Sign (mathematics)
Sign of zero

Within the convention of zero being neither positive nor negative, a specific sign-value 0 may be assigned to the number value 0. This is exploited in the sgn {\displaystyle \operatorname {sgn} } -function, as defined for real numbers. In arithmetic, +0 and −0 both denote the same number 0. There is generally no danger of confusing the value with its sign, although the convention of assigning both signs to 0 does not immediately allow for this discrimination.

In certain European countries, e.g. in Belgium and France, 0 is considered to be both positive and negative following the convention set forth by Nicolas Bourbaki.

In some contexts, such as floating-point representations of real numbers within computers, it is useful to consider signed versions of zero, with signed zeros referring to different, discrete number representations (see signed number representations for more).

The symbols +0 and −0 rarely appear as substitutes for 0 and 0, used in calculus and mathematical analysis for one-sided limits (right-sided limit and left-sided limit, respectively). This notation refers to the behaviour of a function as its real input variable approaches 0 along positive (resp., negative) values; the two limits need not exist or agree.
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