
stetig
steady
Continuous and even, proceeding without interruptions or major fluctuations.
Die Bevölkerungszahl der Stadt verzeichnet ein stetiges Wachstum.
The city's population is showing steady growth.
steady / continuous
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steady
Continuous and even, proceeding without interruptions or major fluctuations.
Die Bevölkerungszahl der Stadt verzeichnet ein stetiges Wachstum.
The city's population is showing steady growth.

continuous
In mathematics, the property of a function having no points of discontinuity. Small changes in the input lead only to small changes in the output.
Im Gegensatz zur Sprungfunktion ist die Funktion f(x) = x² über ihrem gesamten Definitionsbereich stetig.
Unlike the step function, the function f(x) = x² is continuous over its entire domain.
'Stetig' is related to the adverb 'stets' (always). Both words express a form of constancy or duration. A 'stetige Entwicklung' (steady development) is one that always moves in the same direction.
Die Kosten sind stetig gestiegen.
Costs have risen steadily.
'Stetig' can stand before a noun as an adjective or describe a verb as an adverb. As an adverb, its form remains unchanged.
Wir beobachten eine stetige Verbesserung der Situation.
We are observing a steady improvement in the situation.
In its general meaning, 'stetig' is often used to describe trends. Common combinations include 'stetiges Wachstum' (steady growth), 'stetige Zunahme' (steady increase), 'stetig steigen' (to rise steadily), or 'stetig sinken' (to fall steadily).
Die Nachfrage nach Elektroautos wächst stetig.
Demand for electric cars is growing steadily.
The meaning of 'stetig' in connection with functions is a technical term from mathematics. Outside this context, the word is almost never used this way.
Der Dozent erklärte, warum diese Funktion nicht stetig ist.
The lecturer explained why this function is not continuous.
constant
Ständig and stetig can both describe a development over a longer period. Ständig mainly says that something happens continuously or frequently, without evaluating how it progresses. Stetig, on the other hand, emphasizes an even development without major fluctuations. Use stetig when this steadiness is what matters.

Die Zahl der Anmeldungen steigt stetig und ohne große Schwankungen.
The number of registrations is steadily increasing without major fluctuations.
Die Zahl der Anmeldungen steigt ständig, aber sie schwankt von Woche zu Woche stark.
The number of registrations is constantly increasing, but it fluctuates greatly from week to week.