ideal
IPA: aΙͺdΛiΙ«
noun
- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
- (algebra, ring theory) A subring closed under multiplication by its containing ring.
- (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
- (set theory) 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.
- (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) π of a given Lie algebra π such that the Lie bracket [π,π] is a subset of π.
- (algebra) A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
- A city in Georgia, United States.
- An unincorporated community in Illinois.
- An unincorporated community in South Dakota.
adjective
- Optimal; being the best possibility.
- Perfect, flawless, having no defects.
- Pertaining to ideas, or to a given idea.
- Existing only in the mind; conceptual, imaginary.
- Teaching or relating to the doctrine of idealism.
- (mathematics) Not actually present, but considered as present when limits at infinity are included.
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Examples of "ideal" in Sentences
- Without question, Barbie has one quality that merits the term ideal, and that is timelessness.
- Portability: Liberal checkpoint system makes the title ideal for small bursts of gameplay perfect for the on-the-go gamer.
- Still, the word "ideal" is important: Ideal conditions for driving in a fuel-saving manner aren't easy to find or sustain.
- _obedience_ is the only evidence of the ideal rule; for in respect to the conduct of the material world, the _ideal_ and the _actual_ are the same.
- Jehovah's dealing with his people, the mourning for her presence being the completest expression of grief, we can come to understand something of the Jewish ideal of marriage and of the high honor, _because of this ideal_, in which women were held.
- Indeed, ideal observer analyses that go too far in this direction seem to become circular β the Λidealβ’ observer is ideal because she always makes proper judgments, those being defined as just those judgments the ideal observer would make (Broad 1959, p. 263).
- But the ideal is an independent FCC or Congress that pays attention and demands that these companies act in the public interest, that they be aware of their role as the keepers and switches of American information, that they have special duties that go beyond the ordinary companies 'duties.
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