dictionary 路 eo1.org

ideal

Fetched 2026-10-26 (cache).

Synonyms: idea, deal, ideas, ideat, ileal, idear, idal, idel, idean, idead, idell

Antonyms: idea, deal, ideas, ideat, ileal, idear, idal, idel, idean, idead, idell

Related words from Datamuse; suggestions, not definitions.

Adjective

  1. [[pertaining|Pertaining]] to [[idea]]s, or to a given idea.
  2. [[exist|Existing]] only in the [[mind]]; [[conceptual]], [[imaginary]].
  3. [[optimal|Optimal]]; being the [[best]] [[possibility]].
  4. [[perfect|Perfect]], [[flawless]], having no [[defect]]s.
  5. Teaching or relating to the doctrine of [[idealism]].
  6. {{lb|en|mathematics}} Not actually present, but considered as present when [[limit]]s at [[infinity]] are included.

Noun

  1. {{senseid|en|a perfect standard of beauty, intellect etc.}}A [[perfect]] [[standard]] of beauty, intellect etc., or a standard of [[excellence]] to [[aim]] at.
  2. {{lb|en|algebra|ring theory}} A [[two-sided ideal]]; a [[subset]] of a [[ring]] which is [[closed]] under both [[left]] and [[right]] [[multiplication]] by [[elements]] of the ring.
  3. {{lb|en|algebra|order theory|lattice theory}} A non-[[empty set|empty]] [[lower set]] (of a [[partially ordered set]]) which is [[closure|closed]] under binary [[suprema]] (a.k.a. [[join]]s).<ref>{{pedia|Boolean prime ideal theorem#Prime ideal theorems}}</ref>
  4. {{lb|en|set theory}} 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.
  5. {{lb|en|algebra|Lie theory}} A [[Lie subalgebra]] (subspace that is closed under the [[Lie bracket]]) 饾枍 of a given [[Lie algebra]] 饾枌 such that the Lie bracket [饾枌,饾枍] is a [[subset]] of 饾枍.
  6. {{lb|en|algebra}} 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.<ref>{{cite-web|1=en|year=2004|author={{w|Vaughan Pratt}}|work=Chapter 1 : Lattice Theory|url=http://boole.stanford.edu/cs353/handouts/book1.pdf|publisher=boole.stanford.edu|section=&sect;1.3.5}}</ref>

Proper noun

  1. {{place|en|city|s/Georgia|c/USA}}.
  2. {{place|en|unincorporated community|s/Illinois}}.
  3. {{place|en|unincorporated community|s/South Dakota}}.

Source: Wiktionary 路 CC BY-SA 4.0 (Wiktionary dump) 路 cached copy, not a rewrite.