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# Zero

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The concept of zero has many synonyms

- Empty
- None
- Nil
- Null
- Nought or naught (US)
- Void
- Zilch
- ...

## Contents

## The number zero

Zero is usually not considered to belong to the set of natural numbers, as it was not even considered a number by the ancient Greeks and Romans. The number zero is represented by the Hindu-Arabic numeral 0. As a digit, 0 is used as a placeholder in place-value numeral systems.

### Properties of 0

- Additive identity (the empty sum is defined as the
**additive identity**). - Multiplicative absorption element, i.e.
- Nonunit (has no multiplicative inverse) in any number set (thus forbidding division by zero).
- (the empty product, defined as the multiplicative identity).

## The zero matrix

(...)

## The zero constant polynomial

(...)

## See also

## External links

- Weisstein, Eric W., Zero, from MathWorld—A Wolfram Web Resource.
- 0—Wikipedia.org.