læresetningen

Læresetningen is a term used in Norwegian mathematical and logical writing to denote a formal, proven statement within a given theory. It translates roughly to the English “theorem,” though in some texts the word carries a slightly older or more educational connotation. The word combines lære (to learn or teach) with setning (statement).

A læresetning is established by a proof that derives from accepted axioms and previously proven results. Once proven, it becomes a reliable building block for further reasoning, enabling the deduction of corollaries and the development of new theory. The nature of proofs can vary by field; they may be constructive, non-constructive, or rely on established techniques of mathematical logic.

The concept is often contrasted with conjectures (claims without proof) and lemmas (auxiliary statements proven to assist in proving a larger result). Corollaries are results that follow directly from a theorem with little or no additional proof.

Examples frequently cited in Norwegian texts include Pythagoras’ læresetning (the Pythagorean theorem) in geometry, and other widely known theorems such as the Fundamental Theorem of Calculus or Fermat’s Last Theorem. In modern Norwegian usage, setning is the more common term for “theorem,” while læresetningen remains visible in older literature and in some educational contexts as a stylistic variant.

Overall, læresetningen denotes a proven, central statement in a mathematical framework, serving as a cornerstone for logical deduction and further discovery.