Axiom
axiom
The German word "Axiom" is a noun that refers to an "axiom" or a statement that is regarded as being self-evidently true. It is derived from the Greek word "axioma," meaning "that which is deemed worthy" or "attributed as worthy."
In mathematics, logic, and philosophy, an axiom serves as a foundational principle from which other propositions or theorems can be derived.
Similar words in German include "Grundsatz" (principle) and "Postulat" (postulate). The difference is that an axiom is typically accepted without proof and is used purely as a foundation for reasoning, while a postulate may require some justification but can also be assumed for a given discourse. "Grundsatz," on the other hand, can encompass broader principles, not necessarily requiring self-evidence.
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Examples
Das Axiom dieser Theorie wird ausführlich erklärt.noun
The axiom of this theory is explained in detail.
Ein Axiom spielt oft eine wichtige Rolle in der Mathematik.noun
An axiom often plays an important role in mathematics.
Mathematiker verwenden das Axiom in ihren Beweisen.noun
Mathematicians use the axiom in their proofs.
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