ideal vs specific

adj

Pertaining to ideas, or to a given idea.
Not actually present, but considered as present when limits at infinity are included.
Optimal; being the best possibility.
Existing only in the mind; conceptual, imaginary.
Perfect, flawless, having no defects.
Teaching or relating to the doctrine of idealism.

noun

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 subring closed under multiplication by its containing 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 perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
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.

adj

intended for, or applying to, a particular thing.
of a value divided by mass (e.g. specific orbital energy)
similarly referring to a value divided by any measure which acts to standardize it (e.g. thrust specific fuel consumption, referring to fuel consumption divided by thrust)
Serving to identify a particular thing (often a disease or condition), with little risk of mistaking something else for it.
Hyponyms: monospecific, multispecific, oligospecific, paucispecific
limited to a particular antibody or antigen.
a measure compared with a standard reference value by division, to produce a ratio without unit or dimension (e.g. specific refractive index is a pure number, and is relative to that of air)
pertaining to a species, as a taxon or taxa at the rank of species.
special, distinctive or unique.
being a remedy for a particular disease on a deeper level, rather than just masking the symptoms
explicit or definite.

noun