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Uma disciplina hipotético-dedutiva

“A matemática é essencialmente uma disciplina hipotético-dedutiva, que se baseia em pressupostos elementares: os postulados ou axiomas. Com base neles, deduzem-se rigorosamente os diversos resultados. Estes são chamados proposições, lemas, teoremas e corolários. A designação de proposições aplica-se a quaisquer resultados. Lemas são conclusões intermédias, auxiliares na demonstração de teoremas, que serão pois resultados mais importantes. Corolários são resultados que se derivam imediatamente de um teorema. No entanto, nem sempre se segue esta hierarquia. Há lemas importantíssimos que continuam a receber o nome de lemas, apenas por assim serem tradicionalmente chamados. E há teoremas simples e pouco importantes que, em rigor, não mereceriam esse nome.”

Nuno Crato,

Jornal Expresso, 13/04/2002

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