0

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 surprisingly 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.

Dividing by 0

Normally, dividing by a smaller number gives you bigger results. So maybe equals ! But that is not the case. 1 over is the reciprocal or the multiplicative inverse of . Therefore, anything times its reciprocal must equal 1. Therefore, 0 has no reciprocal because anything times 0 is 0.

Operations with 0

• If you add a number to 0, the sum is that number. For example, .
• If you subtract 0 from a number, the difference is that number. For example, .
• If you subtract a number from 0, the difference is that number's opposite. For example, .
• If you multiply any number by any number of 0's, the product is 0. For example, .
• A number divided by 0 is undefined.
  • An exception is divided by , which is indeterminate.
• Dividing any number that is not equal to 0 will result in a quotient of 0. For example, .
• There is a special case when you try to compute . The result is 1. Find more here.
• for any positive .
• is undefined. However, in some contexts, it is useful to define to be .

See also

• Algebraic geometry
• Constant
• Number theory

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