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ideal

EN[-iːəl] [aɪˈdɪəl] [aɪˈdiː.əl]
US
WIdeal
  • Ideal may refer to:
FR idéal

    Definition of ideal in English Dictionary

  • NounPLidealsSUF-eal
    1. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
      1. Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny - Carl Schurz
    2. (mathematics, order theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
      1. If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal.
    3. (for example, algebra) A subring closed under multiplication by its containing ring.
      1. Let be the ring of integers and let be its ideal of even integers. Then the quotient ring is a Boolean ring.
      2. The product of two ideals and is an ideal which is a subset of the intersection of and . This should help to understand why maximal ideals are prime ideals. Likewise, the union of and is a subset of .
  • AdjectiveCOMmore idealSUPmost ideal
    1. Optimal; being the best possibility.
      1. Perfect, flawless, having no defects.
        1. Pertaining to ideas, or to a given idea.
          1. Existing only in the mind; conceptual, imaginary.
            1. Teaching or relating to the doctrine of idealism.
              1. the ideal theory or philosophy
            2. (mathematics) Not actually present, but considered as present when limits at infinity are included.
              1. ideal point
              2. An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.
          2. More Examples
            1. Used in the Middle of Sentence
              • Hundreds of Kanker's troops would have to be thrown into the job of plugging the holes, a difficult task under ideal conditions, but a pig of a task in a “dustout”.
              • The US Constitution aimed to embody the ideals of diverse groups of people, from Puritans to Deists.
              • These precancerous and fully tumorigenic models provide an ideal system to study the role of NRs in lung cancer pathogenesis including preneoplasia and tumor formation.
          • Part-of-Speech Hierarchy
            1. Adjectives
              • Nouns
                • Countable nouns
              Related Links:
              1. en ideals
              2. en idealist
              3. en idealized
              4. en ideally
              5. en idealize
              Source: Wiktionary
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              Meaning of ideal for the defined word.

              Grammatically, this word "ideal" is an adjective. It's also a noun, more specifically, a countable noun.
              Difficultness: Level 1
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              Definiteness: Level 9
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              Definite    ➨     Versatile