"axiom of choice" meaning in Anglais

{
  "categories": [
    {
      "kind": "other",
      "name": "Calques en anglais issus d’un mot en allemand",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "Dates manquantes en anglais",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "Locutions nominales en anglais",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "Anglais",
      "orig": "anglais",
      "parents": [],
      "source": "w"
    }
  ],
  "derived": [
    {
      "word": "axiom of countable choice"
    },
    {
      "word": "axiom of denumerable choice"
    },
    {
      "word": "axiom of dependent choice"
    }
  ],
  "etymology_texts": [
    "(Date à préciser) Calque de l'allemand Axiom der Auswahl, apparu de l'article Untersuchungen über die Grundlagen der Mengenlehre I de Ernst Zermelo publié en 1908."
  ],
  "forms": [
    {
      "form": "axioms of choice",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "Exemples en anglais",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Exemples en anglais à traduire",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Lexique en anglais des mathématiques",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "Thomas Tymoczko, New Directions in the Philosophy of Mathematics: An Anthology, 1993",
          "text": "If V = L then the axioms of choice and the continuum hypothesis are both true, and the assertion that a measurable cardinal exists is false."
        },
        {
          "ref": "Bruno Poizat, traduit par Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, 2000",
          "text": "To clarify these ideas for the reader, let us show, without the axiom of choice, that a product of finitely many nonempty sets is nonempty: This is done by induction on the number n of sets. […] The finite axiom of choice is not an axiom, but rather a theorem that can be proved from the other axioms. In contrast, there are weak forms of the axiom of choice that are not provable."
        }
      ],
      "glosses": [
        "Axiome du choix."
      ],
      "id": "fr-axiom_of_choice-en-noun-~ju3xdnx",
      "topics": [
        "mathematics"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "AC"
    }
  ],
  "word": "axiom of choice"
}

{
  "categories": [
    "Calques en anglais issus d’un mot en allemand",
    "Dates manquantes en anglais",
    "Locutions nominales en anglais",
    "anglais"
  ],
  "derived": [
    {
      "word": "axiom of countable choice"
    },
    {
      "word": "axiom of denumerable choice"
    },
    {
      "word": "axiom of dependent choice"
    }
  ],
  "etymology_texts": [
    "(Date à préciser) Calque de l'allemand Axiom der Auswahl, apparu de l'article Untersuchungen über die Grundlagen der Mengenlehre I de Ernst Zermelo publié en 1908."
  ],
  "forms": [
    {
      "form": "axioms of choice",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "senses": [
    {
      "categories": [
        "Exemples en anglais",
        "Exemples en anglais à traduire",
        "Lexique en anglais des mathématiques"
      ],
      "examples": [
        {
          "ref": "Thomas Tymoczko, New Directions in the Philosophy of Mathematics: An Anthology, 1993",
          "text": "If V = L then the axioms of choice and the continuum hypothesis are both true, and the assertion that a measurable cardinal exists is false."
        },
        {
          "ref": "Bruno Poizat, traduit par Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, 2000",
          "text": "To clarify these ideas for the reader, let us show, without the axiom of choice, that a product of finitely many nonempty sets is nonempty: This is done by induction on the number n of sets. […] The finite axiom of choice is not an axiom, but rather a theorem that can be proved from the other axioms. In contrast, there are weak forms of the axiom of choice that are not provable."
        }
      ],
      "glosses": [
        "Axiome du choix."
      ],
      "topics": [
        "mathematics"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "AC"
    }
  ],
  "word": "axiom of choice"
}