"lexicographic order" meaning in English

{
  "forms": [
    {
      "form": "lexicographic orders",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lexicographic order (plural lexicographic orders)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "68 32",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "60 40",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "71 29",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′)."
      ],
      "id": "en-lexicographic_order-en-noun-YB8iD5-9",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ],
        [
          "Cartesian product",
          "Cartesian product"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′)."
      ],
      "synonyms": [
        {
          "_dis1": "63 37",
          "word": "lexicographical order"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )"
      ],
      "id": "en-lexicographic_order-en-noun-0lkL5G84",
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "wikipedia": [
    "lexicographic order"
  ],
  "word": "lexicographic order"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "Pages with 1 entry",
    "Pages with entries"
  ],
  "forms": [
    {
      "form": "lexicographic orders",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lexicographic order (plural lexicographic orders)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ],
        [
          "Cartesian product",
          "Cartesian product"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′)."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "lexicographical order"
    }
  ],
  "wikipedia": [
    "lexicographic order"
  ],
  "word": "lexicographic order"
}