proven theorem
[ˈpruːvən ˈθiːərəm]
nounpl: proven theorems
teorema provado
1. A mathematical or logical statement that has been rigorously demonstrated to be true through deductive reasoning and formal proof
The Pythagorean theorem is a proven theorem in geometry that states the relationship between the sides of a right triangle.
O teorema de Pitágoras é um teorema provado na geometria que estabelece a relação entre os lados de um triângulo retângulo.
2. A proposition that has been established as valid through systematic mathematical argumentation
Once a conjecture becomes a proven theorem, it can be used as a foundation for further mathematical discoveries.
Uma vez que uma conjectura se torna um teorema provado, ela pode ser usada como base para novas descobertas matemáticas.
In both Brazilian and Portuguese academic environments, the concept of a 'teorema provado' is fundamental to mathematics education. The distinction between conjecture and proven theorem is emphasized heavily in formal mathematical training, reflecting the importance of rigorous proof in scientific culture across both countries and the USA.
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