# Zero (constant)

Zero, or 0, is the name traditionally given to the additive identity in number systems such as abelian groups, rings and fields (especially in the particular examples of the integers, rational numbers, real numbers and complex numbers).

The development of a concept and notation for 0, probably in ancient Indian civilization, and its subsequent transmission to Europe via the Persians and Arabs, was fundamental to the success of western mathematics in fields beyond geometry. It has suprisingly much relevance due to its significance in positional number systems. For instance, normal commercial interactions might be seriously slowed if cashiers had to make change on a purchase of LXIV dollars with bills marked L, X, V and I when handed XC dollars.

## Operations with 0

• If you add a number to 0, the sum is that number. For example, $3+0=3$.
• If you subtract 0 from a number, the difference is that number. For example, $7-0=7$.
• If you subtract a number from 0, the difference is that number's opposite. For example, $0-3=-3$.
• If you multiply any amount of numbers by any amount of 0's, the product is 0. For example, $3\times 0 \times 6\times 0=0$.
• You cannot divide a number by 0.
• Dividing any number which is not equal to 0 will result in a quotient of 0. For example, $0\div 9=0$.
• There is a special case when you try to compute $0!$. The result is 1. Find more by clicking the 1 in brackets: .
• $0^a=0$ for any positive $a\in\mathbb R$.
• $0^0$ is not defined.
• $0$ divided by $0$ is indeterminate.

## See also

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