ideal

1. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.

   Ideal, Idealbild

   идеа́лideál

   ідеа́лideál

2. A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.

   Ideal

   идеа́лideál

3. A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

   идеа́лideál

4. 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. 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.

6. 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.

1. The beach is an ideal place for children to play.

   Пляж — ідеальне місце для дитячих ігор.

   ruПляж — идеальное место для детской игры.

   deAm Strand können Kinder ausgezeichnet spielen.

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2. That would be ideal.

   Це було б ідеально.

   ruЭто было бы идеально.

   deDas wäre ideal.

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3. It's ideal weather for a picnic.

   Це ідеальна погода для пікніка.

   ruЭто идеальная погода для пикника.

   deDas Wetter ist ideal für ein Picknick.

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4. It isn't ideal.

   Це не ідеально.

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5. It's not ideal.

   Це не ідеально.

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