[
  {
    "word": "ideal",
    "phonetic": "/a\u026a\u02c8di\u02d0.\u0259l/",
    "phonetics": [
      {
        "text": "/a\u026a\u02c8di\u02d0.\u0259l/",
        "audio": "https://api.dictionaryapi.dev/media/pronunciations/en/ideal-us.mp3",
        "sourceUrl": "https://commons.wikimedia.org/w/index.php?curid=1749869",
        "license": {
          "name": "BY-SA 3.0",
          "url": "https://creativecommons.org/licenses/by-sa/3.0"
        }
      }
    ],
    "meanings": [
      {
        "partOfSpeech": "noun",
        "definitions": [
          {
            "definition": "A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "A subring closed under multiplication by its containing ring.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "(lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "(Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) \ud835\udd8d of a given Lie algebra \ud835\udd8c such that the Lie bracket [\ud835\udd8c,\ud835\udd8d] is a subset of \ud835\udd8d.",
            "synonyms": [],
            "antonyms": []
          }
        ],
        "synonyms": [
          "Lie ideal"
        ],
        "antonyms": [
          "filter"
        ]
      },
      {
        "partOfSpeech": "adjective",
        "definitions": [
          {
            "definition": "Optimal; being the best possibility.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "Perfect, flawless, having no defects.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "Pertaining to ideas, or to a given idea.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "Existing only in the mind; conceptual, imaginary.",
            "synonyms": [],
            "antonyms": []
          },
          {
            "definition": "Teaching or relating to the doctrine of idealism.",
            "synonyms": [],
            "antonyms": [],
            "example": "the ideal theory or philosophy"
          },
          {
            "definition": "Not actually present, but considered as present when limits at infinity are included.",
            "synonyms": [],
            "antonyms": [],
            "example": "An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle."
          }
        ],
        "synonyms": [],
        "antonyms": []
      }
    ],
    "license": {
      "name": "CC BY-SA 3.0",
      "url": "https://creativecommons.org/licenses/by-sa/3.0"
    },
    "sourceUrls": [
      "https://en.wiktionary.org/wiki/ideal"
    ]
  }
]