Unique

To say there is a unique value x satisfying some property [math]P [/math] is the same as saying that if there were two values [math]x_1 [/math] and [math]x_2 [/math] both satisfying [math]P [/math], then [math]x_1 = x_2 [/math].

Examples

• We require the output of a function to be unambiguous; another way of saying this is that for every [math]x [/math], there is a unique output [math]y [/math].

• In the definition of an injective function, we require that there any [math]x [/math] with [math]f(x) = y [/math] must be unique for all [math]y [/math].

• two-sided inverses are unique

• the quotient and remainder are unique