What is the meaning of Ideal?

Pertaining to ideas, or to a given idea.

Existing only in the mind; conceptual, imaginary.

Optimal; being the best possibility.

Perfect, flawless, having no defects.

Teaching or relating to the doctrine of idealism.

Not actually present, but considered as present when limits at infinity are included.

A thing which exists in the mind but not in reality; in ontological terms, a thing which has essence but not existence.

A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.

A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.

A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

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.

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.

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.

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ideal (optimal, perfect)

ideal:

  1. optimal; being the best possibility.
  2. pertaining to ideas, or to a given idea.

optimal; being the best possibility.

pertaining to ideas, or to a given idea.

ideal: a subring closed under multiplication by its containing ring.

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notional

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fantasy

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ideal (perfect)

ideal; perfect standard

ideal; special subsets of a ring

ideal (model to be imitated)

ambition

ideal (just as what one wants)

worthy of imitation

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Source: wiktionary.org