ideal

Meanings

1. 1
   noun A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
2. 2
   noun A subring closed under multiplication by its containing ring.
3. 3
   noun (lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
4. 4
   noun 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.
5. 5
   noun (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.
6. 6
   adjective Optimal; being the best possibility.
7. 7
   adjective Perfect, flawless, having no defects.
8. 8
   adjective Pertaining to ideas, or to a given idea.
9. 9
   adjective Existing only in the mind; conceptual, imaginary.
10. 10
    adjective Teaching or relating to the doctrine of idealism.
11. 11
    adjective Not actually present, but considered as present when limits at infinity are included.