valid theorem
[ˈvælɪd ˈθɪərəm]
nounpl: valid theorems
teorema válido
1. A mathematical or logical statement that has been proven true based on axioms, previously established theorems, and rules of inference, and is therefore accepted as correct within a formal system.
The Pythagorean theorem is a valid theorem in Euclidean geometry.
O teorema de Pitágoras é um teorema válido na geometria euclidiana.
2. A proposition in mathematics or formal logic that can be demonstrated through rigorous proof and holds within its logical framework.
Every valid theorem must be derived from accepted axioms and previously proven results.
Todo teorema válido deve ser derivado de axiomas aceitos e resultados previamente provados.
This is primarily technical mathematical terminology used universally in academia, research, and formal mathematics education. The concept is culture-neutral and used identically across English and Portuguese-speaking mathematical communities. Understanding valid theorems is fundamental to mathematical discourse in both Brazil and the USA.
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