"mathematical induction" meaning in All languages combined

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  "lang_code": "en",
  "pos": "noun",
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        {
          "ref": "2007, Mark Bridger, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 2",
          "text": "Mathematical induction is often compared to the behavior of dominos. The dominos are stood up on edge close to each other in a long row. When one is knocked over, it hits the next one (analogous to n in S implies n + 1 in S), which in turn hits the next, etc. If then we hit the first (0 in S), then they will all eventually fall (S is all of ℕ). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.",
          "type": "quotation"
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      "glosses": [
        "A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n."
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        "(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n."
      ],
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          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "shùxué guīnàfǎ",
          "sense": "method of proof",
          "word": "數學歸納法 /数学归纳法"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "method of proof",
          "tags": [
            "feminine"
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          "word": "indukcja matematyczna"
        },
        {
          "code": "tl",
          "lang": "Tagalog",
          "sense": "method of proof",
          "word": "sipnaying pamuuran"
        }
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        "mathematical induction"
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  "word": "mathematical induction"
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          "ref": "2007, Mark Bridger, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 2",
          "text": "Mathematical induction is often compared to the behavior of dominos. The dominos are stood up on edge close to each other in a long row. When one is knocked over, it hits the next one (analogous to n in S implies n + 1 in S), which in turn hits the next, etc. If then we hit the first (0 in S), then they will all eventually fall (S is all of ℕ). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.",
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        "A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n."
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        "(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n."
      ],
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  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "shùxué guīnàfǎ",
      "sense": "method of proof",
      "word": "數學歸納法 /数学归纳法"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "method of proof",
      "tags": [
        "feminine"
      ],
      "word": "indukcja matematyczna"
    },
    {
      "code": "tl",
      "lang": "Tagalog",
      "sense": "method of proof",
      "word": "sipnaying pamuuran"
    }
  ],
  "word": "mathematical induction"
}