noun Download 🔗Share A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. Examples : "A good teacher strives for the ideal of creating a supportive learning environment for all students. " "The ideal student in our class is always prepared and actively participates in discussions. " philosophy mind quality value being essential Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share A subring closed under multiplication by its containing ring. Examples : "The set of even numbers is an ideal in the ring of all integers. " math essential Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share (lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins). Examples : "The set of possible exam scores is an ideal in the partially ordered set of all possible grades. " theory math essential Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share 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. Examples : "The set of small, insignificant details about a student's daily schedule forms an ideal, as every aspect of their day and any two activities combined are also part of that collection. " math theory essential Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share (Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍. Examples : "The ideal of the student club was to raise funds for a local charity. " math theory essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Optimal; being the best possibility. Examples : "A quiet study environment is the ideal place for focusing on my schoolwork. " quality philosophy value essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Perfect, flawless, having no defects. Examples : "Her presentation was ideal; it covered all the necessary points without any errors. " quality character philosophy essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Pertaining to ideas, or to a given idea. Examples : "My ideal weekend involves a relaxing morning at home, followed by a picnic in the park. " philosophy mind theory essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Existing only in the mind; conceptual, imaginary. Examples : "My ideal vacation home is a cozy cabin nestled in the mountains. " mind philosophy theory quality essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Teaching or relating to the doctrine of idealism. Examples : "the ideal theory or philosophy" philosophy doctrine education essential Chat with AIVocabulary GamePractice Reading
adjective Download 🔗Share Not actually present, but considered as present when limits at infinity are included. Examples : "An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle." math essential Chat with AIVocabulary GamePractice Reading