What does "ideal" mean?
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
adj, name, noun ·Very common ·Middle school level
This entry combines structured lexical data with WordToolSet review checks. Definitions, examples, synonyms, and usage notes may come from different source tables, so the page is designed to show evidence from more than one angle before you rely on "ideal" in a final draft.
If a word has several senses, prefer the sense that matches your sentence's grammar and surrounding context. A correct definition can still be the wrong choice when the sentence needs a different register, emphasis, or level of specificity.
Read the first definition as a starting point, then check the example, synonyms, and part of speech before treating "ideal" as the right word for your sentence.
If your draft is formal, technical, persuasive, or sensitive, compare "ideal" with a nearby alternative so the final choice matches both meaning and reader expectation.
Check whether "ideal" is acting as adj, name, noun in your sentence. A definition is only useful when the grammar matches the way the word is being used.
Compare it with "paragon" and other nearby choices to see whether the sentence needs a softer, stronger, or more familiar word.
Use the example sentence below as an evidence check, then read your own sentence out loud to catch tone or rhythm problems.
Review note: Definition pages are checked for source coverage, sentence evidence, synonym support, and editorial insight before they are treated as approval-ready pages. If the evidence is too thin, the page remains available to users but is kept out of the approval-facing indexed inventory.
Before publishing a sentence with "ideal", ask whether the word helps the reader understand the idea faster. A precise word should reduce confusion, not simply make the sentence look more polished.
When the definition, synonym evidence, and example context point in the same direction, the word is usually a safer choice. When they conflict, revise the sentence or choose a clearer alternative.
"Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny - Carl Schurz"
"Let #92;mathbb#123;Z#125; be the ring of integers and let 2#92;mathbb#123;Z#125; be its ideal of even integers. Then the quotient ring #92;mathbb#123;Z#125;#47;2#92;mathbb#123;Z#125; is a Boolean ring."
"1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119, An ideal A of L is called complete if it contains all least upper bounds of its subsets that exist in L. Bishop and Schreiner [80] studied conditions under which joins of ideals in the lattices of all ideals and of all complete ideals coincide."
"Formally, an ideal I of a given set X is a nonempty subset of the powerset #92;mathcal#123;P#125;(X) such that: (1)#92;#92;emptyset#92;inI, (2)#92;A#92;inI#92;andB#92;subseteqA#92;impliesB#92;inI and (3)#92;A,B#92;inI#92;impliesA#92;cupB#92;inI."
"If 𝖌 is a Lie algebra, 𝖍 is an ideal and the Lie algebras 𝖍 and 𝖌/𝖍 are solvable, then 𝖌 is solvable."
"The set of natural numbers with multiplication as the monoid operation (instead of addition) has multiplicative ideals, such as, for example, the set {1, 3, 9, 27, 81, ...}. If any member of it is multiplied by a number which is not a power of 3 then the result will not be a power of three."
"The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —"
"1751 April 13, Samuel Johnson, The Rambler, Number 112, reprinted in 1825, The Works of Samuel Johnson, LL. D., Volume 1, Jones & Company, page 194, There will always be a wide interval between practical and ideal excellence; […] ."
"the ideal theory or philosophy"
"ideal point"
"We are haunted by an ideal life, and it is because we have within us the beginning and the possibility for it."
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
Common synonyms include: paragon, absolute, abstract, abstract principle, abstract value, abstruse.
We are haunted by an ideal life, and it is because we have within us the beginning and the possibility for it.
Pronounced /aɪˈdi(ə)l/.
From French idéal, from Late Latin ideālis (“existing in idea”), by surface analysis, idea + -al, from Latin idea (“idea”); see idea. In mathematics, the noun ring theory sense was first introduced by German mathematician Richard Dedekind in his 1871 edition of a text on number theory. The concept was quickly expanded to ring theory and later generalised to order theory. The set theory and Lie theory senses can be regarded as applications of the order theory sense.