# Zero

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**Zero** is a number denoting the lack of any quantity or measure. In the Hindu-Arabic numeration system, it is denoted by the numeral **0**. In algebraic structures, zero is also a name given to an element in an additive monoid, group, ring, or field that acts as the additive identity, such as zero itself (in the context of real numbers), zero vector, zero matrix, and zero function. It is neither a negative or a positive number.

## Zero's properties

Property one: Neither negative nor positive.

Property two: Anything multiplied by zero is zero, including zero multiplied by zero.

Property three: Zero divided by anything is zero, except zero divided by zero is undefined.

Property four: Anything divided by zero is undefined.

Property five: Zero has the lowest possible absolute value.

Property six: Anything to the power of zero is one, except zero to the power of zero is undefined.

Property seven: Zero to any power but itself is zero.

Property eight: Anything added to zero is itself, including zero added to zero.

Property nine: Anything subtracted from zero is itself with changed sign, except zero (which has no sign).