A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
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 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.
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.
Pertaining to ideas, or to a given idea.
Perfect, flawless, having no defects.
Teaching or relating to the doctrine of idealism.
Someone or something with similar claims of quality or distinction as another.
A competitor (person, team, company, etc.) with the same goal as another, or striving to attain the same thing. Defeating a rival may be a primary or necessary goal of a competitor.
Having the same pretensions or claims; standing in competition for superiority.
To be equal to, or match, or to surpass another.
To oppose or compete with.
To strive to equal or excel; to emulate.