# -1 (number)

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

-1 | |
---|---|

Cardinal | -1 |

Binary | -1, or 11111111 in two's complement in a signed byte |

Hexadecimal | -1, or FF in two's complement in a signed byte |

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*.

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*^{a}*x*^{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.