ideal

Pluralideals

1. 1
   adjective

   The best you could possibly have or pick for a purpose.

   Like finding the puzzle piece that fits exactly where you need it.

   This quiet street is an ideal place to raise kids.

   Warm, dry weather is ideal for a long hike.

   Similarperfect, optimal, best, suitable, excellent

   Oppositeunsuitable, poor, inappropriate

2. 2
   adjective

   Perfect, with nothing wrong or missing.

   Like a clean sheet of paper with no marks on it at all.

   In her mind she pictured an ideal world with no hunger.

   No team is ever truly ideal; every group has weak spots.

   Similarperfect, flawless, faultless, impeccable

   Oppositeflawed, imperfect, faulty

3. 3
   nouncountable

   A perfect example or standard that you try to reach.

   Like a finish line you keep moving toward.

   She set high ideals for how the team should behave.

   Honesty was the ideal he tried hardest to live up to.

   Similarstandard, model, principle, value, paragon

   Note
4. 4
   adjective

   Found only in the mind, not in the real world.

   Like a dream city that lives only inside your head.

   The philosopher spoke of an ideal realm beyond the physical world.

   To him, perfect justice was an ideal notion rather than a real thing.

   Similartheoretical, hypothetical, conceptual, imaginary, abstract

   Oppositereal, actual, concrete, material

   Note
5. 5
   adjective

   Having to do with ideas, or with one certain idea.

   The book is less about history and more about ideal questions, such as what truth and beauty are.

   Their discussion stayed at an ideal level, far from practical concerns.

   Similarconceptual

   Oppositematerial

6. 6
   adjective

   Belonging to or teaching the idea-based view called idealism.

   She defended an ideal account of the mind against materialist critics.

   In the ideal philosophy he taught, the world is made of thoughts, not things.

   Oppositematerialist

7. 7
   nouncountable

   In math, a part of a ring that stays inside itself when you multiply its members by any ring element.

   Like a club where multiplying any member by anyone keeps them in the club.

   The students learned how to find an ideal inside a ring.

   Every ring contains at least one ideal made of just zero.

   Note
8. 8
   adjective

   In math, not really there, but treated as present once points at infinity are added.

   Like train tracks that look as if they meet far off on the horizon.

   Two parallel lines meet at an ideal point far away.

   Mathematicians add ideal points to complete the picture.

   Note
9. 9
   nouncountable

   In math, a set that keeps everything below its members and also holds the combination of any two of them.

   Like a list that always adds everyone ranked below those already on it.

   The class showed that this set forms an ideal in the order.

   An ideal must include every element below the ones it already holds.

   Note
10. 10
    nouncountable

    In math, a group of sets treated as small, closed under taking parts and joining two members.

    Like a box of small things: any piece of a small thing is small, and two small things together are still small.

    The empty set always belongs to an ideal of small sets.

    Finite sets form an ideal inside the collection of all sets of numbers.

    Note
11. 11
    nouncountable

    In advanced math, a part of a Lie algebra that stays inside itself when bracketed with any element.

    The students checked whether this subspace was an ideal of the Lie algebra.

    Every Lie algebra has itself as an ideal.

    Note
12. 12
    nouncountable

    In math, a part of a semigroup where adding any outside element to a member gives a result that stays outside.

    The group studied whether this set is an ideal of the semigroup.

    He showed that the subset forms an ideal under the given rule.

    Note

Showing meanings only. Show all 12