boundary vs ideal

boundary

noun
  • (of a set) The set of points in the closure of a set S, not belonging to the interior of that set. 

  • An edge or line marking an edge of the playing field. 

  • The bounds, confines, or limits between immaterial things (such as one’s comfort zone, privacy, or professional sphere and the realm beyond). 

  • The dividing line or location between two areas. 

  • An event whereby the ball is struck and either touches or passes over a boundary (with or without bouncing), usually resulting in an award of 4 (four) or 6 (six) runs respectively for the batting team. 

ideal

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

  • 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 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 π–Œ such that the Lie bracket [π–Œ,𝖍] is a subset of 𝖍. 

adj
  • 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. 

How often have the words boundary and ideal occurred in a corpus of books? (source: Google Ngram Viewer )