306e\u7e70\u308a\u8fd4\u3057\u306e\u5f8c\u7d99\u8005\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002 N= { \u2205 \u3001 \u2205\u2032\u3001 \u2205\u2033\u3001 \u2205\u2034\u3001 … } = { 0 \u3001 \u521d\u3081 \u3001 2 \u3001 3 \u3001 … } {displaystyle mathbb {n} = {emptyset\u3001emptyset ‘\u3001emptyset’ ‘\u3001emptyset’ ”\u3001ldots} = {0,1,2,3\u3001ldots}}} \u3053\u306e\u3088\u3046\u306b\u81ea\u7136\u6570\u3092\u5b9a\u7fa9\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u306b\u306f\u30012\u3064\u306e\u516c\u7406\u304c\u5fc5\u8981\u3067\u3059\u3002InfinityAxiom\u3068Sanctuary Axiom\uff1aInfinity Axiom\u306f\u3001\u5c11\u306a\u304f\u3068\u30821\u3064\u306e\u8a98\u5c0e\u91cf\u304c\u3042\u308b\u3053\u3068\u3092\u78ba\u4fe1\u3057\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3059\u3079\u3066\u306e\u8a98\u5c0e\u91cf\u306b\u30ab\u30c3\u30c8\u3092\u5f62\u6210\u3059\u308b\u3068\u3001\u81ea\u7136\u6570\u306e\u30af\u30e9\u30b9\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u5206\u96e2axiome\u306f\u3001\u30ab\u30c3\u30c8\u3082\u91cf\u3088\u308a\u3082\u304b\u306a\u308a\u306e\u3082\u306e\u3067\u3042\u308a\u3001\u81ea\u7136\u6570\u306e\u30af\u30e9\u30b9\u304c\u672c\u5f53\u306b\u304b\u306a\u308a\u306e\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002 Zermelo-Fraenkele\u306e\u5408\u4f75\u7406\u8ad6\u5185\u3067\u306f\u3001\u3053\u306e\u65b9\u6cd5\u3067\u8a2d\u8a08\u3055\u308c\u305f\u91cf\u304c\u793a\u3055\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 n {displaystyle mathbb {n}} \u30d4\u30a2\u30ce\u516c\u7406\u3092\u5b9f\u73fe\u3057\u307e\u3057\u305f\u3002 n {displaystyle mathbb {n}} \u3057\u305f\u304c\u3063\u3066\u3001\u81ea\u7136\u6570\u306e\u76f4\u611f\u7684\u306a\u6982\u5ff5\u306f\u7406\u8ad6\u7406\u8ad6\u3092\u6349\u3048\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u4ee5\u5916\u306e \u30d0\u30c4 ‘ {displaystyle x ‘} \u3068 \u2205 {displaystyle emptySet} \u3057\u305f\u304c\u3063\u3066\u3001\u3042\u306a\u305f\u306f\u4e3b\u306b\u7b97\u8853\u306e\u3088\u3046\u306b\u66f8\u3044\u3066\u3044\u307e\u3059 \u30d0\u30c4 + \u521d\u3081 {displaystyle x+1} \u307e\u305f\u3002 0 {displaystyle 0} \u3002 \u8a98\u5c0e\u91cf\u306e\u5b9a\u7fa9\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u5b8c\u5168\u306a\u8a98\u5c0e\u306e\u8a3c\u62e0\u306e\u65b9\u6cd5\u3092\u6b63\u5f53\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u3057\u305f\u304c\u3063\u3066\u3001\u540d\u524d\u306f\u540d\u524d\u3067\u3059 \u5e30\u7d0d\u7684 \uff09\uff1a\u3059\u3079\u3066\u306e\u81ea\u7136\u6570\u306b\u306f\u7279\u5b9a\u306e\u7279\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059 \u305d\u3046\u3067\u3059 {displaystyle e} \u3060\u304b\u3089\u7fa4\u8846\u3092\u898b\u3066\u304f\u3060\u3055\u3044 \u3068 \uff1a= { n \u2208 n ‘ \u305d\u3046\u3067\u3059 \uff08 n \uff09\uff09 } \u2286 n {displaystyle e\uff1a= {nin mathbb {n} mid e\uff08n\uff09} subseteq mathbb {n}} \u3002\u4eca\u305d\u308c\u3092\u793a\u3057\u3066\u3044\u307e\u3059 \u305d\u3046\u3067\u3059 \uff08 0 \uff09\uff09 {displaystyle e\uff080\uff09} \u9069\u7528\u3055\u308c\u3001\u30aa\u30d5\u306b\u306a\u308a\u307e\u3059 \u305d\u3046\u3067\u3059 \uff08 n \uff09\uff09 {displaystyle e\uff08n\uff09} \u307e\u305f \u305d\u3046\u3067\u3059 \uff08 n + \u521d\u3081 \uff09\uff09 {displaystyle e\uff08n+1\uff09} \u7d9a\u304f\u3001\u305d\u3046\u3067\u3059 \u3068 {displaystyle e} \u5e30\u7d0d\u7684\u3002 da n {displaystyle mathbb {n}} \u6700\u5c0f\u306e\u8a98\u5c0e\u91cf\u306f\u6709\u52b9\u3067\u3059 n \u2286 \u3068 {displaystyle mathbb {n} subseteq e} \u3057\u305f\u304c\u3063\u3066 n = \u3068 {displaystyle mathbb {n} = e} \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u81ea\u7136\u6570\u306b\u306f\u8ca1\u7523\u304c\u3042\u308a\u307e\u3059 \u305d\u3046\u3067\u3059 {displaystyle e} \u3002 \u30c8\u30e9\u30f3\u30b9\u30d5\u30a3\u30ca\u30a4\u30c8\u9806\u5e8f\u6570 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u305f\u3068\u3048\u3070\u3001\u3055\u3089\u306b\u8a98\u5c0e\u91cf\u306f\u8f38\u8840\u9806\u6570\u3067\u3059\u3002 \u304a\u304a + \u304a\u304a = { 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … \u3001 n \u3001 n + \u521d\u3081 \u3001 … \u3001 \u304a\u304a \u3001 \u304a\u304a + \u521d\u3081 \u3001 \u304a\u304a + 2 \u3001 … } {displaystyle omega +omega = {0,1,2\u3001ldots\u3001n\u3001n +1\u3001ldots\u3001omega\u3001omega +1\u3001omega +2\u3001ldots}}} \u3002\u3053\u3053\u3067\u306f\u3001\u81ea\u7136\u6570\u306f\u30b5\u30d6\u30bb\u30c3\u30c8\u3068\u3057\u3066\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u304c\u3001 \u304a\u304a {displaystyle omega} \u7121\u9650\u306e\u6570\u306e\u9806\u5e8f\u3001\u3064\u307e\u308aH.\u3069\u306e\u81ea\u7136\u6570\u3088\u308a\u3082\u5927\u304d\u3044\u3002 \u2191  \u30ea\u30c1\u30e3\u30fc\u30c9\u30fb\u30c7\u30c7\u30ad\u30f3\u30c9\uff1a \u4f55\u304c\u4f55\u3067\u3059\u304b\uff1f\u6570\u5b57\u306f\u4f55\u3067\u3059\u304b\uff1f Vieweg\u3001Braunschweig 1888\u3001\u00a76\u300171.\u03b2\u306f\u3001\u5b9a\u7fa944\u300137\u300117\u306b\u3088\u308a\u3001\u6697\u9ed9\u7684\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u5f8c\u7d99\u8005\u306e\u6570\u304c\u591a\u5c11\u7570\u5e38\u306a\u7528\u8a9e\u306b\u6e1b\u5c11\u3057\u307e\u3059\u3002\u30bc\u30eb\u30e1\u30ed\u30dc\u30ea\u30e5\u30fc\u30e0\u306e\u898b\u7fd2\u3044\u306b\u63a1\u7528\u3055\u308c\u305fDeDekind\u3092\u53c2\u7167\u3057\u3066\u3001\u81ea\u7531\u306a\u8a00\u8449\u9063\u3044\u306b\u304a\u3044\u3066\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/18000#breadcrumbitem","name":"Indukive Menge  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]