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-1 (number)
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-1 (number)

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

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:

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 xaxb=xa+b, leading to xa/xb=xa+(-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 2sizeof(unsigned int) - 1 if inadvertently cast to an unsigned integer.