ideal vs one

ideal

noun
  • A subring closed under multiplication by its containing ring. 

  • 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 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. 

one

noun
  • The neutral element with respect to multiplication in a ring. 

  • One run scored by hitting the ball and running between the wickets; a single. 

  • A joke or amusing anecdote. 

  • A particularly special or compatible person or thing. 

  • A one-dollar bill. 

  • Used instead of ! to amplify an exclamation, parodying unskilled typists who forget to press the shift key while typing exclamation points, thus typing "1". 

  • One o'clock, either a.m. or p.m. 

  • The digit or figure 1. 

pron
  • The first mentioned of two things or people, as opposed to the other. 

  • Functions as a relative pronoun at the end of a relative clause. 

  • Any person (applying to people in general). 

  • One thing (among a group of others); one member of a group. 

  • Any person, entity or thing. 

  • Used as a noun substituent following a possessive determiner. 

verb
  • To cause to become one; to gather into a single whole; to unite. 

adj
  • Whole, entire. 

  • Being an unknown person with the specified name; see also "a certain". 

  • The same. 

  • In agreement. 

  • Being a preeminent example. 

  • Sole, only. 

  • Being a single, unspecified thing; a; any. 

  • Of a period of time, being particular. 

particle
  • Used to emphasize or explain something, with an implied antecedent. 

  • Used at the end of a sentence to highlight the characteristics of someone or something. 

  • A nominalizer; used to form a noun phrase without a head noun. 

num
  • The cardinality of the smallest nonempty set. 

  • The first positive number in the set of natural numbers. 

  • The number represented by the Arabic numeral 1; the numerical value equal to that cardinal number. 

  • The ordinality of an element which has no predecessor, usually called first or number one. 

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