minimum
das Minimum, die Minima
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minimum
The smallest possible or a very small amount, the smallest possible measure, or the lowest degree of something.
Er beschränkt seine Ausgaben auf ein absolutes Minimum, um Geld zu sparen.
He limits his expenses to an absolute minimum in order to save money.
minimum
In mathematics, the smallest value that a function takes within a specific range.
In der Kurvendiskussion müssen wir das Minimum der Funktion bestimmen.
In curve sketching, we have to determine the minimum of the function.
| gender | neuter das |
|---|---|
| plural | die Minima |
| genitive | des Minimums |
| singular | plural | |
|---|---|---|
| nominative | das Minimum | die Minima |
| accusative | das Minimum | die Minima |
| dative | dem Minimum | den Minima |
| genitive | des Minimums | der Minima |
The article changes with the case; it is shown in colour.
'Minimum' is a word from Latin and means 'the smallest'. It is often used in a somewhat more formal or technical context.
Die Anforderungen für das Projekt wurden auf ein Minimum reduziert.
The requirements for the project were reduced to a minimum.
A very common construction is 'auf ein Minimum' (to a minimum) in combination with verbs such as 'reduzieren' (to reduce), 'beschränken' (to limit), or 'senken' (to lower). It expresses that something is reduced to the smallest possible amount.
Wir müssen unsere Kosten auf ein Minimum reduzieren.
We have to reduce our costs to a minimum.
'Minimum' is often combined with adjectives to specify the type of minimum level. Common combinations are 'ein absolutes Minimum' (an absolute minimum), 'ein gesetzliches Minimum' (a legal minimum), or 'das Existenzminimum' (the subsistence minimum).
Der Lärmpegel sollte auf ein absolutes Minimum beschränkt werden.
The noise level should be limited to an absolute minimum.
You can recognize the mathematical meaning from signal words such as 'Funktion' (function), 'Kurve' (curve), 'berechnen' (to calculate), 'finden' (to find), or 'bestimmen' (to determine). Here it refers to the exact smallest value of a function.
Der Lehrer erklärte, wie man das Minimum einer Parabel berechnet.
The teacher explained how to calculate the minimum of a parabola.
low point
For a function, the Minimum is the smallest value it takes. The Tiefpunkt, by contrast, is the corresponding point on the graph and includes both this value and its position. Minimum is therefore the appropriate term for the value, while Tiefpunkt is the appropriate term for the point.
Das Minimum der Funktion ist 2.
The minimum of the function is 2.
Der Tiefpunkt des Graphen liegt bei (3|2).
The lowest point of the graph is at (3, 2).
