Trivialidade (matemática)

Em matemática, o adjetivo trivial ou trivialidade é frequentemente utilizado para objetos (por exemplo, grupos ou espaços topológicos)^[1], que têm uma estrutura muito simples. O nome trivialidade geralmente se refere a um aspecto técnico simples de alguma prova ou definição. A origem do termo em linguagem matemática vem do currículo trivium medieval. O antônimo, o "não trivial" é comumente usado por engenheiros e matemáticos para indicar uma declaração ou um teorema que não é óbvio ou fácil de provar^[2].

Solução trivial

Uma solução ou um exemplo que é ridiculamente simples e de pouco interesse, é uma solução trivial. Muitas vezes, as soluções ou exemplos triviais que envolvem o número $0$ são considerados triviais. Soluções ou exemplos diferentes de $0$ são considerados não triviais. Por exemplo, a equação de $x+5y=0$ tem a solução trivial de $x=0,y=0$ . Soluções não triviais incluem $x=5,y=-1$ e $x=-2,y=0.4$ ^[3].

Referências

↑ Introduction to partial differential equations with applications, by Zachmanoglou and Thoe, p309
↑ Mathematics for engineers and scientists, por Alan Jeffrey, pag. 502
↑ Trivial por Bruce Simmons em "Mathword"

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