-1 (number)

In mathematics, -1 is the integer number greater than negative two (-2) and less than zero (0).

Negative one has some similar but slightly different properties to positive one. Negative one would have multiplicative identity if it were not for the sign change:

x = | - 1x |

for nonnegative x.

We make the definition that x⁻¹ = 1/x, meaning that we define taking a number to the power −1 to be the same action as taking its reciprocal. This is a sensible definition to make since it allows the analog of the exponent law of x^ax^b=x^a+b, leading to x^a/x^b=x^a+(-b).

The two square roots of the real number negative one are the imaginary units i and −i.

Negative one is one of three possible return values of the Möbius function. Passed a square-free integer with an odd number of distinct prime factors, the Möbius function returns negative one.

Like other negative numbers, computers usually represent negative one in two's complement internally. If a programmer is not careful, negative one held in a signed integer in two's complement could be mistaken for a number of the form 2^{sizeof(unsigned int)} - 1 if inadvertently cast to an unsigned integer.