mathematical / on paper
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mathematical
Based on a calculation or determined by calculating.
Rechnerisch ist das Ergebnis korrekt, aber es scheint in der Praxis nicht umsetzbar zu sein.
Mathematically, the result is correct, but it does not seem feasible in practice.
on paper
Considering something only at the level of numbers and calculations, without taking other aspects into account, such as practical or emotional ones.
Rechnerisch hat die Mannschaft noch eine Chance auf den Titel, aber realistisch ist es kaum noch möglich.
On paper, the team still has a chance at the title, but realistically it is hardly possible anymore.
The adjective 'rechnerisch' (mathematical / computational) is derived directly from the verb 'rechnen' (to calculate). It describes anything that has to do with calculations or is based on them.
Der Computer hat einen rechnerischen Fehler gemacht.
The computer made a calculation error.
'Rechnerisch' (mathematically / on paper) is very often used as an adverb at the beginning of a sentence to introduce a statement. In this position, it stands in position 1, followed by the verb.
Rechnerisch ergibt die Formel den richtigen Wert.
Mathematically, the formula gives the correct value.
As an adjective before a noun, 'rechnerisch' (mathematical / computational) is often combined with words like 'Fehler' (error), 'Vorteil' (advantage), 'Aufwand' (effort), or 'Nachweis' (proof).
Der rechnerische Aufwand für diese Simulation ist enorm.
The computational effort for this simulation is enormous.
In the second meaning, a contrast between theory and practice is often expressed. A typical pattern is: 'Rechnerisch ..., aber ...' (On paper ..., but ...).
Rechnerisch ist der Sieg noch möglich, aber die Mannschaft spielt zu schlecht.
On paper, victory is still possible, but the team is playing too badly.
mathematical
Mathematisch generally refers to mathematics or its methods. Rechnerisch, by contrast, emphasizes that a specific result was determined by calculation. Mathematisch is therefore appropriate for a formula or method, while rechnerisch is used for the numerical value calculated from it.
Rechnerisch ergibt sich für die Fläche ein Wert von 24 Quadratmetern.
The calculation gives an area of 24 square meters.
Mathematisch lässt sich die Fläche mit dieser Formel bestimmen.
Mathematically, the area can be determined using this formula.
