Limes / limit
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Limes
A fortified border system, especially the former outer border of the Roman Empire in Europe and the Middle East.
Die Wanderung führte uns entlang der Überreste des römischen Limes.
The hike took us along the remains of the Roman Limes.
limit
In mathematics, the limit that a function or sequence approaches.
Im Unterricht berechnen wir heute den Limes einer unendlichen Reihe.
In class today, we are calculating the limit of an infinite series.
'Limes' is a Latin word that originally meant 'border path' or 'border'. Knowing this helps you understand both meanings: the historical border of the Roman Empire and the mathematical limit.
Der Limes war die befestigte Grenze des Römischen Reiches.
The Limes was the fortified border of the Roman Empire.
You can easily recognize the meaning of 'Limes' from context. Words like 'römisch' (Roman), 'Grenze' (border), 'Wandern' (hiking), or 'Archäologie' (archaeology) point to the historical meaning. Terms like 'Funktion' (function), 'Folge' (sequence), 'berechnen' (to calculate), or 'konvergiert' (converges) point to the mathematical meaning.
Wir haben den Verlauf des römischen Limes auf der Karte verfolgt.
We traced the course of the Roman Limes on the map.
Der Student konnte den Limes der komplizierten Funktion nicht berechnen.
The student could not calculate the limit of the complicated function.
In a historical context, 'Limes' is often used with the preposition 'entlang' (along) to describe movement or location. Verbs like 'verlaufen' (to run/course), 'sichern' (to secure), or 'erforschen' (to research/explore) are also typical.
Der Obergermanisch-Raetische Limes ist UNESCO-Weltkulturerbe.
The Upper Germanic-Rhaetian Limes is a UNESCO World Heritage Site.
Ein bekannter Wanderweg verläuft entlang des Limes.
A well-known hiking trail runs along the Limes.
In mathematics, 'Limes' is usually combined with verbs like 'berechnen' (to calculate), 'bestimmen' (to determine), or 'finden' (to find). One also says that a sequence or function 'gegen einen Limes strebt' (approaches a limit) or 'einen Limes hat' (has a limit).
Können Sie den Limes dieser Folge bestimmen?
Can you determine the limit of this sequence?
Die Funktion strebt gegen den Limes unendlich.
The function approaches the limit infinity.
