Zero

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.

Properties

1. Neither negative nor positive.
2. Anything multiplied by zero is zero, including zero multiplied by zero.
3. Zero divided by anything is zero, except zero divided by zero is undefined.
4. Anything divided by zero is undefined.
5. Zero has the lowest possible absolute value.
6. Anything to the power of zero is one, except zero to the power of zero is undefined.
7. Zero to any power but itself is zero.
8. Anything added to zero is itself, including zero added to zero.
9. Anything subtracted from zero is itself with changed sign, except zero (which has no sign).