ideal background

ideal

/aɪˈdiː.əl/

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noun

理想，典范。

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

Examples :

"A good teacher strives for the ideal of creating a supportive learning environment for all students. "

一个好老师努力追求的目标是创建一个支持所有学生的理想学习环境。

"The ideal student in our class is always prepared and actively participates in discussions. "

我们班的理想学生总是做好准备，并积极参与讨论。

philosophy mind quality value being essential

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noun

理想，理想子环

A subring closed under multiplication by its containing ring.

Examples :

"The set of even numbers is an ideal in the ring of all integers. "

偶数集合是整数环中的一个理想，更准确地说是理想子环。

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noun

理想，下集，并闭集

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

Examples :

"The set of possible exam scores is an ideal in the partially ordered set of all possible grades. "

所有可能考试分数的集合，是所有可能成绩的部分有序集合中的一个理想（下集，并闭集）。

theory math essential

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noun

理想集合

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.

Examples :

"The set of small, insignificant details about a student's daily schedule forms an ideal, as every aspect of their day and any two activities combined are also part of that collection. "

关于学生每日行程的细小琐碎细节集合可以构成一个理想集合，因为他们每天的任何方面，以及任意两项活动的结合，也都是这个集合的一部分.

math theory essential

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noun

理想，李理想。

(Lie theory) 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.

Examples :

"The ideal of the student club was to raise funds for a local charity. "

这个学生俱乐部的理想目标是为当地慈善机构筹集资金。(Zhège xuésheng jùlèbù de lǐxiǎng mùbiāo shì wèi dāngdì císhàn jīgòu chóují zījīn.)

math theory essential

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adjective

理想的，完美的。

Optimal; being the best possibility.

Examples :

"A quiet study environment is the ideal place for focusing on my schoolwork. "

一个安静的学习环境是专注于学业的理想场所。

quality philosophy value essential

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adjective

理想的，完美的。

Perfect, flawless, having no defects.

Examples :

"Her presentation was ideal; it covered all the necessary points without any errors. "

她的演示非常理想，完美无瑕，涵盖了所有必要的要点，而且没有任何错误。

quality character philosophy essential

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adjective

理想的，观念的。

Pertaining to ideas, or to a given idea.

Examples :

"My ideal weekend involves a relaxing morning at home, followed by a picnic in the park. "

我理想中的周末是这样的：早上在家里放松地度过，然后去公园野餐。

philosophy mind theory essential

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adjective

理想的，空想的

Existing only in the mind; conceptual, imaginary.

Examples :

"My ideal vacation home is a cozy cabin nestled in the mountains. "

我理想中的度假小屋，只是存在于想象中，是一个依偎在山间舒适的小木屋。

mind philosophy theory quality essential

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adjective

唯心主义的，理想主义的

Teaching or relating to the doctrine of idealism.

Examples :

"the ideal theory or philosophy"

唯心主义的理论或哲学

philosophy doctrine education essential

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adjective

理想的，完美的。

Not actually present, but considered as present when limits at infinity are included.

Examples :

"An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle."

双曲盘上的理想三角形是由三条测地线围成的，这三条测地线恰好在圆上相交，可以想象成在无穷远处相交。