das Ideal
ideal
An idea of perfect beauty, perfection, or a perfect state that is regarded as the highest goal.
EXAMPLE
Für ihn ist ein friedliches Zusammenleben das Ideal.
For him, peaceful coexistence is the ideal.
das Ideal
ideal
das Ideal, die Ideale
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Meanings
das Ideal
ideal
A person or thing regarded as a perfect embodiment of certain qualities and used as a model to follow.
EXAMPLE
Sie war für viele junge Ärztinnen das Ideal einer engagierten Medizinerin.
For many young female doctors, she was the ideal of a dedicated physician.
das Ideal
ideal
In mathematics, a particular subset of a ring that satisfies certain closure conditions under addition and multiplication by elements of the ring.
EXAMPLE
Das Ideal wird in diesem Beweis als Teilmenge des Polynomrings betrachtet.
In this proof, the ideal is considered as a subset of the polynomial ring.
Forms
Forms adapted from the German Wiktionary entry Ideal, by Wiktionary contributors, licence CC BY-SA 4.0.
At a glance
| gender | neuter das |
|---|---|
| plural | die Ideale |
| genitive | des Ideals |
The four cases
| singular | plural | |
|---|---|---|
| nominative | das Ideal | die Ideale |
| accusative | das Ideal | die Ideale |
| dative | dem Ideal | den Idealen |
| genitive | des Ideals | der Ideale |
The article changes with the case; it is shown in colour.
Usage tips
Typical collocations
Common collocations include „ein Ideal anstreben“ (to strive for an ideal), „seine Ideale verwirklichen“ (to realize one's ideals), and „seine Ideale aufgeben“ (to give up one's ideals). These expressions describe how someone deals with their ideas of a perfect state.
EXAMPLE
Mit diesem sozialen Projekt möchte sie ihre Ideale verwirklichen.
She wants to realize her ideals through this social project.
Genitive complement
„Das Ideal eines …“ (the ideal of a …) or „das Ideal einer …“ (the ideal of a …) can be used to indicate what type of person or thing someone or something perfectly embodies. This combination is often used with the verb „verkörpern“ (to embody).
EXAMPLE
Für das Team verkörpert die neue Chefin das Ideal einer gerechten Führungskraft.
For the team, the new manager embodies the ideal of a fair leader.
Mathematical collocations
In mathematical texts, „in einem Ideal liegen“ (to lie in an ideal) is a typical collocation. It indicates that an element belongs to this subset; „in“ is used with the dative here.
EXAMPLE
Im nächsten Schritt zeigen wir, dass dieses Element in dem Ideal liegt.
In the next step, we show that this element lies in the ideal.
In real life
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