ideal vs limit

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. 

limit

noun
  • A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge). 

  • A restriction; a bound beyond which one may not go. 

  • The cone of a diagram through which any other cone of that same diagram can factor uniquely. 

  • A determining feature; a distinguishing characteristic. 

  • Fixed limit. 

  • The final, utmost, or furthest point; the border or edge. 

  • The first group of riders to depart in a handicap race. 

  • A person who is exasperating, intolerable, astounding, etc. 

  • Any of several abstractions of this concept of limit. 

verb
  • To restrict; not to allow to go beyond a certain bound, to set boundaries. 

  • To have a limit in a particular set. 

adj
  • Being a fixed limit game. 

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