deductive proof
[/dɪˈdʌktɪv pruːf/]
nounpl: deductive proofs
prova dedutiva
1. A logical argument in which a conclusion is derived from a set of premises through the application of valid logical rules, guaranteeing that if the premises are true, the conclusion must be true.
The mathematician presented a deductive proof that all angles in a triangle sum to 180 degrees.
O matemático apresentou uma prova dedutiva de que todos os ângulos de um triângulo somam 180 graus.
2. A method of reasoning that starts from general principles or axioms and applies them to reach specific conclusions.
Using a deductive proof, we can establish that if all humans are mortal and Socrates is human, then Socrates must be mortal.
Usando uma prova dedutiva, podemos estabelecer que se todos os humanos são mortais e Sócrates é humano, então Sócrates deve ser mortal.
The term 'deductive proof' is fundamental in both Brazilian and American mathematical and philosophical education. In Brazil, it is commonly taught in mathematics curricula from secondary school onwards, emphasizing logical rigor. In the USA, deductive proofs are central to formal mathematics, computer science, and philosophy courses. Both cultures value deductive reasoning as a cornerstone of rational argumentation and scientific methodology.
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