"2 + 3 = 5.
The equation above is an example of an equality: a proposition which states that two constants are equal. Equalities may be true or false.
Equations are often used to state the equality of two expressions containing one or more variables. In the reals we can say, for example, that for any given value of x it is true that
x(x − 1) = x2 − x.
The equation above is an example of an identity; an equation that is true regardless of the values of any variables that appear in it. The following equation is not an identity:
x2 − x = 0.
It is false for an infinite number of values of x, and true for only two, the roots or solutions of the equation, x = 0 and x = 1. Therefore, if the equation is known to be true, it carries information about the value of x. To solve an equation means to find its solutions.
Many authors reserve the term equation for an equality which is not an identity. The distinction between the two concepts can be subtle; for example,
(x + 1)2 = x2 + 2x + 1
is an identity, while
(x + 1)2 = 2x2 + x + 1 "(
what if we where ruled by a mere world of mathematical equations and probablities?
1 comment:
Se existe algum que me impressiona é a tua originalidade, sempre presente.
Bom trabalho, de inicio pensei que se tratava de um relógio de sol, mas depois de ler o texto compreendi, que se tratava de um outro problema.
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