ideal

IPA: aɪdˈiɫ

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) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
(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.

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.

Examples of "ideal" in Sentences

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