"axiom of extensionality" meaning in All languages combined

{
  "head_templates": [
    {
      "args": {
        "1": "en",
        "2": "noun"
      },
      "expansion": "axiom of extensionality",
      "name": "head"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Polish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements."
      ],
      "id": "en-axiom_of_extensionality-en-noun-f~PdylR0",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "axiom",
          "axiom"
        ]
      ],
      "raw_glosses": [
        "(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "axiom of extensionality",
          "word": "ekstensionaalisuusaksiooma"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "axiom of extensionality",
          "tags": [
            "neuter"
          ],
          "word": "Extensionalitätsaxiom"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "axiom of extensionality",
          "tags": [
            "masculine"
          ],
          "word": "aksjomat ekstensjonalności"
        }
      ],
      "wikipedia": [
        "axiom of extensionality"
      ]
    }
  ],
  "word": "axiom of extensionality"
}

{
  "head_templates": [
    {
      "args": {
        "1": "en",
        "2": "noun"
      },
      "expansion": "axiom of extensionality",
      "name": "head"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Finnish translations",
        "Terms with German translations",
        "Terms with Polish translations",
        "en:Logic",
        "en:Mathematics",
        "en:Set theory"
      ],
      "glosses": [
        "One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "axiom",
          "axiom"
        ]
      ],
      "raw_glosses": [
        "(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "axiom of extensionality"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "axiom of extensionality",
      "word": "ekstensionaalisuusaksiooma"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "axiom of extensionality",
      "tags": [
        "neuter"
      ],
      "word": "Extensionalitätsaxiom"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "axiom of extensionality",
      "tags": [
        "masculine"
      ],
      "word": "aksjomat ekstensjonalności"
    }
  ],
  "word": "axiom of extensionality"
}