{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0XKWSSY8P2"
    },
    {
      "field": "uses",
      "target": "3KM7HQWKXP"
    },
    {
      "field": "uses",
      "target": "3KX0KQ7V05"
    },
    {
      "field": "uses",
      "target": "8A4GGX1MEY"
    },
    {
      "field": "uses",
      "target": "8JYC7S28JX"
    },
    {
      "field": "uses",
      "target": "8VB096R12H"
    },
    {
      "field": "uses",
      "target": "CTXX2CXFRB"
    },
    {
      "field": "uses",
      "target": "E0V3N93DX8"
    },
    {
      "field": "uses",
      "target": "HBHNB63J7R"
    },
    {
      "field": "uses",
      "target": "HK3BRMK912"
    },
    {
      "field": "uses",
      "target": "J0NR3YRW07"
    },
    {
      "field": "uses",
      "target": "RT62ZAN3JB"
    },
    {
      "field": "uses",
      "target": "T34R8Q0FJD"
    },
    {
      "field": "uses",
      "target": "T4RFYT8HDN"
    },
    {
      "field": "uses",
      "target": "WXV3ZNS2F9"
    },
    {
      "field": "about",
      "target": "8A4GGX1MEY"
    }
  ],
  "body": "\n## Summary\n\nA sequence has a limit $L$ when its terms come and stay arbitrarily close to $L$ for large indices. Limits of sequences are the base of the notions of convergence, continuity and series in analysis. The node [[limit of a sequence|0XKWSSY8P2]] gives the precise definition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "KH9EY8G6YZ"
    ],
    "kind": "concept",
    "msc": [
      "40A05"
    ],
    "name": "Limit of a sequence",
    "same_as": {
      "wikidata": "Q847204",
      "wikipedia": "Limit of a sequence"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Limit_of_a_sequence"
      }
    ],
    "tag": "05M5SWSZZD"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/05M5SWSZZD/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/05M5SWSZZD.md",
  "msc": [
    "40A05"
  ],
  "name": "Limit of a sequence",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/05M/05M5SWSZZD.md",
  "status": null,
  "tag": "05M5SWSZZD",
  "uri": "m2://05M5SWSZZD",
  "url": "https://tamnd.github.io/math2/wiki/limit-of-a-sequence/",
  "writing": {
    "tag": "05M5SWSZZD",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
