Zero

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The concept of zero has many synonyms

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

The number zero

Zero is usually not considered to belong to the set $\scriptstyle \mathbb {N} \,$ 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. $\scriptstyle 0\,\cdot \,k\,=\,0,\,\forall k.\,$
• Nonunit (has no multiplicative inverse) in any number set (thus forbidding division by zero).
• $\scriptstyle 0^{0}\,=\,0!\,=\,1\,$ (the empty product, defined as the multiplicative identity).

The zero matrix

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The zero constant polynomial

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See also

• One (1)
• Units

External links

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