"quotient set" meaning in English

{
  "forms": [
    {
      "form": "quotient sets",
      "tags": [
        "plural"
      ]
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  "head_templates": [
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      "expansion": "quotient set (plural quotient sets)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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          "kind": "other",
          "name": "English entries with incorrect language header",
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          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
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            "Sciences",
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        }
      ],
      "examples": [
        {
          "text": "Given the set of integers ℤ, and the equivalence relation a∼b⟺a≡b( mod 2)⟺(a-b)%2=0, the quotient set is written ℤ/∼=̄0,̄1, consisting of the even and the odd integers."
        }
      ],
      "glosses": [
        "the set consisting of all equivalence classes"
      ],
      "id": "en-quotient_set-en-noun-hpve6Byf",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "set",
          "set"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ],
        [
          "equivalence class",
          "equivalence class"
        ]
      ],
      "qualifier": "given some set and an equivalence relation on that set",
      "raw_glosses": [
        "(mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes"
      ],
      "related": [
        {
          "english": "a topology on a quotient set derived from a topology on the generating set",
          "word": "quotient topology"
        },
        {
          "english": "a topological space constructed by endowing the quotient set with its quotient topology",
          "word": "quotient space"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "set of all equivalence classes",
          "word": "tekijäjoukko"
        }
      ]
    }
  ],
  "word": "quotient set"
}

{
  "forms": [
    {
      "form": "quotient sets",
      "tags": [
        "plural"
      ]
    }
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  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "english": "a topology on a quotient set derived from a topology on the generating set",
      "word": "quotient topology"
    },
    {
      "english": "a topological space constructed by endowing the quotient set with its quotient topology",
      "word": "quotient space"
    }
  ],
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      "examples": [
        {
          "text": "Given the set of integers ℤ, and the equivalence relation a∼b⟺a≡b( mod 2)⟺(a-b)%2=0, the quotient set is written ℤ/∼=̄0,̄1, consisting of the even and the odd integers."
        }
      ],
      "glosses": [
        "the set consisting of all equivalence classes"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "set",
          "set"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ],
        [
          "equivalence class",
          "equivalence class"
        ]
      ],
      "qualifier": "given some set and an equivalence relation on that set",
      "raw_glosses": [
        "(mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes"
      ],
      "topics": [
        "mathematics",
        "sciences"
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    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "set of all equivalence classes",
      "word": "tekijäjoukko"
    }
  ],
  "word": "quotient set"
}