In mathematics, the concept of sign originates from the property of every real number being either positive or negative or zero. Depending on local conventions, zero is either considered as being neither a positive nor a negative number (having no sign or a specific sign of its own), or as belonging to both negative and positive numbers (having both signs). If not specifically mentioned, this article adheres to the first convention. In some contexts it makes sense to consider a signed zero, e.g., in floating point representations of real numbers within computers. The phrase "change of sign" is associated throughout mathematics and physics to generate the additive inverse (negation, or multiplication by −1) of any object that allows for this construction, and is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate other binary aspects of mathematical objects that resemble positivity and negativity, such as odd and even (sign of a permutation), sense of orientation or rotation (cw/ccw), one sided limits, and others, below.

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