Igualdade matemática

Dois objetos matemáticos são iguais se e somente se são precisamente o mesmo em todo caminho. Isto define uma relação binária, igualdade, denotada pelo sinal de igualdade "=" em tal modo que a sentença "x = y" significa que x e y são iguais.

Equivalência, em sentido mais geral, é provido pela construção de uma relação de equivalência entre dois conjuntos. Uma sentença que duas expressões denotam quantidades iguais é uma equação.

Algumas propriedades lógicas da igualdade

A propriedade da substituição afirma que:

  • Para qualquer quantidade a e b e qualquer expressão F(x), se a = b, então F(a) = F(b).

A propriedade reflexiva afirma que: para qualquer quantidade a, a <= a.

Esta propriedade é geralmente utilizada nas provas matemática como um passo intermediário.

A propriedade simétrica afirma que:

  • Para qualquer quantidade a e b, se a = b, então b = a.

A propriedade da transitividade afirma:

  • Para qualquer quantidade a, b, e c, se a = b e b = c, então a = c.
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