"lexicographic order" meaning in All languages combined

{
  "forms": [
    {
      "form": "lexicographic orders",
      "tags": [
        "plural"
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
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          "_dis": "68 32",
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      "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"
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        [
          "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"
        }
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      "topics": [
        "mathematics",
        "sciences"
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      ],
      "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 )"
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      "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 )"
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  "wikipedia": [
    "lexicographic order"
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  "word": "lexicographic order"
}

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  "forms": [
    {
      "form": "lexicographic orders",
      "tags": [
        "plural"
      ]
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  "senses": [
    {
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      ],
      "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′)."
      ],
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      "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′)."
      ],
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      "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 )"
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      "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 )"
      ],
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  "synonyms": [
    {
      "word": "lexicographical order"
    }
  ],
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    "lexicographic order"
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  "word": "lexicographic order"
}