A signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does have a sign "+", so that −0, +0 and 0 are identical. However, in fictional googology, some formulations of the Existential Axiom allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero).
Properties[]
A positive number multiplied by -0 equal to -0, but if multiplied with a negative number the value is +0 because the signs law, multiplying -0 times +0 equal to -0 and -0 times -0 is +0 by the same reason.
Another properties are:
- (-0) + (+0) = 0
- (-0)^2 = +0
- 1/-0 = negative infinity and 1/+0 equal to positive infinite
In computing[]
Signed zeros appear in computing, where a number may be represented as an unsigned number with a juxtaposed sign bit, which creates 2 distinct signed representations of 0. This occurs in both the IEEE-754 floating-point formats and all one's complement integer formats.