flaw vs ideal

flaw

verb
  • To add a flaw to, to make imperfect or defective. 

  • To become imperfect or defective; to crack or break. 

noun
  • A storm of short duration. 

  • An inclusion, stain, or other defect of a diamond or other gemstone. 

  • A sudden burst of noise and disorder 

  • A crack or breach, a gap or fissure; a defect of continuity or cohesion. 

  • A defect or error in a contract or other document which may make the document invalid or ineffective. 

  • A defect, fault, or imperfection, especially one that is hidden. 

  • A sudden burst or gust of wind of short duration; windflaw. 

ideal

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
  • 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 flaw and ideal occurred in a corpus of books? (source: Google Ngram Viewer )