Difference between revisions of "Division by zero"
Karl Jones (Talk | contribs) (Created page with "In mathematics, '''division by zero''' is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 wh...") |
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== Description == | == Description == | ||
| − | In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form | + | In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form. |
| − | There are mathematical structures in which a/0 is defined for some a such as in the Riemann sphere and the projectively extended real line; however, such structures cannot satisfy every ordinary rule of arithmetic (the field axioms). | + | Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in [[George Berkeley]]'s criticism of [[Calculus|infinitesimal calculus]] in ''[[The Analyst]]'' ("ghosts of departed quantities"). |
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| + | There are [[mathematical structures]] in which a/0 is defined for some a such as in the Riemann sphere and the projectively extended real line; however, such structures cannot satisfy every ordinary rule of arithmetic (the field axioms). | ||
In [[computing]], a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value, a freeze via infinite loop, or a crash. | In [[computing]], a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value, a freeze via infinite loop, or a crash. | ||
Latest revision as of 08:01, 2 November 2016
In mathematics, division by zero is division where the divisor (denominator) is zero.
Such a division can be formally expressed as a/0 where a is the dividend (numerator).
Description
In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form.
Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in The Analyst ("ghosts of departed quantities").
There are mathematical structures in which a/0 is defined for some a such as in the Riemann sphere and the projectively extended real line; however, such structures cannot satisfy every ordinary rule of arithmetic (the field axioms).
In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value, a freeze via infinite loop, or a crash.
See also
External links
- Division by zero @ Wikipedia
