atom vs ideal

atom

noun
  • A non-zero member of a partially ordered set that has only zero below it (assuming that the poset has a least element, its "zero"). 

  • The smallest possible amount of matter which still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons. 

  • In logical atomism, a fundamental fact that cannot be further broken down. 

  • The smallest medieval unit of time, equal to fifteen ninety-fourths of a second. 

  • An age group division in hockey for nine- to eleven-year-olds. 

  • An element of a set that is not itself a set; an urelement. 

  • A mote of dust in a sunbeam. 

  • A hypothetical particle posited by Greek philosophers as an ultimate and indivisible component of matter. 

  • The smallest, indivisible constituent part or unit of something. 

  • A very small amount; a whit. 

  • An individual number or symbol, as opposed to a list; a scalar value. 

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