closure vs ideal

closure

noun
  • The smallest closed set which contains the given set. 

  • An event or occurrence that signifies an ending. 

  • A device to facilitate temporary and repeatable opening and closing. 

  • An abstraction that represents a function within an environment, a context consisting of the variables that are both bound at a particular time during the execution of the program and that are within the function's scope. 

  • That which closes or shuts; that by which separate parts are fastened or closed. 

  • The smallest set that both includes a given subset and possesses some given property. 

  • A method of ending a parliamentary debate and securing an immediate vote upon a measure before a legislative body. 

  • The process whereby the reader of a comic book infers the sequence of events by looking at the picture panels. 

  • The phenomenon by which a group maintains its resources by the exclusion of others from their group based on varied criteria. แต‚แต– 

  • The act of shutting or closing something permanently or temporarily. 

  • The act of shutting; a closing. 

  • A feeling of completeness; the experience of an emotional conclusion, usually to a difficult period. 

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) ๐– of a given Lie algebra ๐–Œ such that the Lie bracket [๐–Œ,๐–] is a subset of ๐–. 

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